@article{chorsi2024controllable,
  title = {Ultra-confined controllable cyclic peptides as supramolecular biomaterials},
  author = {Chorsi, Meysam and Linthicum, Will and Pozhidaeva, Alexandra and Mundrane, Caitlyn and Mulligan, Vikram Khipple and Chen, Yihang and Tavousi, Pouya and Gorbatyuk, Vitaliy and Vinogradova, Olga and Hoch, Jeffrey C. and Huey, Bryan D. and Nguyen, Thanh D. and Soh, H. Tom and Kazerounian, Kazem and Ilies, Horea},
  journal = {Nano Today},
  volume = {56},
  pages = {102247},
  year = {2024},
  issn = {1748-0132},
  doi = {https://doi.org/10.1016/j.nantod.2024.102247}
}

The capacity to design molecules capable of orchestrated movements in response to specific stimuli could yield functional biomaterials suitable for diverse innovative materials and devices. However, the rational design of molecules capable of precisely orchestrated movements remains exceedingly difficult. As a stepping-stone toward this goal, we have developed a method for manufacturing precisely designed cyclic peptide molecules with a single degree of freedom. We demonstrate that the structural configuration of these molecules can be precisely determined under different external stimuli and explore the mechanism by which these molecules form supramolecular self-assemblies. Our experimental analysis of these assemblies reveals that our constrained cyclic peptides form nanotube structures through sheet-like hydrogen bonding. Unexpectedly, these higher-order structures can achieve remarkably rigid (∼10 GPa) and stable architectures at high temperatures—comparable to the most rigid proteinaceous materials in nature. The design strategy described here could facilitate the development of molecular machines, smart materials, and other applications that require fine-tuned regulation of biomolecular behavior.

@article{behzadi2023CAD,
  author = {Behzadi, Mohammad. M. and Ilie{\c{s}}, Horea T},
  volume = {168},
  pages = {103634},
  year = {2024},
  issn = {0010-4485},
  doi = {https://doi.org/10.1016/j.cad.2023.103634},
  journal = {Computer-Aided Design},
  title = {Taming Connectedness in Machine-Learning-based Topology Optimization with Connectivity Graphs}
}

Despite the remarkable advancements in machine learning (ML) techniques for topology optimization, the predicted solutions often overlook the necessary structural connectivity required to meet the load-carrying demands of the resulting designs. Consequently, these predicted solutions exhibit subpar structural performance because disconnected components are unable to bear loads effectively and significantly compromise the manufacturability of the designs.

In this paper, we propose an approach to enhance the topological accuracy of ML-based topology optimization methods by em- ploying a predicted dual connectivity graph. We show that the tangency graph of the Maximal Disjoint Ball Decomposition (MDBD), which accurately captures the topology of the optimal design, can be used in conjunction with a point transformer network to improve the connectivity of the design predicted by Generative Adversarial Networks and Convolutional Neural Networks. Our experiments show that the proposed method can significantly improve the connectivity of the final predicted structures. Specifically, in our exper- iments the error in the number of disconnected components was reduced by a factor of 4 or more without any loss of accuracy. We demonstrate the flexibility of our approach by presenting examples including various boundary conditions (both seen and unseen), domain resolutions, and initial design domains. Importantly, our method can seamlessly integrate with other existing deep learning- based optimization algorithms, utilize training datasets with models using any valid geometric representations, and naturally extend to three-dimensional applications.

@article{chorsi2023highly,
  author = {Chorsi, Meysam T. and Le, Thinh T. and Lin, Feng and Vinikoor, Tra and Das, Ritopa and Stevens, James F. and Mundrane, Caitlyn and Park, Jinyoung and Tran, Khanh T. M. and Liu, Yang and Pfund, Jacob and Thompson, Rachel and He, Wu and Jain, Menka and Morales-Acosta, M. Daniela and Bilal, Osama R. and Kazerounian, Kazem and Ilies, Horea and Nguyen, Thanh D.},
  date-modified = {2023-10-11 14:27:44 -0400},
  doi = {https://doi.org/10.1126/sciadv.adg6075},
  journal = {Science Advances},
  number = {24},
  pages = {eadg6075},
  publisher = {American Association for the Advancement of Science},
  title = {Highly piezoelectric, biodegradable, and flexible amino acid nanofibers for medical applications},
  volume = {9},
  year = {2023},
  bdsk-url-1 = {https://doi.org/10.1126/sciadv.adg6075}
}

Amino acid crystals are an attractive piezoelectric material as they have an ultrahigh piezoelectric coefficient and have an appealing safety profile for medical implant applications. Unfortunately, solvent-cast films made from glycine crystals are brittle, quickly dissolve in body fluid, and lack crystal orientation control, reducing the overall piezoelectric effect. Here, we present a material processing strategy to create biodegradable, flexible, and piezoelectric nanofibers of glycine crystals embedded inside polycaprolactone (PCL). The glycine-PCL nanofiber film exhibits stable piezoelectric performance with a high ultrasound output of 334 kPa [under 0.15 voltage root-mean-square (Vrms)], which outperforms the state-of-the-art biodegradable transducers. We use this material to fabricate a biodegradable ultrasound transducer for facilitating the delivery of chemotherapeutic drug to the brain. The device remarkably enhances the animal survival time (twofold) in mice-bearing orthotopic glioblastoma models. The piezoelectric glycine-PCL presented here could offer an excellent platform not only for glioblastoma therapy but also for developing medical implantation fields.

@article{peddada2022toward,
  author = {Peddada, Satya R. T. and Zeidner, Lawrence E. and Ilies, Horea T. and James, Kai A. and Allison, James T.},
  date-added = {2023-10-11 14:38:18 -0400},
  date-modified = {2023-10-11 15:39:23 -0400},
  doi = {10.1115/1.4055055},
  eprint = {https://asmedigitalcollection.asme.org/mechanicaldesign/article-pdf/144/12/120801/6911953/md\_144\_12\_120801.pdf},
  issn = {1050-0472},
  journal = {Journal of Mechanical Design},
  month = aug,
  number = {12},
  pages = {120801},
  title = {{Toward Holistic Design of Spatial Packaging of Interconnected Systems With Physical Interactions ({SPI2})}},
  url = {https://doi.org/10.1115/1.4055055},
  volume = {144},
  year = {2022},
  bdsk-url-1 = {https://doi.org/10.1115/1.4055055}
}

Three-dimensional spatial packaging of interconnected systems with physical interactions (SPI2) design plays a vital role in the functionality, operation, energy usage, and life cycle of practically all engineered systems, from chips to ships. SPI2 design problems are highly nonlinear, involving tightly constrained component placement, governed by coupled physical phenomena (thermal, hydraulic, electromagnetic, etc.), and involve energy and material transfer through intricate geometric interconnects. While many aspects of engineering system design have advanced rapidly in the last few decades through breakthroughs in computational support, SPI2 design has largely resisted automation and in practice requires at least some human-executed design steps. SPI2 system reasoning and design decisions can quickly exceed human cognitive abilities at even moderate complexity levels, thwarting efforts to accelerate design cycles and tackle increasingly complex systems. Existing design methods treat pieces of the SPI2 problem separately without a fundamental systems approach, are sometimes inefficient to evaluate various possible designs, and present barriers to effective adoption in practice. This article explores a vision of a holistic SPI2 design approach needed to develop next-generation automated design methods capable of rapidly producing viable SPI2 design candidates. We review several technical domains related to holistic SPI2 design, discuss existing knowledge gaps and practical challenges, examine exciting opportunities at the intersection of multiple domains that can enable comprehensive exploration of SPI2 design spaces, and present one viable two-stage SPI2 design automation framework. Holistic SPI2 design opens up a new direction of high industrial and societal relevance for the design research community.

@article{chen2022graph,
  author = {Chen, Jiangce and Ilies, Horea T. and Ding, Caiwen},
  date-added = {2023-10-11 14:30:37 -0400},
  date-modified = {2023-10-11 14:30:50 -0400},
  doi = {https://doi.org/10.1016/j.cad.2021.103125},
  issn = {0010-4485},
  journal = {Computer-Aided Design},
  keywords = {Representation agnostic, Graph CNN, Graph kernel, Shape classification, Shape retrieval, Substructure matching},
  pages = {103125},
  title = {Graph-Based Shape Analysis for Heterogeneous Geometric Datasets: Similarity, Retrieval and Substructure Matching},
  url = {https://www.sciencedirect.com/science/article/pii/S0010448521001366},
  volume = {143},
  year = {2022},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0010448521001366},
  bdsk-url-2 = {https://doi.org/10.1016/j.cad.2021.103125}
}

Practically all existing shape analysis and processing algorithms have been developed for specific geometric representations of 3D models. However, the product development process always involves a large number of often incompatible geometric representations tailored to specific computational tasks that take place during this process. Consequently, a substantial effort has been expended to develop robust geometric data translation and conversion algorithms, but the existing methods have well known limitations. The Maximal Disjoint Ball Decomposition (MDBD) was recently defined as a unique and stable geometric construction and used to define universal shape descriptors based on the contact graph associated with MDBD. In this paper, we demonstrate that by applying graph analysis tools to MDBD in conjunction with graph convolutional neural networks and graph kernels, one can effectively develop methods to perform similarity, retrieval and substructure matching from geometric models regardless of their native geometric representation. We show that our representation-agnostic approach achieves comparable performance with state-of-the-art geometric processing methods on standard yet heterogeneous benchmark datasets while supporting all valid geometric representations.

@article{madani2022improved,
  author = {Madani, Mohammad and Behzadi, Mohammad Mahdi and Song, Dongjin and Ilies, Horea T and Tarakanova, Anna},
  date-modified = {2023-10-11 14:33:11 -0400},
  doi = {https://doi.org/10.1016/j.csbj.2022.11.020},
  journal = {Computational and Structural Biotechnology Journal},
  pages = {6138--6148},
  publisher = {Elsevier},
  title = {Improved inter-residue contact prediction via a hybrid generative model and dynamic loss function},
  volume = {20},
  year = {2022},
  bdsk-url-1 = {https://doi.org/10.1016/j.csbj.2022.11.020}
}

Protein contact maps represent spatial pairwise inter-residue interactions, providing a protein’s translationally and rotationally invariant topological representation. Accurate contact map prediction has been a critical driving force for improving protein structure determination. Contact maps can also be used as a stand-alone tool for varied applications such as prediction of protein–protein interactions, structure-aware thermal stability or physicochemical properties. We develop a novel hybrid contact map prediction model, CGAN-Cmap, that uses a generative adversarial neural network embedded with a series of modified squeeze and excitation residual networks. To exploit features of different dimensions, we introduce two parallel modules. This architecture improves the prediction by increasing receptive fields, surpassing redundant features and encouraging more meaningful ones from 1D and 2D inputs. We also introduce a new custom dynamic binary cross-entropy loss function to address the input imbalance problem for highly sparse long-range contacts in proteins with insufficient homologs. We evaluate the model’s performance on CASP 11, 12, 13, 14, and CAMEO test sets. CGAN-Cmap outperforms state-of-the-art models, improving precision of medium and long-range contacts by at least 3.5%. As a direct assessment between our model and AlphaFold2, the leading available protein structure prediction model, we compare extracted contact maps from AlphaFold2 and predicted contact maps from CGAN-Cmap. The results show that CGAN-Cmap has a mean precision higher by 1% compared to AlphaFold2 for most ranges of contacts. These results demonstrate an efficient approach for highly accurate contact map prediction toward accurate characterization of protein structure, properties and functions from sequence.

@article{behzadi2022gantl,
  author = {Behzadi, Mohammad Mahdi and Ilie{\c{s}}, Horea T},
  date-modified = {2023-10-11 14:15:06 -0400},
  doi = {https://doi.org/10.1115/1.4052757},
  journal = {Journal of Mechanical Design},
  number = {2},
  pages = {021711},
  publisher = {American Society of Mechanical Engineers},
  title = {{GANTL}: Toward practical and real-time topology optimization with conditional generative adversarial networks and transfer learning},
  volume = {144},
  year = {2022},
  bdsk-url-1 = {https://doi.org/10.1115/1.4052757}
}

A number of machine learning methods have been recently proposed to circumvent the high computational cost of the gradient-based topology optimization solvers. By and large, these methods show tight generalizability to unseen boundary and external loading conditions, require prohibitively large datasets for training, and do not take into consideration topological constraints of the predictions, which results in solutions with unpredictable connectivity. To address these limitations, we propose a design exploration framework for topology optimization that exploits the knowledge transfer capability of the transfer learning methods and the generative power of conditional generative adversarial networks (GANs). We show that the proposed framework significantly exceeds the generalization ability of current methods. Moreover, the proposed architecture is capable of reusing the knowledge learned on low-resolution and computationally inexpensive samples, which notably reduces both the size of the required high-resolution training datasets and the demand on the computational infrastructure needed to generate the training data. Finally, we propose and evaluate novel approaches to improve the structural connectivity of the predicted optimal topology by including topological metrics into the loss function. We show that by including the bottleneck distance between the persistence diagrams of the predicted and ground truth structures, we significantly improve the connectivity of the prediction. Together, our results reveal the ability of generative adversarial networks implemented in a transfer learning environment to serve as powerful and practical real-time design exploration tools in topology optimization. 

@article{huber2021functional,
  author = {Huber, Martin and Eschbach, Matthew and Kazerounian, Kazem and Ilies, Horea},
  date-added = {2023-10-11 14:43:06 -0400},
  date-modified = {2023-10-11 14:43:27 -0400},
  doi = {10.1115/1.4051626},
  eprint = {https://asmedigitalcollection.asme.org/medicaldevices/article-pdf/15/4/041003/6731400/med\_015\_04\_041003.pdf},
  issn = {1932-6181},
  journal = {Journal of Medical Devices},
  month = jul,
  number = {4},
  pages = {041003},
  title = {{Functional Evaluation of a Personalized Orthosis for Knee Osteoarthritis: A Motion Capture Analysis}},
  url = {https://doi.org/10.1115/1.4051626},
  volume = {15},
  year = {2021},
  bdsk-url-1 = {https://doi.org/10.1115/1.4051626}
}

Orthotic treatments for knee osteoarthritis (OA) typically rely on simple mechanisms such as three-point bending straps and single-pin hinges. These commonly prescribed braces cannot treat bicompartmental knee OA, do not consider the muscle weakness that typically accompanies the condition, and employ hinges that restrict the knee’s natural biomechanics. Utilizing a novel, personalized joint mechanism in conjunction with magnetorheological dampers, we have developed and evaluated a brace which attempts to address these shortcomings. This process has respected three principal design goals: reducing the load experienced across the entire knee joint, generating a supportive moment to aid the thigh muscles in shock absorption, and interfering minimally with gait kinematics. Two healthy volunteers were chosen to test the system’s basic functionality through gait analysis in a motion capture laboratory. Combining the collected kinematic and force-plate data with data taken from sensors onboard the brace, we integrated the brace and leg system into a single inverse dynamics analysis, from which we were able to evaluate the effect of the brace design on the subjects’ knee loads and moments. Of the three design goals: a reduction in knee contact forces was demonstrated; increased shock absorption was observed, but not to statistical significance; and natural gait was largely preserved. Taken in total, the outcome of this study supports additional investigation into the system’s clinical effectiveness, and suggests that further refinement of the techniques presented in this paper could open the doors to more effective OA treatment through patient specific braces.

@article{chorsi2021kinematic,
  author = {Chorsi, Meysam T. and Tavousi, Pouya and Mundrane, Caitlyn and Gorbatyuk, Vitaliy and Kazerounian, Kazem and Ilies, Horea},
  date-added = {2023-10-11 14:41:14 -0400},
  date-modified = {2023-10-11 14:41:27 -0400},
  doi = {10.1115/1.4051472},
  eprint = {https://asmedigitalcollection.asme.org/micronanomanufacturing/article-pdf/9/2/021005/6727636/jmnm\_009\_02\_021005.pdf},
  issn = {2166-0468},
  journal = {Journal of Micro and Nano-Manufacturing},
  month = jul,
  number = {2},
  pages = {021005},
  title = {{Kinematic Design of Functional Nanoscale Mechanisms From Molecular Primitives}},
  url = {https://doi.org/10.1115/1.4051472},
  volume = {9},
  year = {2021},
  bdsk-url-1 = {https://doi.org/10.1115/1.4051472}
}

Natural nanomechanisms such as capillaries, neurotransmitters, and ion channels play a vital role in the living systems. But the design principles developed by nature through evolution are not well understood and, hence, not applicable to engineered nanomachines. Thus, the design of nanoscale mechanisms with prescribed functions remains a challenge. Here, we present a systematic approach based on established kinematics techniques to designing, analyzing, and controlling manufacturable nanomachines with prescribed mobility and function built from a finite but extendable number of available “molecular primitives.” Our framework allows the systematic exploration of the design space of irreducibly simple nanomachines, built with prescribed motion specification by combining available nanocomponents into systems having constrained, and consequently controllable motions. We show that the proposed framework has allowed us to discover and verify a molecule in the form of a seven link, seven revolute (7R) closed-loop spatial linkage with mobility (degree-of-freedom (DOF)) of one. Furthermore, our experiments exhibit the type and range of motion predicted by our simulations. Enhancing such a structure into functional nanomechanisms by exploiting and controlling their motions individually or as part of an ensemble could galvanize development of the multitude of engineering, scientific, medical, and consumer applications that can benefit from engineered nanomachines.

@article{behzadi2021real,
  author = {Behzadi, Mohammad Mahdi and Ilie{\c s}, Horea T.},
  date-added = {2023-10-11 14:40:27 -0400},
  date-modified = {2023-10-11 15:40:10 -0400},
  doi = {https://doi.org/10.1016/j.cad.2021.103014},
  issn = {0010-4485},
  journal = {Computer-Aided Design},
  keywords = {Topology optimization, Transfer learning, Real-time predictions, Design space explorations, Deep learning},
  pages = {103014},
  title = {Real-Time Topology Optimization in {3D} via Deep Transfer Learning},
  url = {https://www.sciencedirect.com/science/article/pii/S0010448521000257},
  volume = {135},
  year = {2021},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0010448521000257},
  bdsk-url-2 = {https://doi.org/10.1016/j.cad.2021.103014}
}

The published literature on topology optimization has exploded over the last two decades to include methods that use shape and topological derivatives or evolutionary algorithms formulated on various geometric representations and parametrizations. One of the key challenges of all these methods is the massive computational cost associated with 3D topology optimization problems. We introduce a transfer learning method based on a convolutional neural network that (1) can handle high-resolution 3D design domains of various shapes and topologies; (2) supports real-time design space explorations as the domain and boundary conditions change; (3) requires a much smaller set of high-resolution examples for the improvement of learning in a new task compared to traditional deep learning networks; (4) is multiple orders of magnitude more efficient than the established gradient-based methods, such as SIMP. We provide numerous 2D and 3D examples to showcase the effectiveness and accuracy of our proposed approach, including for design domains that are unseen to our source network, as well as the generalization capabilities of the transfer learning-based approach. Our experiments achieved an average binary accuracy around 95% at real-time prediction rates. These properties, in turn, suggest that the proposed transfer-learning method may serve as the first practical underlying framework for real-time 3D design exploration based on topology optimization.

@article{chen2020maximal,
  author = {Chen, Jiangce and Ilie{\c s}, Horea T.},
  date-added = {2023-10-11 14:44:21 -0400},
  date-modified = {2023-10-11 14:44:31 -0400},
  doi = {https://doi.org/10.1016/j.cad.2020.102850},
  issn = {0010-4485},
  journal = {Computer-Aided Design},
  keywords = {Geometric representations, Shape analysis, System interoperability, Shape similarity},
  pages = {102850},
  title = {Maximal Disjoint Ball Decompositions for shape modeling and analysis},
  url = {https://www.sciencedirect.com/science/article/pii/S0010448520300439},
  volume = {126},
  year = {2020},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0010448520300439},
  bdsk-url-2 = {https://doi.org/10.1016/j.cad.2020.102850}
}

A large number of geometric representations have been proposed to address the needs of specific engineering applications. This, in turn, exacerbates the inherent challenges associated with system interoperability for downstream engineering applications. In this paper, we define the Maximal Disjoint Ball Decomposition (MDBD) as the location of the largest d-dimensional closed balls recursively placed in the interior of a d-dimensional domain and show that the proposed decomposition can be used to provide an underlying common analysis framework for geometric models using different representation schemes. Importantly, our decomposition only relies on the ability of an existing geometric representation to compute distances, which must be supported by any valid geometric representation scheme, and does not require an explicit representation conversion. Moreover, MDBD is unique for a given domain up to rigid body transformation, reflection, as well as uniform scaling, and its formulation suggests appealing stability and robustness properties against small boundary modifications. Furthermore, we show that MDBD can be used as a universal shape descriptor to perform shape similarity of models coming from various geometric representation schemes. A salient attribute of this decomposition is that it provides adequate support for key downstream applications for models coming from disparate geometric representations. For example, MDBD can be naturally used to carry out meshless solutions to boundary value problems; efficient collision detection; and 3D mesh generation of models that use any valid geometric representation scheme. Finally, our hierarchical formulation of the proposed Maximal Disjoint Ball Decomposition allows for a choice of model complexity at run-time to match the available computational resources.

@article{chorsi2019piezoelectric,
  author = {Chorsi, Meysam T. and Curry, Eli J. and Chorsi, Hamid T. and Das, Ritopa and Baroody, Jeffrey and Purohit, Prashant K. and Ilies, Horea and Nguyen, Thanh D.},
  date-added = {2023-10-11 14:45:18 -0400},
  date-modified = {2023-10-11 14:45:29 -0400},
  doi = {https://doi.org/10.1002/adma.201802084},
  eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/adma.201802084},
  journal = {Advanced Materials},
  keywords = {bioactuators, biodevices, biomaterials, biosensors, piezoelectricity},
  number = {1},
  pages = {1802084},
  title = {Piezoelectric Biomaterials for Sensors and Actuators},
  url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201802084},
  volume = {31},
  year = {2019},
  bdsk-url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201802084},
  bdsk-url-2 = {https://doi.org/10.1002/adma.201802084}
}

Abstract Recent advances in materials, manufacturing, biotechnology, and microelectromechanical systems (MEMS) have fostered many exciting biosensors and bioactuators that are based on biocompatible piezoelectric materials. These biodevices can be safely integrated with biological systems for applications such as sensing biological forces, stimulating tissue growth and healing, as well as diagnosing medical problems. Herein, the principles, applications, future opportunities, and challenges of piezoelectric biomaterials for medical uses are reviewed thoroughly. Modern piezoelectric biosensors/bioactuators are developed with new materials and advanced methods in microfabrication/encapsulation to avoid the toxicity of conventional lead-based piezoelectric materials. Intriguingly, some piezoelectric materials are biodegradable in nature, which eliminates the need for invasive implant extraction. Together, these advancements in the field of piezoelectric materials and microsystems can spark a new age in the field of medicine.

@article{corcodel2018printability,
  author = {Corcodel, Radu I and Ilies, Horea T},
  date-modified = {2023-10-11 14:46:00 -0400},
  journal = {Computer-Aided Design and Applications},
  number = {3},
  pages = {318--329},
  publisher = {Taylor \& Francis},
  title = {Printability analysis in additive manufacturing},
  volume = {15},
  year = {2018}
}

In recent years Additive Manufacturing (AM) has advanced from design and fitting validation to
biomedical, rapid tooling, tissue engineering, the arts and even food manufacturing. The corre-
sponding scale reduction did not coincide with improving two of the most important process
characteristics, namely print accuracy and build time. In this paper we introduce a computational
framework for computing the maximum build volume for given non-circular extruders and printing
machines that have 2, 3 and perhaps higher number of degrees of freedom (DOF). The proposed
method also outputs the accessible configuration space of a multi-DOF AM machine that is instru-
mental in planning the final (temporal) motion of single or multiple print heads. Furthermore, we
show that the proposed method allows the ranking of multiple extruders based on their volumet-
ric deviation from nominal geometry. This formulation makes no assumption about the number of
machine DOFs, nor about the planarity of the target contour, making it applicable to emerging AM
technologies such as 6-axis printing with non-planar layers, and layer-less additive manufacturing.

@article{williams2018practical,
  author = {Williams, Reed M. and Ilie{\c s}, Horea T.},
  date-added = {2023-10-11 14:48:00 -0400},
  date-modified = {2023-10-11 14:48:51 -0400},
  doi = {https://doi.org/10.1016/j.cagd.2018.10.003},
  issn = {0167-8396},
  journal = {Computer Aided Geometric Design},
  keywords = {Point clouds, Heat kernel, Shape recognition, Spectral signature, Clustering, Microsoft Kinect},
  pages = {97-120},
  title = {Practical shape analysis and segmentation methods for point cloud models},
  url = {https://www.sciencedirect.com/science/article/pii/S0167839618301213},
  volume = {67},
  year = {2018},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0167839618301213},
  bdsk-url-2 = {https://doi.org/10.1016/j.cagd.2018.10.003}
}

Current point cloud processing algorithms do not have the capability to automatically extract semantic information from the observed scenes, except in very specialized cases. Furthermore, existing mesh analysis paradigms cannot be directly employed to automatically perform typical shape analysis tasks directly on point cloud models. We present a potent framework for shape analysis, similarity and segmentation of noisy point cloud models for real objects of engineering interest, models that may be incomplete. The proposed framework relies on spectral methods and the heat diffusion kernel to construct compact shape signatures, and we show that the framework supports a variety of clustering techniques that have traditionally been applied only on mesh models. We developed and implemented one practical and convergent estimate of the Laplace–Beltrami operator for point clouds as well as a number of clustering techniques adapted to work directly on point clouds to produce geometric features of engineering interest. The key advantage of this framework is that it supports practical shape analysis capabilities that operate directly on point cloud models of objects without requiring surface reconstruction or global meshing. We show that the proposed technique is robust against typical noise present in possibly incomplete point clouds, and segment point clouds scanned by depth cameras (e.g. Kinect) into semantically-meaningful sub-shapes.

@article{curry2018biodegradable,
  author = {Curry, Eli J and Ke, Kai and Chorsi, Meysam T and Wrobel, Kinga S and Miller III, Albert N and Patel, Avi and Kim, Insoo and Feng, Jianlin and Yue, Lixia and Wu, Qian and others},
  date-modified = {2023-10-11 14:47:17 -0400},
  doi = {https://doi.org/10.1073/pnas.1710874115},
  journal = {Proceedings of the National Academy of Sciences},
  number = {5},
  pages = {909--914},
  publisher = {National Academy of Sciences},
  title = {Biodegradable piezoelectric force sensor},
  volume = {115},
  year = {2018},
  bdsk-url-1 = {https://doi.org/10.1073/pnas.1710874115}
}

Measuring physiological pressures such as lung pressure, brain pressure, eye pressure, etc. is important for monitoring health status, preventing the buildup of dangerous internal forces in impaired organs, and enabling novel approaches of using mechanical stimulation for tissue regeneration. Pressure sensors are often implanted and directly integrated with soft biological systems. Therefore, the devices should be flexible and at the same time biodegradable to avoid invasive removal surgery. Here, we present the study and processing of a biodegradable polymer which can convert mechanical force to electricity, and employ the polymer to develop a biocompatible implanted force sensor. The sensor, relying solely on common medical materials, can monitor important biological forces and eventually self-vanish, causing no harm to the body.

@article{behandish2017shape,
  author = {Behandish, Morad and Ilies, Horea T},
  date-modified = {2023-10-11 14:51:06 -0400},
  journal = {arXiv preprint arXiv:1712.00238},
  title = {Shape complementarity analysis for objects of arbitrary shape},
  year = {2017}
}

The basic problem of shape complementarity analysis appears fundamental to applications as diverse as mechanical design, assembly automation, robot motion planning, micro- and nano-fabrication, protein-ligand binding, and rational drug design. However, the current challenge lies in the lack of a general mathematical formulation that applies to objects of arbitrary shape. We propose that a measure of shape complementarity can be obtained from the extent of approximate overlap between shape skeletons. A space-continuous implicit generalization of the skeleton, called the skeletal density function (SDF) is defined over the Euclidean space that contains the individual assembly partners. The SDF shape descriptors capture the essential features that are relevant to proper contact alignment, and are considerably more robust than the conventional explicit skeletal representations. We express the shape complementarity score as a convolution of the individual SDFs. The problem then breaks down to a global optimization of the score over the configuration space of spatial relations, which can be efficiently implemented using fast Fourier transforms (FFTs) on nonequispaced samples. We demonstrate the effectiveness of the scoring approach for several examples from 2D peg-in-hole alignment to more complex 3D examples in mechanical assembly and protein docking. We show that the proposed method is reliable, inherently robust against small perturbations, and effective in steering gradient-based optimization. 

@article{williams2017adaptive,
  author = {Williams, Reed M and Ilie{\c{s}}, Horea T},
  date-modified = {2023-10-11 14:50:20 -0400},
  doi = {https://doi.org/10.1080/16864360.2017.1287679},
  journal = {Computer-Aided Design and Applications},
  number = {6},
  pages = {770--777},
  publisher = {Taylor \& Francis},
  title = {Adaptive eigensystem truncation for spectral shape signatures},
  volume = {14},
  year = {2017},
  bdsk-url-1 = {https://doi.org/10.1080/16864360.2017.1287679}
}

The ability to compare the shapes of objects is crucial to the practice of engineering design. Spectral shape signatures provide a high-quality similarity measure based on diffusion physics by means of the spectrum of an estimate of the Laplace-Beltrami operator for the surface of an object.

However, point cloud and mesh models often have very large intrinsic sizes and subsequently large Laplace-Beltrami estimate matrices. Recommendations from the current spectral shape signature literature are to use only a fixed number of arithmetically greatest eigenvalues and their corresponding eigenvectors in the computation of a spectral shape signature. This recommendation “seems to work well”, but it is not yet understood the degree to which this fixed number of eigenpairs approximates the full spectrum for the purposes of shape similarity measures or even what fixed number to use. Using a fixed number of eigenpairs for all model sizes and samplings also introduces inconsistencies between different samplings of the same shape at different intrinsic sizes and may cost unnecessary computational effort on resource-limited systems (e.g., drones or robots).

In this paper we briefly examine the performance of fixed numbers of eigenpairs on approximating the spectrum of models of different sizes, propose an adaptive cutoff selection method which improves consistency between models for spectral signature use, demonstrate the method on Heat and Wave Kernel signatures (HKS and WKS) for point clouds, and briefly discuss the trade-off between running time and desired error or convergence properties.

@article{behandish2017haptic,
  author = {Behandish, Morad and Ilies, Horea T},
  date-modified = {2023-10-11 15:43:59 -0400},
  journal = {arXiv preprint arXiv:1712.00750},
  title = {Haptic Assembly and Prototyping: {A}n Expository Review},
  year = {2017}
}

An important application of haptic technology to digital product development is in virtual prototyping (VP), part of which deals with interactive planning, simulation, and verification of assembly-related activities, collectively called virtual assembly (VA). In spite of numerous research and development efforts over the last two decades, the industrial adoption of haptic-assisted VP/VA has been slower than expected. Putting hardware limitations aside, the main roadblocks faced in software development can be traced to the lack of effective and efficient computational models of haptic feedback. Such models must 1) accommodate the inherent geometric complexities faced when assembling objects of arbitrary shape; and 2) conform to the computation time limitation imposed by the notorious frame rate requirements—namely, 1 kHz for haptic feedback compared to the more manageable 30-60 Hz for graphic rendering. The simultaneous fulfillment of these competing objectives is far from trivial.
This survey presents some of the conceptual and computational challenges and opportunities as well as promising future directions in haptic-assisted VP/VA, with a focus on haptic assembly from a geometric modeling and spatial reasoning perspective. The main focus is on revisiting definitions and classifications of different methods used to handle the constrained multibody simulation in real-time, ranging from physics-based and geometry-based to hybrid and unified approaches using a variety of auxiliary computational devices to specify, impose, and solve assembly constraints. Particular attention is given to the newly developed ’analytic methods’ inherited from motion planning and protein docking that have shown great promise as an alternative paradigm to the more popular combinatorial methods. 

@article{zhao2017learned,
  author = {Zhao, Xiaojun and Ilie{\c{s}}, Horea T},
  date-modified = {2023-10-11 15:42:57 -0400},
  journal = {Computer-Aided Design and Applications},
  number = {4},
  pages = {507--515},
  publisher = {Taylor \& Francis},
  title = {Learned 3D shape descriptors for classifying {3D} point cloud models},
  volume = {14},
  year = {2017}
}

Recent hardware advances in the field of 3D imaging are democratizing 3D sensing with tremendous
scientific and societal implications. Point cloud processing has traditionally required meshing the
point clouds output by 3D cameras followed by surface reconstruction, and geometric feature recog-
nition. However, meshing a point cloud is fundamentally an ill-posed problem, and the definition of
a good solution is not general. This, in turn, demands new paradigms for processing point cloud
information.

In this paper, we focus on the task of classifying 3D point clouds captured with commercial 3D
cameras, and we integrate supervised machine learning algorithms with three different yet under-
explored shape descriptors, namely Light-Field Descriptors, Angular Radial Transform (ART), and
Zernike Descriptors (ZD). We evaluate the classification performance of different machine learning
algorithms combined with these different shape descriptors on point cloud models obtained from
the Google 3D Warehouse, and we demonstrate good classification performance for 3D point clouds.
Furthermore, we show that Zernike Descriptors are practically insensitive to noise levels typically
found in point cloud models captured via 3D sensing

@article{behandish2016haptic,
  author = {Behandish, Morad and Ilie{\c{s}}, Horea T},
  date-modified = {2023-10-11 15:43:49 -0400},
  doi = {https://doi.org/10.1115/DETC2015-47923},
  journal = {Journal of Computing and Information Science in Engineering},
  number = {2},
  pages = {021002},
  publisher = {American Society of Mechanical Engineers},
  title = {Haptic assembly using skeletal densities and {F}ourier transforms},
  volume = {16},
  year = {2016},
  bdsk-url-1 = {https://doi.org/10.1115/DETC2015-47923}
}

Haptic-assisted virtual assembly and prototyping has seen significant attention over the past two decades. However, in spite of the appealing prospects, its adoption has been slower than expected. We identify the main roadblocks as the inherent geometric complexities faced when assembling objects of arbitrary shape, and the computation time limitation imposed by the notorious 1 kHz haptic refresh rate. We solved the first problem in a recent work by introducing a generic energy model for geometric guidance and constraints between features of arbitrary shape. In the present work, we address the second challenge by leveraging Fourier transforms to compute the constraint forces and torques. Our new concept of ‘geometric energy’ field is computed automatically from a cross-correlation of ‘skeletal densities’ in the frequency domain, and serves as a generalization of the manually specified virtual fixtures or heuristically identified mating constraints proposed in the literature. The formulation of the energy field as a convolution enables efficient computation using GPU-accelerated Fast Fourier Transforms (FFT). We show that our method is effective for low-clearance assembly of objects of arbitrary geometric and syntactic complexity.

@article{behandish2016analytic,
  author = {Behandish, Morad and Ilie{\c s}, Horea T.},
  date-added = {2023-10-11 14:51:51 -0400},
  date-modified = {2023-10-11 14:52:02 -0400},
  doi = {https://doi.org/10.1016/j.cad.2015.06.016},
  issn = {0010-4485},
  journal = {Computer-Aided Design},
  keywords = {Analytic methods, Shape correlation, Spherical sampling, Fourier transform, Collision detection},
  note = {SPM 2015},
  pages = {100-115},
  title = {Analytic methods for geometric modeling via spherical decomposition},
  url = {https://www.sciencedirect.com/science/article/pii/S0010448515000962},
  volume = {70},
  year = {2016},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0010448515000962},
  bdsk-url-2 = {https://doi.org/10.1016/j.cad.2015.06.016}
}

Analytic methods are emerging in solid and configuration modeling, while providing new insights into a variety of shape and motion related problems by exploiting tools from group morphology, convolution algebras, and harmonic analysis. However, most convolution-based methods have used uniform grid-based sampling to take advantage of the fast Fourier transform (FFT) algorithm. We propose a new paradigm for more efficient computation of analytic correlations that relies on a grid-free discretization of arbitrary shapes as countable unions of balls, in turn described as sublevel sets of summations of smooth radial kernels at adaptively sampled ‘knots’. Using a simple geometric lifting trick, we interpret this combination as a convolution of an impulsive skeletal density and primitive kernels with conical support, which faithfully embeds into the convolution formulation of interactions across different objects. Our approach enables fusion of search-efficient combinatorial data structures prevalent in time-critical collision and proximity queries with analytic methods popular in path planning and protein docking, and outperforms uniform grid-based FFT methods by leveraging nonequispaced FFTs. We provide example applications in formulating holonomic collision constraints, shape complementarity metrics, and morphological operations, unified within a single analytic framework.

@article{ragsdell2015new,
  author = {Ragsdell, Kenneth and Papalambros, Panos and Mistree, Farrokh and Williams, Christopher and Rai, Rahul and Panchal, Jitesh and Ferguson, Scott and DuPont, Bryony and Allison, James and Ilies, Horea and others},
  date-modified = {2023-10-11 15:42:08 -0400},
  doi = {10.1115/1.4030256},
  journal = {Journal of Mechanical Design, Transactions of the ASME},
  number = {5},
  pages = {050301},
  publisher = {American Society of Mechanical Engineers (ASME)},
  title = {New Perspectives on {D}esign {A}utomation: Celebrating the 40th anniversary of the {ASME} Design Automation Conference},
  volume = {137},
  year = {2015},
  bdsk-url-1 = {https://doi.org/10.1115/1.4030256}
}

The ASME Design Automation Conference and Committee (DAC) were initiated more than 40 years ago by a group of engineering visionaries to mark the dawn of the computer era in engineering design. Along the way, a strong and diverse community of academic, industrial, and government researchers have made the DAC community what it is today: a vibrant and energetic research community and a place to share the thoughts and ideas that fuel a common passion for engineering design automation (DA).

To celebrate the legacy of the DAC and to spark common visions of the DAC’s future, the Design Automation Committee organized a 40th anniversary symposium at the 2014 ASME International Design Engineering Technical Conferences (IDETC). A capacity crowd of hundreds of DA researchers attended the program, which was organized into three segments. First, Kenneth Ragsdell, one of the founding members of the DAC, spoke of the founding of the conference.

@article{behandish2015peg,
  author = {Behandish, Morad and Ilie{\c{s}}, Horea T},
  date-modified = {2023-10-11 15:40:58 -0400},
  doi = {https://doi.org/10.1115/1.4030749},
  journal = {Journal of Computing and Information Science in Engineering},
  number = {4},
  pages = {041004},
  publisher = {American Society of Mechanical Engineers},
  title = {Peg-in-hole revisited: {A} generic force model for haptic assembly},
  volume = {15},
  year = {2015},
  bdsk-url-1 = {https://doi.org/10.1115/1.4030749}
}

The development of a generic and effective force model for semi-automatic or manual virtual assembly with haptic support is not a trivial task, especially when the assembly constraints involve complex features of arbitrary shape. The primary challenge lies in a proper formulation of the guidance forces and torques that effectively assist the user in the exploration of the virtual environment (VE), from repulsing collisions to attracting proper contact. The secondary difficulty is that of efficient implementation that maintains the standard 1 kHz haptic refresh rate. We propose a purely geometric model for an artificial energy field that favors spatial relations leading to proper assembly, differentiated to obtain forces and torques for general motions. The energy function is expressed in terms of a cross-correlation of shape-dependent affinity fields, precomputed offline separately for each object. We test the effectiveness of the method using familiar peg-in-hole examples. We show that the proposed technique unifies the two phases of free motion and precise insertion into a single interaction mode and provides a generic model to replace the ad hoc mating constraints or virtual fixtures, with no restrictive assumption on the types of the involved assembly features.

@article{tavousi2015protofold,
  author = {Tavousi, Pouya and Behandish, Morad and Ilie{\c{s}}, Horea T and Kazerounian, Kazem},
  date-modified = {2023-10-11 15:40:26 -0400},
  doi = {10.1115/1.4032759},
  journal = {Journal of Nanotechnology in Engineering and Medicine},
  number = {3},
  pages = {034601},
  publisher = {American Society of Mechanical Engineers},
  title = {Protofold {II}: {E}nhanced model and implementation for kinetostatic protein folding},
  volume = {6},
  year = {2015},
  bdsk-url-1 = {https://doi.org/10.1115/1.4032759}
}

A reliable prediction of three-dimensional (3D) protein structures from sequence data remains a big challenge due to both theoretical and computational difficulties. We have previously shown that our kinetostatic compliance method (KCM) implemented into the Protofold package can overcome some of the key difficulties faced by other de novo structure prediction methods, such as the very small time steps required by the molecular dynamics (MD) approaches or the very large number of samples needed by the Monte Carlo (MC) sampling techniques. In this paper, we improve the free energy formulation used in Protofold by including the typically underrated entropic effects, imparted due to differences in hydrophobicity of the chemical groups, which dominate the folding of most water-soluble proteins. In addition to the model enhancement, we revisit the numerical implementation by redesigning the algorithms and introducing efficient data structures that reduce the expected complexity from quadratic to linear. Moreover, we develop and optimize parallel implementations of the algorithms on both central and graphics processing units (CPU/GPU) achieving speed-ups up to two orders of magnitude on the GPU. Our simulations are consistent with the general behavior observed in the folding process in aqueous solvent, confirming the effectiveness of model improvements. We report on the folding process at multiple levels, namely, the formation of secondary structural elements and tertiary interactions between secondary elements or across larger domains. We also observe significant enhancements in running times that make the folding simulation tractable for large molecules.

@article{flanagan2012jaw,
  author = {Flanagan, Dennis and Ilies, Horea and O'brien, Brendan and McManus, Anne and Larrow, Beau},
  date-modified = {2023-10-11 15:05:05 -0400},
  doi = {10.1563/AAID-JOI-D-10-00101},
  journal = {Journal of Oral Implantology},
  number = {4},
  pages = {361--364},
  publisher = {The American Academy of Implant Dentistry},
  title = {Jaw bite force measurement device},
  volume = {38},
  year = {2012},
  bdsk-url-1 = {https://doi.org/10.1563/AAID-JOI-D-10-00101}
}

We describe a cost-effective device that uses an off-the-shelf force transducer to measure patient bite force as a diagnostic aid in determining dental implant size, number of implants, and prosthetic design for restoring partial edentulism. The main advantages of the device are its accuracy, simplicity, modularity, ease of manufacturing, and low cost. 

@article{eftekharian2012medial,
  author = {Eftekharian, Ata A. and Ilie{\c s}, Horea T.},
  date-added = {2023-10-11 15:04:20 -0400},
  date-modified = {2023-10-11 15:42:34 -0400},
  doi = {https://doi.org/10.1016/j.cad.2011.12.003},
  issn = {0010-4485},
  journal = {Computer-Aided Design},
  keywords = {Medial zones, Medial axis, Skeletons, Distance functions, R-functions},
  number = {5},
  pages = {413-423},
  title = {Medial Zones: {F}ormulation and Applications},
  url = {https://www.sciencedirect.com/science/article/pii/S0010448511003198},
  volume = {44},
  year = {2012},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0010448511003198},
  bdsk-url-2 = {https://doi.org/10.1016/j.cad.2011.12.003}
}

The popularity of medial axis in shape modeling and analysis comes from several of its well known fundamental properties. For example, medial axis captures the connectivity of the domain, has a lower dimension than the space itself, and is closely related to the distance function constructed over the same domain. We propose the new concept of a medial zone of an n-dimensional semi-analytic domain Ω that subsumes the medial axis MA(Ω) of the same domain as a special case, and can be thought of as a ‘thick’ skeleton having the same dimension as that of Ω. We show that by transforming the exact, non-differentiable, distance function of domain Ω into approximate but differentiable distance functions, and by controlling the geodesic distance to the crests of the approximate distance functions of domain Ω, one obtains families of medial zones of Ω that are homeomorphic to the domain and are supersets of MA(Ω). We present a set of natural properties for the medial zones MZ(Ω) of Ω and discuss practical approaches to compute both medial axes and medial zones for 3-dimensional semi-analytic sets with rigid or evolving boundaries. Due to the fact that the medial zones fuse some of the critical geometric and topological properties of both the domain itself and of its medial axis, re-formulating problems in terms of medial zones affords the ‘best of both worlds’ in applications such as geometric reasoning, robotic and autonomous navigation, and design automation.

@article{periverzov20123d,
  author = {Periverzov, Frol and Ilie{\c{s}}, Horea T},
  date-modified = {2023-10-11 15:45:25 -0400},
  doi = {https://doi.org/10.1007/3DRes.03(2012)1},
  journal = {3D Research},
  number = {3},
  pages = {1--15},
  publisher = {3D Display Research Center},
  title = {{3D} Imaging for hand gesture recognition: {E}xploring the software-hardware interaction of current technologies},
  volume = {3},
  year = {2012},
  bdsk-url-1 = {https://doi.org/10.1007/3DRes.03(2012)1}
}

Interaction with 3D information is one of the fundamental and most familiar tasks in virtually all areas of engineering and science. Several recent technological advances pave the way for developing hand gesture recognition capabilities available to all, which will lead to more intuitive and efficient 3D user interfaces (3DUI). These developments can unlock new levels of expression and productivity in all activities concerned with the creation and manipulation of virtual 3D shapes and, specifically, in engineering design. Building fully automated systems for tracking and interpreting hand gestures requires robust and efficient 3D imaging techniques as well as potent shape classifiers. We survey and explore current and emerging 3D imaging technologies, and focus, in particular, on those that can be used to build interfaces between the users’ hands and the machine. The purpose of this paper is to categorize and highlight the relevant differences between these existing 3D imaging approaches in terms of the nature of the information provided, output data format, as well as the specific conditions under which these approaches yield reliable data. Furthermore we explore the impact of each of these approaches on the computational cost and reliability of the required image processing algorithms. Finally we highlight the main challenges and opportunities in developing natural user interfaces based on hand gestures, and conclude with some promising directions for future research. 

@article{eftekharian2011family,
  address = {USA},
  author = {Eftekharian, Ata a. and Ilie\c{s}, Horea t.},
  date-added = {2023-10-11 15:07:55 -0400},
  date-modified = {2023-10-11 15:08:10 -0400},
  doi = {10.1017/S0890060411000229},
  issn = {0890-0604},
  issue_date = {November 2011},
  journal = {Artif. Intell. Eng. Des. Anal. Manuf.},
  keywords = {Path Planning, Half-Space, R-Function, Medial Zone, Boolean Expression},
  month = nov,
  number = {4},
  numpages = {18},
  pages = {375--392},
  publisher = {Cambridge University Press},
  title = {A Family of Skeletons for Motion Planning and Geometric Reasoning Applications},
  url = {https://doi.org/10.1017/S0890060411000229},
  volume = {25},
  year = {2011},
  bdsk-url-1 = {https://doi.org/10.1017/S0890060411000229}
}

The task of planning a path between two spatial configurations of an artifact moving among obstacles is an important problem in practically all geometrically intensive applications. Despite the ubiquity of the problem, the existing approaches make specific limiting assumptions about the geometry and mobility of the obstacles, or those of the environment in which the motion of the artifact takes place. We present a strategy to construct a family of paths, or roadmaps, for two-and three-dimensional solids moving in an evolving environment that can undergo drastic topological changes. Our approach is based on a potent paradigm for constructing geometric skeletons that relies on constructive representations of shapes with R-functions that operate on real-valued half-spaces as logic operations. We describe a family of skeletons that have the same homotopy as that of the environment and contains the medial axis as a special case. Of importance, our skeletons can be designed so that they are "attracted to" or "repulsed by" prescribed spatial sites of the environment. Moreover, the R-function formulation suggests the new concept of a medial zone, which can be thought of as a "thick" skeleton with significant applications for motion planning and other geometric reasoning applications. Our approach can handle problems in which the environment is not fully known a priori, and intrinsically supports local and parallel skeleton computations for domains with rigid or evolving boundaries. Furthermore, our path planning algorithm can be implemented in any commercial geometric kernel, and has attractive computational properties. The capability of the proposed technique are explored through several examples designed to simulate highly dynamic environments.

@article{eftekharian2011curve,
  author = {Eftekharian, Ata A and Ilies, Horea T},
  date-modified = {2023-10-11 15:07:14 -0400},
  doi = {doi:10.3722/cadaps.2011.87-97},
  journal = {Computer-Aided Design and Applications},
  number = {1},
  pages = {87--97},
  publisher = {Taylor \& Francis},
  title = {Curve Skeletons of Planar Domains},
  volume = {8},
  year = {2011},
  bdsk-url-1 = {https://doi.org/10.3722/cadaps.2011.87-97}
}

Curve skeletons are 1D entities that capture the essential topology and geometry of a shape in a simple and very compact form, and have found a multitude of applications in engineering and science. The concept itself is ill-defined, which is why the many existing definitions are ad-hoc and employ heuristic algorithms revolving around the (unique) medial axis. We propose a framework for computing curve skeletons for arbitrary planar domains that relies on a modified medial axis, and is based on R-functions that can be thought of as continuous forms of the Boolean logic functions. Furthermore, we propose one particular definition of such a curve skeleton that preserves the homotopy of the domain, is stable in the presence of noise and is well-suited to downstream applications. The framework can be implemented in any commercial geometric kernel for planar domains, and has attractive computational properties. Furthermore, the mathematical concepts are extendable to medial surfaces and curve skeletons in 3D domains.

@article{wu2011shaping,
  author = {Wu, Nier and Ilies, Horea T},
  date-modified = {2023-10-11 15:11:30 -0400},
  doi = {10.3722/cadaps.2011.249-268},
  journal = {Computer-Aided Design and Applications},
  number = {2},
  pages = {249--268},
  publisher = {Taylor \& Francis},
  title = {Shaping with deformations},
  volume = {8},
  year = {2011},
  bdsk-url-1 = {https://doi.org/10.3722/cadaps.2011.249-268}
}

Parametric modeling changed the way we design and reason about mechanical artifacts due to the ability to handle (mainly 2-dimensional) constraints imposed on geometric entities. However, the inherent history dependence of parametric models limits the changes that can be achieved with a given parameterization.

We propose a new history-independent approach to edit geometric models via a geometric deformation procedure that relies on motion interpolation to define and control local geometric modifications. Our approach generates useful geometric deformations such as stretching, bending, and twisting of existing point sets without relying on pre-existing parameterizations or on specific representations of the geometry. The proposed approach provides a small set of parameters that allow direct control and editing of the geometric modifications, and can preserve important geometric invariants such as constant cross-sectional properties of the deformed models. Furthermore, our shape deformation paradigm complements emerging direct boundary manipulation capabilities, and maintains the ability to perform parametric optimization of the associated models.

@article{shahbazi2010hydrogen,
  author = {Shahbazi, Zahra and Ilie{\c s}, Horea T. and Kazerounian, Kazem},
  date-added = {2023-10-11 15:13:56 -0400},
  date-modified = {2023-10-11 15:14:09 -0400},
  doi = {10.1115/1.4001088},
  eprint = {https://asmedigitalcollection.asme.org/mechanismsrobotics/article-pdf/2/2/021009/5675459/021009\_1.pdf},
  issn = {1942-4302},
  journal = {Journal of Mechanisms and Robotics},
  month = apr,
  number = {2},
  pages = {021009},
  title = {{Hydrogen Bonds and Kinematic Mobility of Protein Molecules}},
  url = {https://doi.org/10.1115/1.4001088},
  volume = {2},
  year = {2010},
  bdsk-url-1 = {https://doi.org/10.1115/1.4001088}
}

Modeling protein molecules as kinematic chains provides the foundation for developing powerful approaches to the design, manipulation, and fabrication of peptide based molecules and devices. Nevertheless, these models possess a high number of degrees of freedom (DOFs) with considerable computational implications. On the other hand, real protein molecules appear to exhibit a much lower mobility during the folding process than what is suggested by existing kinematic models. The key contributor to the lower mobility of real proteins is the formation of hydrogen bonds during the folding process. In this paper, we explore the pivotal role of hydrogen bonds in determining the structure and function of the proteins from the point of view of mechanical mobility. The existing geometric criteria on the formation of hydrogen bonds are reviewed and a new set of geometric criteria is proposed. We show that the new criteria better correlate the number of predicted hydrogen bonds with those established by biological principles than other existing criteria. Furthermore, we employ established tools in kinematics mobility analysis to evaluate the internal mobility of protein molecules and to identify the rigid and flexible segments of the proteins. Our results show that the developed procedure significantly reduces the DOF of the protein models, with an average reduction of 94\%. Such a dramatic reduction in the number of DOF can have enormous computational implications in protein folding simulations.

@article{erdim2010comparison,
  author = {Erdim, H{\"u}seyin and Ilie{\c s}, Horea T.},
  date-added = {2023-10-11 15:12:01 -0400},
  date-modified = {2023-10-11 15:12:11 -0400},
  doi = {https://doi.org/10.1016/j.cad.2009.06.002},
  issn = {0010-4485},
  journal = {Computer-Aided Design},
  keywords = {Solid sweeping, Boundary evaluation, Space sampling, Marching cubes, Octrees},
  note = {Application-driven Shape Development},
  number = {8},
  pages = {657-669},
  title = {A comparison of sampling strategies for computing general sweeps},
  url = {https://www.sciencedirect.com/science/article/pii/S0010448509001717},
  volume = {42},
  year = {2010},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0010448509001717},
  bdsk-url-2 = {https://doi.org/10.1016/j.cad.2009.06.002}
}

Sweeping moving objects has become one of the basic geometric operations used in engineering design, analysis and physical simulation. Despite its relevance, computing the boundary of the set swept by a non-polyhedral moving object is largely an open problem due to well-known theoretical and computational difficulties of the envelopes. We have recently introduced a generic point membership classification (PMC) test for general solid sweeping. Importantly, this PMC test provides complete geometric information about the set swept by the moving object, including the ability to compute the self-intersections of the sweep itself. In this paper, we compare two recursive strategies for sampling points of the space in which the object moves, and show that the sampling based on a fast marching cubes algorithm possesses the best combination of features in terms of performance and accuracy for the boundary evaluation of general sweeps. Furthermore, we show that the PMC test can be used as the foundation of a generic sweep boundary evaluator in conjunction with efficient space sampling strategies for solids of arbitrary complexity undergoing affine motions.

@article{frank2010fast,
  author = {Frank, Mikhail and ILIE{\c{S}}, HOREA T},
  date-modified = {2023-10-11 15:13:16 -0400},
  doi = {https://doi.org/10.1142/S0218654310001286},
  journal = {International Journal of Shape Modeling},
  number = {01n02},
  pages = {57--79},
  publisher = {World Scientific Publishing Company},
  title = {Fast Hierarchical Discretization of Parametric Boundary Representations},
  volume = {16},
  year = {2010},
  bdsk-url-1 = {https://doi.org/10.1142/S0218654310001286}
}

Prevalent discretization methods based on Delaunay triangulations and advancing fronts, which sample and mesh simultaneously, can guarantee well shaped triangles but at a fairly high computational cost. In this paper we present a novel and flexible two-part sampling and meshing algorithm, which produces topologically correct meshes on arbitrary boundary representations whose faces are represented parametrically, without requiring an initial coarse mesh. Our method is based on a hybrid spatial partitioning scheme driven by user-designed subdivision rules that combines the power of quadtree decomposition with the flexibility of the binary decompositions to produce meshes that favor prescribed geometric properties. Importantly, the algorithm offers a performance increase of approximately two orders of magnitude over Delaunay based methods and at least one order of magnitude over advancing front methods. At the same time, our algorithm is practically as fast as the computationally optimal algorithm based on a pure quadtree decomposition, but with a markedly better distribution in the regions with parametric distortion. The hierarchical nature of our surface decomposition is well suited to interactive applications and multithreaded implementation.

@article{iliecs2009continuous,
  author = {Ilie{\c s}, Horea T.},
  date-added = {2023-10-11 15:17:51 -0400},
  date-modified = {2023-10-11 15:44:41 -0400},
  doi = {10.1115/1.3130142},
  eprint = {https://asmedigitalcollection.asme.org/computingengineering/article-pdf/9/2/021007/5502557/021007\_1.pdf},
  issn = {1530-9827},
  journal = {Journal of Computing and Information Science in Engineering},
  month = jun,
  number = {2},
  pages = {021007},
  title = {{Continuous Collision and Interference Detection for {3D} Geometric Models}},
  url = {https://doi.org/10.1115/1.3130142},
  volume = {9},
  year = {2009},
  bdsk-url-1 = {https://doi.org/10.1115/1.3130142}
}

This paper describes a new approach to perform continuous collision and interference detection between a pair of arbitrarily complex objects moving according to general three-dimensional affine motions. Our approach, which does not require any envelope computations, recasts the problem of detecting collisions and computing the interfering subsets in terms of inherently parallel set membership classification tests of specific curves against the original (static) geometric representations. We show that our approach can compute the subsets of the moving objects that collide and interfere, as well as the times of collision, which has important applications in mechanical design and manufacturing. Our approach can be implemented for any geometric representation that supports curve-solid intersections, such as implicit and parametric representations. We describe an implementation of the proposed technique for solids given as a boundary representation (B-rep), and illustrate its effectiveness for several rigid and deformable moving objects bounded by tesselated and freeform surfaces of various complexities. Furthermore, we show that our approach can be extended to also identify the local and global self-intersections of the envelopes of the moving objects without requiring to compute these envelopes explicitly. The paper concludes by summarizing the proposed approach as well as reviewing relevant computational improvements that can decrease the computational cost of the prototype implementation by orders of magnitude.

@article{flanagan2009force,
  author = {Flanagan, Dennis and Ilies, Horea and Lasko, Brian and Stack, Jeffrey},
  date-modified = {2023-10-11 15:17:26 -0400},
  doi = {https://doi.org/10.1563/1548-1336-35.6.270},
  journal = {Journal of Oral Implantology},
  number = {6},
  pages = {270--276},
  publisher = {American Academy of Implant Dentistry},
  title = {Force and movement of non-osseointegrated implants: an in vitro study},
  volume = {35},
  year = {2009},
  bdsk-url-1 = {https://doi.org/10.1563/1548-1336-35.6.270}
}

Dental implants have enabled a dramatic increase in the quality of life for many partially edentulous and edentulous patents. Immediate loading of newly placed dental implants is a recent advancement that attempts to meet patient demand. However, immediate loading of a just placed implant may induce implant failure to osseointegrate. Some patients can generate a biting force that can reach approximately 1300 Newtons (N) in the posterior jaws. The magnitude of bite force that would cause failure of osseointegration of newly placed implants is currently unknown. It has been proposed that osseointegration would fail if an implant is luxated in bone more than 50 to 150 microns. Fibrous tissue, not bone, would form. This study investigated the quantity of various off-axial forces required to move a nonosseointegrated 4.3 x 13 mm implant 50 microns. The previously published pilot study for this study found that the amount of horizontal force required to displace an implant 50 microns was approximately 150 N. This study found that the force needed to move the implants 100 microns at a horizontal approach, 0 degrees, averaged 50 N, with a range of 23-79 N; at 22 degrees, averaged 52 N, with a range of 27-70 N; and at 60 degrees averaged 87 N, with a range of 33-105 N. 

@article{madden2009residue,
  author = {Madden, Christopher and Bohnenkamp, Peter and Kazerounian, Kazem and Ilie{\c{s}}, Horea T},
  date-modified = {2023-10-11 15:18:51 -0400},
  doi = {https://doi.org/10.1177/0278364908098092},
  journal = {The International Journal of Robotics Research},
  number = {4},
  pages = {450--463},
  publisher = {SAGE Publications Sage UK: London, England},
  title = {Residue level three-dimensional workspace maps for conformational trajectory planning of proteins},
  volume = {28},
  year = {2009},
  bdsk-url-1 = {https://doi.org/10.1177/0278364908098092}
}

The function of a protein macromolecule often requires conformational transitions between two native conformations. Understanding these transitions is essential to the understanding of how proteins function, as well as to the ability to design and manipulate protein-based nanomechanical systems. In this paper we propose a set of 3D Cartesian workspace maps for exploring protein pathways. These 3D maps are constructed in the Euclidean space for triads of chain segments of protein molecules that have been shown to have a high probability of occurrence in naturally observed proteins based on data obtained from more than 38,600 proteins from the Protein Data Bank (PDB). We show that the proposed 3D propensity maps are more effective navigation tools than the propensity maps constructed in the angle space. We argue that the main reason for this improved efficiency is the fact that, although there is a one-to-one mapping between the 2D dihedral angle maps and the 3D Cartesian maps, the propensity distributions are significantly different in the two spaces. Hence, the 3D maps allow the pathway planning to be performed directly in the 3D Euclidean space based on propensities computed in the same space, which is where protein molecules change their conformations.

@article{eftekharian2009distance,
  author = {Eftekharian, Ata A. and Ilie{\c s}, Horea T.},
  date-added = {2023-10-11 15:16:12 -0400},
  date-modified = {2023-10-11 15:16:23 -0400},
  doi = {https://doi.org/10.1016/j.cad.2009.05.006},
  issn = {0010-4485},
  journal = {Computer-Aided Design},
  keywords = {Geometric skeletons, Medial axis, Straight skeleton, C-skeleton, R-functions, Distance functions},
  number = {12},
  pages = {865-876},
  title = {Distance functions and skeletal representations of rigid and non-rigid planar shapes},
  url = {https://www.sciencedirect.com/science/article/pii/S0010448509001699},
  volume = {41},
  year = {2009},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0010448509001699},
  bdsk-url-2 = {https://doi.org/10.1016/j.cad.2009.05.006}
}

Shape skeletons are fundamental concepts for describing the shape of geometric objects, and have found a variety of applications in a number of areas where geometry plays an important role. Two types of skeletons commonly used in geometric computations are the straight skeleton of a (linear) polygon, and the medial axis of a bounded set of points in the k-dimensional Euclidean space. However, exact computation of these skeletons of even fairly simple planar shapes remains an open problem. In this paper we propose a novel approach to construct exact or approximate (continuous) distance functions and the associated skeletal representations (a skeleton and the corresponding radius function) for solid 2D semi-analytic sets that can be either rigid or undergoing topological deformations. Our approach relies on computing constructive representations of shapes with R-functions that operate on real-valued halfspaces as logic operations. We use our approximate distance functions to define a new type of skeleton, i.e, the C-skeleton, which is piecewise linear for polygonal domains, generalizes naturally to planar and spatial domains with curved boundaries, and has attractive properties. We also show that the exact distance functions allow us to compute the medial axis of any closed, bounded and regular planar domain. Importantly, our approach can generate the medial axis, the straight skeleton, and the C-skeleton of possibly deformable shapes within the same formulation, extends naturally to 3D, and can be used in a variety of applications such as skeleton-based shape editing and adaptive motion planning.

@article{iliecs2008determining,
  author = {Ilie{\c s}, Horea T. and Flanagan, Dennis and McCullough, Paul T. and McQuoid, Scott},
  date-added = {2023-10-11 15:22:44 -0400},
  date-modified = {2023-10-11 15:22:56 -0400},
  doi = {10.1115/1.2889058},
  eprint = {https://asmedigitalcollection.asme.org/medicaldevices/article-pdf/2/1/011003/5586450/011003\_1.pdf},
  issn = {1932-6181},
  journal = {Journal of Medical Devices},
  month = mar,
  number = {1},
  pages = {011003},
  title = {{Determining the Fatigue Life of Dental Implants}},
  url = {https://doi.org/10.1115/1.2889058},
  volume = {2},
  year = {2008},
  bdsk-url-1 = {https://doi.org/10.1115/1.2889058}
}

Dental implants are used to retain and support fixed and removable dental prostheses. In many clinical situations, local bone morphology requires dental implants that have a diameter that is significantly smaller than the typical implant diameters. In these cases, the fatigue life of the smaller diameter implants becomes a critical therapeutic parameter. However, this fatigue life depends on the implant itself, on the physical properties of the bone, as well as on other morphological characteristics that are patient dependent. In other words, this fatigue life varies greatly with each newly placed implant, but the capability to predict the fatigue life of dental implants does not exist today. In this paper, we present the first steps towards establishing such a methodology. We develop a finite element based fatigue model for rigidly mounted dental implants, and correlate its results with both analytical predictions as well as physical measurements. This implies that such a model can be used as a valid predictor of fatigue life of dental implants themselves, and can be used as a valuable implant design tool. Furthermore, we present the design of a cost effective device to measure the fatigue life of dental implants that can be either rigidly or bone mounted (in vitro). This device was used to measure the fatigue life of an initial sample of nine dental implants, and we show that the results predicted by the finite element model correlated well with our initial experimental results.

@article{iliecs2008measuring,
  author = {Ilie{\c s}, Horea T. and Flanagan, Dennis and Raby, Matthew and Stevenson, Richard},
  date-added = {2023-10-11 15:23:34 -0400},
  date-modified = {2023-10-11 15:23:50 -0400},
  doi = {10.1115/1.2889057},
  eprint = {https://asmedigitalcollection.asme.org/medicaldevices/article-pdf/2/1/014501/5586491/014501\_1.pdf},
  issn = {1932-6181},
  journal = {Journal of Medical Devices},
  month = mar,
  number = {1},
  pages = {014501},
  title = {{Measuring Luxation of Dental Implants In Vitro}},
  url = {https://doi.org/10.1115/1.2889057},
  volume = {2},
  year = {2008},
  bdsk-url-1 = {https://doi.org/10.1115/1.2889057}
}

Loading of dental implants immediately after placement is an important attribute for the patients receiving the implants, but may induce a failure in the osseointegration of the implant. Even though the loading required to induce such failures is currently unknown, it is estimated that the osseointegration may fail if an implant is luxated in bone by more than 50μm. Therefore, the ability to measure this loading can provide the practicing dentist with critical information in estimating the functional life of a newly placed implant. This paper discusses the design and fabrication of a cost-effective test setup for measuring the amount of horizontal force required to displace a nonosseointegrated implant, and presents the results of our pilot in vitro load measurements for dental implants mounted in a bovine mandible. Although the sample size of our measurements is not statistically significant, the initial data show that the amount of horizontal force required to displace a 4.3×13mm implant by 50μm is in the order of 150N, and therefore the implant may fail to osseointegrate for biting forces that are as low as 440N, which is about half of the typical biting force of an adult in the molar area. One implication of our study is that implants having smaller diameters may move and fail to osseointegrate for even lower biting forces. Furthermore, our work represents the first steps in developing appropriate metrics to correlate the measured biting force generated by a patient with his or her candidacy for immediate functional implant loading.

@article{erdim2008classifying,
  author = {Erdim, H{\"u}seyin and Ilie{\c s}, Horea T.},
  date-added = {2023-10-11 15:20:14 -0400},
  date-modified = {2023-10-11 15:20:25 -0400},
  doi = {https://doi.org/10.1016/j.cad.2008.07.005},
  issn = {0010-4485},
  journal = {Computer-Aided Design},
  keywords = {Point membership classification, Sweep, Singularities, Fold points, Envelopes},
  number = {9},
  pages = {987-998},
  title = {Classifying points for sweeping solids},
  url = {https://www.sciencedirect.com/science/article/pii/S0010448508001310},
  volume = {40},
  year = {2008},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0010448508001310},
  bdsk-url-2 = {https://doi.org/10.1016/j.cad.2008.07.005}
}

Many diverse engineering problems can be modeled with solid sweeping in a conceptually simple and intuitive way, and sweeps are considered to be one of the basic representation schemes in solid modeling. However, many properties of sweeps as well as their “informational completeness” are not well understood, which is the primary reason why computational support for solid sweeping remains scarce. We propose a generic point membership classification (PMC) for sweeping solids of arbitrary complexity moving according to one parameter affine motions. The only restrictive assumption that we make in this paper is that the initial and final configurations of the moving object do not intersect during the sweep. Our PMC test is defined in terms of inverted trajectory tests against the original geometric representation of the generator object, which implies that this test can be implemented in any geometric representation that supports curve-solid intersections. Importantly, this PMC test provides complete geometric information about the set swept by 3-dimensional objects in general motions. At the same time, it establishes the foundations for developing a new generation of computational tools for sweep boundary evaluation and trimming, as well as a number of practical applications such as shape synthesis, contact analysis and path planning.

@article{flanagan2008measurement,
  author = {Flanagan, Dennis and Ilies, Horea and McCullough, Paul and McQuoid, Scott},
  date-modified = {2023-10-11 15:22:16 -0400},
  doi = {https://doi.org/10.1563/1548-1336(2008)34[7:MOTFLO]2.0.CO;2},
  journal = {Journal of Oral Implantology},
  number = {1},
  pages = {7--11},
  title = {Measurement of the fatigue life of mini dental implants: a pilot study},
  volume = {34},
  year = {2008},
  bdsk-url-1 = {https://doi.org/10.1563/1548-1336(2008)34%5B7:MOTFLO%5D2.0.CO;2}
}

The fatigue life of mini or small-diameter dental implants is of particular interest because these implants are used to retain and support fixed and removable dental prostheses. The fatigue life of an implant depends on both the implant itself as well as on the physical properties of the bone. However, the capability to predict the fatigue life of a newly placed implant is currently inexistent. This pilot study represents the first step in developing such a methodology and focuses on the design of a cost-effective device to measure the fatigue life of a dental implant. In our measurements, the implant has been mounted in an essentially rigid support, but test specimens can also be bone mounted in vitro. Furthermore, we developed a finite element-based computer model capable of predicting the corresponding fatigue life. The finite element analysis was performed in ABAQUS, and the results predicted by the model correlated fairly well with our initial experimental results. Most of the 2-mm diameter implants fractured after more than a million cycles.

@article{flanagan2008force,
  author = {Flanagan, Dennis and Ilies, Horea and Raby, Matthew and Stevenson, Richard},
  date-modified = {2023-10-11 15:21:46 -0400},
  doi = {https://doi.org/10.1563/1548-1336(2008)34[128:FRTLAN]2.0.CO;2},
  journal = {Journal of Oral Implantology},
  number = {3},
  pages = {128--134},
  title = {Force required to luxate a newly placed dental implant in bone: an in vitro pilot study},
  volume = {34},
  year = {2008},
  bdsk-url-1 = {https://doi.org/10.1563/1548-1336(2008)34%5B128:FRTLAN%5D2.0.CO;2}
}

Immediate loading of newly placed dental implants is a consideration when attempting to meet patients’ demands. However, immediate loading may induce implant failure to osseointegrate, particularly in the case of a patient who can generate a biting force that can reach approximately 1300 Newtons (N) in the posterior jaws. The range of biting forces that prevent osseointegration of newly placed implants is currently unknown. However, it is suspected that osseointegration may fail if an implant is luxated in bone more than 50 μm, in which case fibrous tissue will be formed instead of bone. This pilot study was focused on finding the amount of horizontal off-axial force required to move a nonosseointegrated 4.3 × 13–mm implant 50 μm. The initial data show that the amount of horizontal force required to displace such an implant by 50 μm was on the order of 150 N. Assuming that the angle between the direction of the biting force and the vertical lies between 0\,^∘ and 20\,^∘, our data show that a 4.3 × 13–mm implant may fail to osseointegrate for biting forces that are as low as 440 N. One implication of our study is that implants having smaller diameters may move and fail to osseointegrate for even lower biting forces.

@article{bohnenkamp2007structural,
  author = {Bohnenkamp, P and Kazerounian, K and Ilies, HT},
  date-modified = {2023-10-11 15:25:09 -0400},
  journal = {Proc 12th IFToMM World Congr},
  number = {6},
  title = {Structural prediction of peptide based Nano systems via progressive landscape evolution},
  volume = {1},
  year = {2007}
}

Protein molecules are the nano machines of the biological world and one of the most suitable mechanisms to manipulate matter at nano level. Predicting the final configuration of the folded protein remains one of the most important open problems in science. The ab initio approaches to protein folding seek to develop a framework, based on first physical principles, for predicting the final protein configuration by minimizing the total potential energy of the protein. However, navigating the utterly complex energy landscape of a protein remains one of the main bottlenecks in protein folding today due to the large number of local energy minima that effectively act as energy traps for any and all simulation algorithms.

This paper proposes two generic strategies for locally modifying the energy landscape aimed at avoiding these energy traps, namely, segmental manipulation and progressive side chain scaling. These strategies are implemented in ProtoFold, our comprehensive approach to protein folding based on kineto-static compliance of the protein chain. We show that these strategies effectively extricate the protein molecule from the trapped configurations, and allow the numerical simulation to proceed. 

@article{erdim2007detecting,
  author = {Erdim, H{\"u}seyin and Ilie{\c s}, Horea T.},
  date-added = {2023-10-11 15:25:35 -0400},
  date-modified = {2023-10-11 15:25:48 -0400},
  doi = {https://doi.org/10.1016/j.cad.2007.03.007},
  issn = {0010-4485},
  journal = {Computer-Aided Design},
  keywords = {Singularities, Envelopes, Undercutting, Fold points, Sweep, Higher pairs},
  number = {10},
  pages = {829-840},
  title = {Detecting and quantifying envelope singularities in the plane},
  url = {https://www.sciencedirect.com/science/article/pii/S0010448507000802},
  volume = {39},
  year = {2007},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0010448507000802},
  bdsk-url-2 = {https://doi.org/10.1016/j.cad.2007.03.007}
}

The mathematical envelopes of families of both rigid and non-rigid moving shapes play a fundamental role in a variety of problems from very diverse application domains, from engineering design and manufacturing to computer graphics and computer assisted surgery. Geometric singularities in these envelopes are known to induce malfunctions or unintended system behavior, and the corresponding theoretical and computational difficulties induced by these singularities are not only massive, but also well documented. We describe a new approach to detect and quantify the envelope singularities induced by 2-dimensional shapes of arbitrary complexity moving according to general non-periodic and non-singular planar affine motions. Our approach, which does not require any envelope computations, is reframing the problem in terms of “fold points” and “fold regions” in the neighborhood of geometric singularities, and we show that the existence of these fold points is a necessary condition for the existence of singularities. We establish a mathematically well defined duality between the 2-dimensional Euclidean space in which the motion takes place and a 2+1 spacetime domain. Based on this duality, we recast the problem of detecting and quantifying geometric singularities into inherently parallel tests against the original geometric representation in the 2-dimensional Euclidean space. We conclude by discussing the significance of our results, and the extension of our approach to 3-dimensional moving shapes.

@article{ilies2004equivalence,
  author = {Ilies¸, Horea T. and Shapiro, Vadim},
  date-added = {2023-10-11 15:29:19 -0400},
  date-modified = {2023-10-11 15:29:32 -0400},
  doi = {10.1115/1.1641794},
  eprint = {https://asmedigitalcollection.asme.org/computingengineering/article-pdf/4/1/20/5773397/20\_1.pdf},
  issn = {1530-9827},
  journal = {Journal of Computing and Information Science in Engineering},
  month = mar,
  number = {1},
  pages = {20-27},
  title = {{Equivalence Classes for Shape Synthesis of Moving Mechanical Parts }},
  url = {https://doi.org/10.1115/1.1641794},
  volume = {4},
  year = {2004},
  bdsk-url-1 = {https://doi.org/10.1115/1.1641794}
}

Moving parts in contact have been traditionally synthesized through specialized techniques that focus on completely specified nominal shapes. Given that the functionality does not completely constrain the geometry of any given part, the design process leads to arbitrarily specified portions of geometry, without providing support for systematic generation of alternative shapes satisfying identical or altered functionalities. Hence the design cycle of a product is forced to go into numerous and often redundant iterative stages that directly impact its effectiveness. We argue that the shape synthesis of mechanical parts is more efficient and less error prone if it is based on techniques that identify the functional surfaces of the part without imposing arbitrary restrictions on its geometry. We demonstrate that such techniques can be formally defined for parts moving in contact through equivalence classes of mechanical parts that satisfy a given functionality. We show here that by replacing the completely specified geometry of the traditional approaches with partial geometry and functional specification, we can formally define classes of mechanical parts that are equivalent, in the sense that all members of the class satisfy the same functional specifications. Moreover, these classes of functionally equivalent parts are computable, may be represented unambiguously by maximal elements in each class, and contain all other functional designs that perform the same function.

@article{iliecs2002class,
  author = {Ilie{\c{s}}, Horea and Shapiro, Vadim},
  date-modified = {2023-10-11 15:31:14 -0400},
  doi = {https://doi.org/10.1007/s00163-002-0014-0},
  journal = {Research in Engineering Design},
  pages = {157--166},
  publisher = {Springer-Verlag},
  title = {A class of forms from function: the case of parts moving in contact},
  volume = {13},
  year = {2002},
  bdsk-url-1 = {https://doi.org/10.1007/s00163-002-0014-0}
}

We consider the general problem of designing mechanical parts moving in contact under the influence of externally applied loads. Geometrically, the problem may be characterized in terms of a conjugate triplet, which is formed by the two shapes moving in contact and their relative motion. We show that every such triplet belongs to one or more classes of functionally equivalent designs that may be represented uniquely by maximal triplets, corresponding respectively to the two largest contact shapes that are guaranteed to contain all other possible solutions to the contact design problem. In practical terms, the proposed characterization of the contact problem enables the systematic exploration of the design space using fully defined representatives of the functionally equivalent class of parts. Furthermore, such exploration may be performed using standard tools from geometric modeling, and without assuming any particular parameterization that necessarily restrict both the design space and possible computational techniques for exploring feasible designs. Because the proposed approach supports the generation of an essentially unlimited space of design solutions for a given contact problem, it is particularly effective at the conceptual design stage.

@article{ilies2000shaping,
  author = {Ilies¸, Horea T. and Shapiro, Vadim},
  date-added = {2023-10-11 15:32:13 -0400},
  date-modified = {2023-10-11 15:32:25 -0400},
  doi = {10.1115/1.1319319},
  eprint = {https://asmedigitalcollection.asme.org/mechanicaldesign/article-pdf/122/4/567/5687072/567\_1.pdf},
  issn = {1050-0472},
  journal = {Journal of Mechanical Design},
  month = feb,
  number = {4},
  pages = {567-574},
  title = {{On Shaping With Motion }},
  url = {https://doi.org/10.1115/1.1319319},
  volume = {122},
  year = {1999},
  bdsk-url-1 = {https://doi.org/10.1115/1.1319319}
}

Mechanical parts are modeled as (predominantly rigid) solid shapes that may move in space in order to function, be manufactured (for example, machine or be machined), and be assembled or disassembled. While it is clear that such mechanical shapes are greatly influenced by collision, interference, containment, and contact constraints through prescribed motions, the motion itself is usually not part of these shape models. This in turn leads to proliferation of computational methods for modeling and analysis of various motion-related constraints. We show that all motion-related constraints can be formulated and applied within the same computational framework that treats motion as an integral part of the model. Our approach relies on two computational utilities. The first one is the unsweep operation which, given an arbitrary n-dimensional subset of Euclidean space E and a general motion M, returns the largest subset of E that remains inside E under M. The second modeling utility is a disjoint decomposition of space induced by the operations of unsweep and the standard set operations. The proposed approach subsumes and unifies the traditional sweep-based modeling of moving parts, and provides improved computational support for mechanical shape design. [S1050-0472(00)02404-1]

@article{ilies1999dual,
  author = {Ilies, Horea T. and Shapiro, Vadim},
  date-added = {2023-10-11 21:58:15 -0400},
  date-modified = {2023-10-11 21:58:27 -0400},
  doi = {https://doi.org/10.1016/S0010-4485(99)00015-9},
  issn = {0010-4485},
  journal = {Computer-Aided Design},
  keywords = {Unsweep, Sweep, Geometric and solid modeling, Motion, Point membership test, Set operators},
  number = {3},
  pages = {185-201},
  title = {The dual of sweep},
  url = {https://www.sciencedirect.com/science/article/pii/S0010448599000159},
  volume = {31},
  year = {1999},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0010448599000159},
  bdsk-url-2 = {https://doi.org/10.1016/S0010-4485(99)00015-9}
}

As an infinite union operation, sweep of a moving object through space is a powerful and natural addition to the Boolean set operations that incorporates motion-related information for the purposes of shaping, collision detection, and simulation of moving objects. Use of sweep has been hindered by limited computational support and by the fact that it is a ‘material growing’ operation, whereas many applications, such as interference elimination and mechanism design, appear to be better modeled by a ‘material removal’ operation. This article formally defines a new geometric modeling operation of unsweep. Given an arbitrary subset E of Euclidean space and a general motion M, unsweep(E,M) returns the largest subset of E that remains inside the original E under M. When M is a translation, unsweep (E,M) naturally reduces to the standard Minkowski difference of E and the trajectory generated by the inverted motion M̂. In this sense, the operation of unsweep is a generalization of Minkowski difference that corresponds to a ‘material removal’ operation, it can be also defined as an infinite intersection operation, and is the dual of sweep in a precise set-theoretic sense. We show that unsweep has attractive theoretical and computational properties, including a practical point membership test for arbitrary general motions. Using duality, the established properties of unsweep is extended to the general sweep operation, and can be used to improve the computational support for general sweeps.

@article{ostoja1996cauchy,
  author = {Ostoja-Starzewski, M. and Ilies, H.},
  date-added = {2023-10-11 15:35:57 -0400},
  date-modified = {2023-10-11 15:39:06 -0400},
  doi = {https://doi.org/10.1016/0020-7683(95)00072-0},
  issn = {0020-7683},
  journal = {International Journal of Solids and Structures},
  number = {8},
  pages = {1119-1136},
  title = {The {C}auchy and characteristic boundary value problems of random rigid-perfectly plastic media},
  url = {https://www.sciencedirect.com/science/article/pii/0020768395000720},
  volume = {33},
  year = {1996},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/0020768395000720},
  bdsk-url-2 = {https://doi.org/10.1016/0020-7683(95)00072-0}
}

Effects of spatial random fluctuations in the yield condition of rigid-perfectly plastic continuous media are analysed in cases of Cauchy and characteristic boundary value problems. A weakly random plastic microstructure is modeled, on a continuum mesoscale, by an isotropic yield condition with the yield limit taken as a locally averaged random field. The solution method is based on a stochastic generalization of the method of sliplines, whose significant feature is that the deterministic characteristics are replaced by the forward evolution cones containing random characteristics. Comparisons of response of this random medium and of a deterministic homogeneous medium, with a plastic limit equal to the average of the random one, are carried out numerically in several specific examples of the two boundary value problems under study. An application of the method is given to the limit analysis of a cylindrical tube under internal traction. The major conclusion is that weak material randomness always leads to a relatively stronger scatter in the position and field variables, as well as to a larger size of the domain of dependence—effects which are amplified by both presence of shear traction and inhomogeneity in the boundary data. Additionally, it is found that there is hardly any difference between stochastic slipline fields due to either Gaussian or uniform noise in the plastic limit.

@inbook{ki2024ark,
  author = {Kazerounian, Kazem and Ilie\c{s}, Horea},
  title = {The Evolving Role of Robot Kinematics in Bio-Nanotechnology},
  journal = {Advances in Robot Kinematics},
  editor = {{J. Lenar\v{c}i\v{c}}},
  year = {2024},
  note = {to appear}
}

The fusion of kinematics, a field centered on motion and geometry, with molecular biology has opened new avenues in disease diagnosis, treatment, drug de- velopment, nanomachines, nano-robots, nanotechnology, and sustainability. Despite the potential of these interdisciplinary ideas, the extensive application of advanced kinematic principles in bio-nanotechnology remains underutilized.

This review paper explores the critical role of applied robot kinematics in biotech- nology, particularly in the evolution and discovery of innovative bio-nanomachines and bio-nano robots over the past 25 years. By reviewing the progress within the authors’ research lab during this time leading to establishing the foundation for incorporating kinematic principles in innovative bio-nanomachines, this paper ex- plores future trends, and issues a call to action to the robot kinematics community. Emphasizing the importance of precise kinematic approaches in understanding pro- tein molecules’ behavior for nano machine development, we argue that the robot kinematics community remains ideally positioned to drive groundbreaking progress in bio-nanotechnology and broaden the scope of these approaches in drug design, nanomachines, and development of new architected materials. This interdisciplinary fusion is poised to lead to landmark achievements in the application of a historically rooted science of kinematics. The future of kinematics driven discoveries at small scales is very bright, having only witnessed the initial impact of AI and quantum computing on protein engineering, and kinematics can profoundly accelerate our ability to systematically discover and create new, highly effective proteins.

@inbook{chorsi2023materials,
  address = {Oxford},
  author = {Chorsi, Meysam T. and Le, Thinh T. and Das, Ritopa and Vinikoor, Tra and Chorsi, Hamid T. and Kazerounian, Kazem and Ilies, Horea and Nguyen, Thanh D.},
  booktitle = {Encyclopedia of Materials: Electronics},
  date-added = {2023-10-11 14:29:23 -0400},
  date-modified = {2023-10-11 22:04:41 -0400},
  doi = {https://doi.org/10.1016/B978-0-12-819728-8.00100-5},
  editor = {Haseeb, A.S.M.A.},
  isbn = {978-0-12-819735-6},
  keywords = {Biodevices, Biomaterials, Biosensors, Piezoelectricity},
  pages = {180-198},
  publisher = {Academic Press},
  title = {Materials for Biocompatible Piezoelectric Devices},
  url = {https://www.sciencedirect.com/science/article/pii/B9780128197288001005},
  year = {2023},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/B9780128197288001005},
  bdsk-url-2 = {https://doi.org/10.1016/B978-0-12-819728-8.00100-5}
}

Advances in materials, engineering, and biotechnology have opened up exciting research directions in the areas of biosensors and bioactuators. An exciting and promising direction is to construct biodevices based on biocompatible piezoelectric materials. These biodevices present distinctive, innovative, and safe integrating approaches with biological systems for applications in sensing biological forces, stimulating tissue growth and healing, and diagnosing medical problems, to name a few. In this chapter, we present a general overview of the fundamentals, applications, and the future opportunities as well as challenges of biocompatible piezoelectric materials. Piezoelectric biosensors and actuators are developed with advanced methods in microfabrication and materials-processing to avoid any toxicity from conventional piezoelectric materials. Interestingly, several piezoelectric materials are biodegradable in nature, which eliminates the need for invasive implant extraction. We will also review them in this chapter. Advancements in the field of piezoelectric biomaterials integrated with microsystems hold great promises for biomedical applications.

@inbook{mundrane2022exploring,
  address = {Cham},
  author = {Mundrane, Caitlyn and Chorsi, Meysam and Vinogradova, Olga and Ilies, Horea and Kazerounian, Kazem},
  booktitle = {Advances in Robot Kinematics 2022},
  date-added = {2023-10-11 14:34:42 -0400},
  date-modified = {2023-10-11 22:06:55 -0400},
  doi = {10.1007/978-3-031-08140-8_28},
  editor = {Altuzarra, Oscar and Kecskem{\'e}thy, Andr{\'e}s},
  isbn = {978-3-031-08140-8},
  pages = {257--265},
  publisher = {Springer International Publishing},
  title = {Exploring Electric Field Perturbations as the Actuator for Nanorobots and Nanomachines},
  year = {2022},
  bdsk-url-1 = {https://doi.org/10.1007/978-3-031-08140-8_28}
}

Nanomachines and nanorobots are nanoscale mechanisms that transform an input motion or force into some desirable output. These machines offer significant applications in nanotechnology, biotechnology, and medicine. To perform a specific task, nanomachines must have a controllable kinematic structure. Our team in past has proposed amino acids as the links for these kinematic chains (peptide chains). The kinematic formulation of these chains are now well developed. One noteworthy outcome has been design and development of 7-R closed loop one-degree-of-freedom spatial mechanisms (cyclic peptide). Unlike in macro-scale machines and robots, traditional kinematic pairs such as prismatic and revolute actuators cannot be employed in nano kinematic chains. However, a one-degree-of-freedom nano-scale kinematic chain can be a viable alternative to traditional actuators and can be used as the driving module in more complex nano systems. We have designed, simulated, fabricated, and tested several 7-R closed loop systems. Due to the one-degree-of-freedom nature of 7-R kinematic chains, their geometry as a function of one input parameter is completely predictable and repeatable. However, controlling this input parameter in real applications remains an open question. In this work, we explore perturbation of the electric force field as a control mechanism to manipulate the motions of these kinematic nano robots and machines. Two different external electric field models, uniform and non-uniform, are developed. Protofold II, an in-house developed protein folding software, is used to simulate the range of motion for closed-loop cyclic 7-R peptides with electric field perturbations. The results show that one-degree-of-freedom closed loop systems have the potential to be precisely controlled by external physical stimuli. This discovery presents significant potential in design and implementation of nanorobots and nano machines for applications in biotechnology.

@inbook{chorsi2021one,
  address = {Cham},
  author = {Chorsi, Meysam T. and Tavousi, Pouya and Mundrane, Caitlyn and Gorbatyuk, Vitaliy and Ilies, Horea and Kazerounian, Kazem},
  booktitle = {Advances in Robot Kinematics 2020},
  date-added = {2023-10-11 14:42:02 -0400},
  date-modified = {2023-10-11 22:07:39 -0400},
  doi = {https://doi.org/10.1007/978-3-030-50975-0_6},
  editor = {Lenar{\v{c}}i{\v{c}}, Jadran and Siciliano, Bruno},
  isbn = {978-3-030-50975-0},
  pages = {41--48},
  publisher = {Springer International Publishing},
  title = {One Degree of Freedom {7-R} Closed Loop Linkage as a Building Block of Nanorobots},
  year = {2021},
  bdsk-url-1 = {https://doi.org/10.1007/978-3-030-50975-0_6}
}

A robotic manipulator is a series of links connected with kinematic pairs designed so that its configuration (three dimensional pose – particularly at the end effector) is controllable. The control is achieved through a series of one degree of freedom revolute or prismatic joints. Nanorobots are linkage mechanisms at nanoscale. These robots offer considerable promise in diverse applications in nanotechnology, biotechnology and medicine. Similar to their macro-scale siblings, a nanorobot must have a controllable kinematic structure to perform tasks. However, at nanometer levels creation of controllable single degree of freedom kinematic pairs are unlikely. Therefore controllability of the nanorobot remains a technological challenge. In this paper, we present a peptide-based linkage composed of protein building-block molecules designed as a one degree-of-freedom closed-loop 7R spatial mechanism. Traditional spatial kinematic notation and formulations are used to solve the loop closure equations implicitly. Two different kinematic branches of this molecular linkage are identified. The designed molecule is fabricated and its motion is observed at distinct configurations using nuclear magnetic resonance (NMR) spectroscopy. These results validate our formulation, and indicate that 7R spatial closed loop linkages are a suitable building block for nanorobots and nanomachines.

@inbook{huber2015novel,
  address = {Cham},
  author = {Huber, Martin and Eschbach, Matthew and Ilies, Horea and Kazerounian, Kazem},
  booktitle = {Interdisciplinary Applications of Kinematics},
  date-added = {2023-10-11 14:55:09 -0400},
  date-modified = {2023-10-11 22:03:08 -0400},
  editor = {Kecskem{\'e}thy, Andr{\'e}s and Geu Flores, Francisco},
  isbn = {978-3-319-10723-3},
  pages = {53--61},
  publisher = {Springer International Publishing},
  title = {Novel Quasi-Passive Knee Orthosis with Hybrid Joint Mechanism},
  year = {2015}
}

Loss of personal mobility is a large and growing issue that can be caused by a variety of medical problems. Knee pain, muscle weakness, and their associated conditions are among the most common causes of impaired walking. Currently, conventional solutions include simple braces, canes, and medication. In more extreme cases, surgery is also routine. We propose a design for a novel quasi-passive orthotic knee brace which combines a smart support system employing magnetorheological (MR) fluid with a passive load reduction system. To work in concert with the walking motion of the knee, we have designed a four-bar linkage in conjunction with a compliant mechanism. The resulting orthotic knee brace will alleviate common symptoms related to knee pain and restore lost mobility, most notably in cases of osteoarthritis.

@inbook{cassidy2014topological,
  address = {Cham},
  author = {Cassidy, Hugh P. and Peters, Thomas J. and Ilies, Horea and Jordan, Kirk E.},
  booktitle = {Topological Methods in Data Analysis and Visualization III},
  date-added = {2023-10-11 14:59:32 -0400},
  date-modified = {2023-10-13 12:44:18 -0400},
  editor = {Bremer, Peer-Timo and Hotz, Ingrid and Pascucci, Valerio and Peikert, Ronald},
  isbn = {978-3-319-04099-8},
  pages = {167--183},
  publisher = {Springer International Publishing},
  title = {Topological Integrity for Dynamic Spline Models During Visualization of Big Data},
  year = {2014}
}

In computer graphics and scientific visualization, B-splines are common geometric representations. A typical display method is to render a piecewise linear (PL) approximation that lies within a prescribed tolerance of the curve. In dynamic applications it is necessary to perturb specified points on the displayed curve. The distance between the perturbed PL structure and the perturbed curve it represents can change significantly, possibly changing the underlying topology and introducing unwanted artifacts to the display. We give a strategy to perturb the curve smoothly and keep track of the error introduced by perturbations. This allows us to refine the PL curve when appropriate and avoid spurious topological changes. This work is motivated by applications to visualization of Big Data from simulations on high performance computing architectures.

@inbook{kazerounian2013protein,
  author = {Kazerounian, Kazem and Ilie{\c{s}}, Horea T},
  booktitle = {21st Century Kinematics: The 2012 NSF Workshop},
  date-modified = {2023-10-11 22:02:37 -0400},
  doi = {https://doi.org/10.1007/978-1-4471-4510-3_8},
  organization = {Springer London},
  pages = {217--244},
  title = {Protein molecules: evolution's design for kinematic machines},
  year = {2013},
  bdsk-url-1 = {https://doi.org/10.1007/978-1-4471-4510-3_8}
}

The study of geometry in motion can be traced back to the scientists of the ancient world. Since then, kinematics developed into a mature and sophisticated set of tools that can be used to describe and analyze the motion of geometry. Since folding of proteins is fundamentally nothing but coordinated movement of geometry (atoms) under the influence of internal constraints and external stimuli, kinematics can naturally play a key role in the understanding of how proteins fold, which, in itself, is one of the crucial problems in science today. In this chapter we review some of the central kinematic elements used to model proteins and study their folding and flexibility.

@inbook{madden2011predicting,
  address = {Dordrecht},
  author = {Madden, Christopher and Bohnenkamp, Peter and Kazerounian, Kazem and Ilie{\c{s}}, Horea T.},
  booktitle = {Interdisciplinary Applications of Kinematics},
  date-added = {2023-10-11 15:09:37 -0400},
  date-modified = {2023-10-11 22:00:38 -0400},
  editor = {Kecskem{\'e}thy, Andr{\'e}s and Potkonjak, Veljko and M{\"u}ller, Andreas},
  isbn = {978-94-007-2978-0},
  pages = {135--149},
  publisher = {Springer Netherlands},
  title = {Predicting Protein Conformational Transitions by Trajectory Planning Through Torsion Angle Propensity Maps},
  year = {2011}
}

The function of a protein macromolecule often requires conformational transitions between two native configurations. Understanding these transitions is essential to the understanding of how proteins function, as well as to the ability to design and manipulate proteinbased nano-mechanical systems. It is widely accepted that the pathway connecting two native protein conformations in nature should satisfy a minimum energy criterion. The premise of this paper is that such a pathway can be found by using dihedral angle combinations that have been shown to have a high probability of occurrence in naturally observed proteins. In order to quantify this probability, we are proposing statistical propensity torque maps for tuples of dihedral angles. These maps are constructed in the angle space, similar to the Ramachandran Charts, but are based on data obtained from more than 38,600 proteins from Protein Data Bank (PDB) so that each map contains the experimentally observed pairs of dihedral angles (ϕi, \psii), (ϕi, \psii\thinspace+\thinspace1), (ϕi, ϕi\thinspace+\thinspace1) and (\psii, \psii\thinspace+\thinspace1).

@inbook{shahbazi2010kinematic,
  address = {Dordrecht},
  author = {Shahbazi, Z. and Pimentel, T. A. P. F. and Ilies, H. and Kazerounian, K. and Burkhard, P.},
  booktitle = {Advances in Robot Kinematics: Motion in Man and Machine},
  date-added = {2023-10-11 15:14:37 -0400},
  date-modified = {2023-10-11 22:01:54 -0400},
  editor = {Lenarcic, Jadran and Stanisic, Michael M.},
  isbn = {978-90-481-9262-5},
  pages = {203--210},
  publisher = {Springer Netherlands},
  title = {A Kinematic Observation and Conjecture for Creating Stable Constructs of a Peptide Nanoparticle},
  year = {2010}
}

The integration of traditional mechanism theory with biology and medicine at the molecular level enables the use of polypeptide chains to design, manipulate and fabricate biomimetic artificial nano-machines. In this paper we establish a procedure to analyze the mobility of protein molecules based on predicting the formation of hydrogen bonds, which, in turn, is the primary cause for mobility reduction in proteins. We improved our graph-based approach by including side chain and mixed chain hydrogen bond prediction capabilities as well as an energy analysis of these interactions. This method has been emploied to evaluate the internal mobility and identify the rigid and flexible segments of the protein molecules. This computational procedure has been used to assess the stability and mobility of three specific candidate proteins to build a nanobiodevice. Our simulations show that only one of these structures is capable of producing a stable nanoparticle, which is in agreement with the experimental results.

@inproceedings{behzadi2023idetc,
  author = {Behzadi, M.M and Ilies, H.},
  booktitle = {ASME IDETC \& CIE},
  date-added = {2023-10-13 12:45:55 -0400},
  date-modified = {2023-10-13 12:48:43 -0400},
  title = {On the Connectedness of the Topology Optimization Predictors},
  year = {2023}
}

Deep learning-based topology optimization predictors have been shown to be effective in generating optimal designs. How- ever, these predictors are prone to topological errors, partic- ularly for high-resolution domains. Although various methods have been developed to enhance the accuracy of predicted struc- tures, such as using large training datasets, complex networks, and physics-based loss functions, they do not include topologi- cal metrics in the deep learning models. Similar issues arise in other applications, such as blood vessels, neurons, or road seg- mentation from images, and several modifications to typical loss functions have been proposed to improve the topological validity of the predictions. In this study, we evaluate and compare four distinct topological loss functions to explore their influence on the performance of deep learning-based topology optimization predictors. Our findings offer insights into the advantages and limitations of these modified loss functions and provide a ba- sis for future research and development aimed at improving the accuracy and efficiency of deep learning predictors in topology optimization.

@inproceedings{behandish2015haptic,
  author = {Behandish, Morad and Ilie{\c{s}}, Horea T},
  booktitle = {International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},
  date-modified = {2023-10-11 15:43:41 -0400},
  doi = {https://doi.org/10.1115/DETC2015-47923},
  organization = {American Society of Mechanical Engineers},
  pages = {V01BT02A060},
  title = {Haptic assembly using skeletal densities and {F}ourier transforms},
  volume = {57052},
  year = {2015},
  bdsk-url-1 = {https://doi.org/10.1115/DETC2015-47923}
}

Haptic-assisted virtual assembly and prototyping has seen significant attention over the past two decades. However, in spite of the appealing prospects, its adoption has been slower than expected. We identify the main roadblocks as the inherent geometric complexities faced when assembling objects of arbitrary shape, and the computation time limitation imposed by the notorious 1 kHz haptic refresh rate. We solved the first problem in a recent work by introducing a generic energy model for geometric guidance and constraints between features of arbitrary shape. In the present work, we address the second challenge by leveraging Fourier transforms to compute the constraint forces and torques. Our new concept of ‘geometric energy’ field is computed automatically from a cross-correlation of ‘skeletal densities’ in the frequency domain, and serves as a generalization of the manually specified virtual fixtures or heuristically identified mating constraints proposed in the literature. The formulation of the energy field as a convolution enables efficient computation using GPU-accelerated Fast Fourier Transforms (FFT). We show that our method is effective for low-clearance assembly of objects of arbitrary geometric and syntactic complexity.

@inproceedings{periverzov2015ids,
  author = {Periverzov, Frol and Ilie{\c{s}}, Horea},
  booktitle = {2015 IEEE symposium on 3D user interfaces (3DUI)},
  date-modified = {2023-10-11 15:43:20 -0400},
  doi = {10.1109/3DUI.2015.7131736},
  organization = {IEEE},
  pages = {121--128},
  title = {{IDS}: {T}he intent driven selection method for natural user interfaces},
  year = {2015},
  bdsk-url-1 = {https://doi.org/10.1109/3DUI.2015.7131736}
}

We present a new selection technique that facilitates the use of natural hand gestures for virtual object manipulation in 3D. Our method supports the use of 3D imaging techniques for tracking the user’s body and therefore it does not require the use of any hand held devices that would restrict the manipulative capabilities of the user’s hands. The key contribution of our work is the novel use of characteristic behavioral cues, which are representative for general goal directed movement, to infer the object targeted by the user during selection. The resulting technique enables us to select objects whose largest dimension is smaller than the sensing resolution of our system in spite of body tracking uncertainties and hand placement faults. Furthermore, by means of intention inference, our method automatically adapts to the user’s subjective need for variable levels of tolerance to hand placement faults, jitter, or tracking noise.

@inproceedings{eschbach2014customizable,
  author = {Eschbach, Matthew and Huber, Martin and Ilies, Horea and Kazerounian, Kazem},
  booktitle = {International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},
  date-modified = {2023-10-11 15:00:52 -0400},
  doi = {10.1115/DETC2014-35238},
  organization = {American Society of Mechanical Engineers},
  pages = {V05AT08A019},
  title = {Customizable Joint Mechanism for Knee Orthosis},
  volume = {46360},
  year = {2014},
  bdsk-url-1 = {https://doi.org/10.1115/DETC2014-35238}
}

Knee pain, muscle weakness, and their associated medical conditions cause a significant loss of mobility for a large and growing number of people. Accordingly, the need for effective, simple, and noninvasive methods for controlling these problems is becoming more apparent. To that end, we have designed a quasi-passive knee-orthosis that employs a “hybrid joint mechanism” as a central component. This joint combines a four-bar linkage with a compliant mechanism to follow natural knee motion. A poorly fitted knee orthosis can detrimentally affect its effectiveness due to the large variability in the patient-specific knee motion. Our design can be optimized to fit a given user, based on both motion capture data and their particular condition, which leads to several potential advantages over standardized hinges. In this paper, we will explore the design and individualization process of the joint mechanism as well as the background covering various design decisions.

@inproceedings{behandish2013gpu,
  author = {Behandish, Morad and Tavousi, Pouya and Ilie{\c{s}}, Horea T and Kazerounian, Kazem},
  booktitle = {International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},
  date-modified = {2023-10-11 15:44:10 -0400},
  doi = {10.1115/DETC2013-12675},
  organization = {American Society of Mechanical Engineers},
  pages = {V02AT02A009},
  title = {{GPU}-accelerated computation of solvation free energy for kinetostatic protein folding simulation},
  volume = {55850},
  year = {2013},
  bdsk-url-1 = {https://doi.org/10.1115/DETC2013-12675}
}

A realistic computer simulation of protein folding requires a comprehensive account of interaction energetics, placing a substantial demand on processing power. This paper presents an improved computational framework for protein folding software package PROTOFOLD, that enables efficient computation of solvation free energy effects in addition to Coulombic and van der Waals interactions. Efficient data structures have been utilized to speed-up the sequential running times from O(n2) to O(n), n being the number of atoms. It turns out, however, that an accurate evaluation of molecular surface areas characterizing the solvation effects imposes a computational bottleneck to the entire simulation. Massive computational power offered by Graphics Processing Units (GPU) was exploited to develop a simple and efficient Single-Instruction Multiple-Thread (SIMT) algorithm for the latter step. The running times were monitored for different steps of the folding simulation for different molecular sizes. Significant performance improvements were observed, yielding promising results where numerous iterative runs are needed.

@inproceedings{tavousi2013improved,
  author = {Tavousi, Pouya and Behandish, Morad and Kazerounian, Kazem and Ilie{\c{s}}, Horea T},
  booktitle = {International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},
  date-modified = {2023-10-11 15:03:52 -0400},
  doi = {10.1115/DETC2013-12671},
  organization = {American Society of Mechanical Engineers},
  pages = {V06AT07A006},
  title = {An improved free energy formulation and implementation for kinetostatic protein folding simulation},
  volume = {55935},
  year = {2013},
  bdsk-url-1 = {https://doi.org/10.1115/DETC2013-12671}
}

Protein structure prediction remains one of the significant challenges in computational biology. We have previously shown that our kinetostatic compliance method can overcome some of the key difficulties faced by other de novo structural prediction methods, such as the very small time steps required by the molecular dynamics approaches, or the very large number of samples required by the sampling based techniques. In this paper we extend the previous free energy formulation by adding the solvent effects, which contribute predominantly to the folding phenomena. We show that the addition of the solvation effects, which complement the existing Coulombic and van der Waals interactions, lead to a physically effective energy function. Furthermore, we achieve significant computational speed-up by employing efficient algorithms and data structures that effectively reduce the time complexity from O(n2) to O(n), n being the number of atoms. Our simulations are consistent with the general behavior observed in protein folding, and show that the hydrophobic atoms tend to pack inside the core of the molecule in an aqueous solvent, while a vacuum environment produces no such effect.

@inproceedings{williams2012towards,
  author = {Williams, Reed M and Ilies, Horea T},
  booktitle = {Workshop on Algebraic Topology and Machine Learning at Neural Information Processing Symposium},
  title = {Towards multi-scale heat kernel signatures for point cloud models of engineering artifacts},
  volume = {2012},
  year = {2012}
}

@inproceedings{shahbazi2011kinematic,
  author = {Shahbazi, Zahra and Ilies{\c{}}, Horea T and Kazerounian, Kazem},
  booktitle = {International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},
  date-modified = {2023-10-11 15:10:37 -0400},
  doi = {https://doi.org/10.1115/DETC2011-48519},
  pages = {535--542},
  title = {Kinematic motion constraints of the protein molecule chains},
  volume = {54839},
  year = {2011},
  bdsk-url-1 = {https://doi.org/10.1115/DETC2011-48519}
}

The function of protein molecules is defined by their 3-D geometry, as well as their internal mobility, which is heavily influenced by the internal hydrogen bonds. The correct identification of these hydrogen bonds and the prediction of their effect on the mobility of protein molecules can provide an invaluable mechanism to understand protein behavior. Applications of this study ranges from nano-engineering to new drug design. We are extending our recent approach from identifying main-chain main-chain hydrogen bonds to all types of hydrogen bonds that occur in protein structures, such as α-helices and β-sheets. We use the Gru¨bler-Kutzbach kinematic mobility criterion to determine the degrees of freedom of all closed loops (rigid loops as well as closed loops of one or more degrees of freedom) formed by Hydrogen bonds. Furthermore, we systematically develop constraint equations for non-rigid closed loops. Several examples of protein molecules from PDB are used to show that these additions both improve the accuracy of mobility analysis and enable us to study a broader range of the motion of protein molecules. This approach offers theoretical insight as well as extensive numerical efficiencies in protein simulations.

@inproceedings{eftekharian2011shape,
  author = {Eftekharian, Ata A and Ilies{\c{}}, Horea T},
  booktitle = {International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},
  date-modified = {2023-10-11 15:09:03 -0400},
  doi = {10.1115/DETC2011-48363},
  pages = {687--696},
  title = {Shape and topology optimization with medial zones},
  volume = {54822},
  year = {2011},
  bdsk-url-1 = {https://doi.org/10.1115/DETC2011-48363}
}

Shape optimization (with topological changes) has become a de facto standard approach for synthesizing new designs. Current approaches heavily rely on voxelized modifications of the initial domain, followed by heuristic reconstruction procedures that result in a detailed shape design. The initial domain is almost always conservatively estimated so that the design space spans a sufficiently large set of possible solutions. We propose a novel approach to shape optimization that exploits the geometric and topologic properties of medial zones and a new shape modification paradigm to synthesize shapes with topological guarantees. The medial zone is a ‘thick skeleton’ of the domain induced by prescribed boundary conditions, and represents an initial solution that is topologically valid. We modify such an initial solution by adding or subtracting ‘bubbles’ of material defined via prescribed shape functions. The proposed approach has many advantages in terms of topological guarantees, shape control, and computational cost, supports parametric optimization of free-form geometry, and can be implemented in any geometric representation that supports distance computations.

@inproceedings{erdim2008contact,
  author = {Erdim, Hu{\"{}} seyin and Ilies, Horea T},
  booktitle = {International Design Engineering Technical Conferences and Computers and Information in Engineering Conference},
  pages = {637--645},
  title = {Contact analysis between a moving solid and the boundary of its swept volume},
  volume = {43253},
  year = {2008}
}

@inproceedings{ilies2003synthesis,
  author = {Ilies, Horea and Shapiro, Vadim},
  booktitle = {2003 AAAI Spring Symposium on Computational Synthesis},
  date-modified = {2023-10-11 15:29:54 -0400},
  pages = {24--26},
  title = {On the synthesis of functionally equivalent mechanical designs},
  year = {2003}
}

Conventional mechanical design focuses on a single completely specified nominal shape that is later toleranced to allow for variations in form. The corresponding design processes usually involve arbitrary decisions affecting the geometry and do not support systematic generation of alternative shapes satisfying identical or altered functionalities. This places a serious handicap on the design cycle of a product, since most new designs are obtained by modifying existing products to comply with new functional specifications. Since the functionality of a part does not usually define all of its geometry, a more coherent approach would be to design classes of equivalent mechanical parts that satisfy a given functionality. We show here that, by replacing the completely specified geometry of the traditional approaches with partial geometry and functional specification, we can generate classes of mechanical parts that are equivalent, in the sense that all members of the class satisfy the same functional specifications. Ability to define, compute, and represent classes of functionally equivalent parts will allow one to generate, compare and modify functionally equivalent designs, perhaps having dissimilar geometries. We identify three such equivalence classes for artifacts with parts moving in contact, which presume, at the very least, contact between parts, spatial containment during their relative motion, and external loads applied on the moving parts. We show that these classes of functionally equivalent parts are computable and may be represented unambiguously by maximal elements of each class.

@inproceedings{ilies1997approach,
  address = {Boston, MA},
  author = {Ilies, Horea T. and Shapiro, Vadim},
  booktitle = {Product Modeling for Computer Integrated Design and Manufacture: TC5/WG5.2 International Workshop on Geometric Modeling in Computer Aided Design 19--23 May 1996, Airlie, Virginia, USA},
  date-added = {2023-10-11 15:32:57 -0400},
  date-modified = {2023-10-13 12:44:40 -0400},
  doi = {10.1007/978-0-387-35187-2_2},
  editor = {Pratt, M. J. and Sriram, R. D. and Wozny, M. J.},
  isbn = {978-0-387-35187-2},
  pages = {17--31},
  publisher = {Springer US},
  title = {An Approach to Systematic Part Design},
  url = {https://doi.org/10.1007/978-0-387-35187-2_2},
  year = {1997},
  bdsk-url-1 = {https://doi.org/10.1007/978-0-387-35187-2_2}
}

The rise of solid modeling as a principal medium for mechanical product description can be traced to the requirement of informational completeness of geometric representations. Unfortunately, traditional geometry-based systems do not contain important information needed for many engineering activities and tend to force costly iterations in a product development cycle. We seek to understand spatial properties and combinatorial structure of mechanical parts in terms of simple interacting constructs related to part functionality and manufacturing processes. Existence of such a structure is illustrated for a simple part that is characterized in terms of its kinematics, strength, spatial containment, and manufacturing characteristics. The resulting explicit representation of correspondence between mechanical characteristics and spatial elements allows systematic product development, efficient modification procedures, and rational tolerancing approaches — eliminating many costly errors and iterations in a product development cycle. The study also highlights the lack of and the need for formal models supporting systematic design process.

@inproceedings{ilies1997unsweep,
  author = {Ilies, Horea T and Shapiro, Vadim},
  booktitle = {Proceedings of the fourth ACM symposium on Solid modeling and applications},
  date-modified = {2023-10-11 15:39:37 -0400},
  doi = {https://doi.org/10.1145/267734.267775},
  pages = {155--167},
  title = {{UNSWEEP}: Formulation and computational properties},
  year = {1997},
  bdsk-url-1 = {https://doi.org/10.1145/267734.267775}
}

We introduce and formally define a new geometric modeling operation unsweep(E, M) which, given an arbitrary n-dimensional subset of Euclidean space E and a general motion M, returns the subset of E that remains inside E under M. This new operation is dual to the usual sweeping operation and has important applications in mechanical design. When M is a translation, unsweep(E, M) naturally reduces to the usual Minkowski difference of E and the trajectory generated by the inverted motion k. We show that unsweep has attractive computational properties and give a practical point membership test for arbitrary general motions. By duality, the established properties of unsweep can be used to develop a practical point membership test for general sweeps.

@misc{ilies2019apparatus,
  author = {Ilies, Horea and Corcodel, Radu Ioan},
  date-modified = {2023-10-11 15:50:58 -0400},
  month = aug,
  note = {US Patent App. 16/280,445},
  title = {Apparatus and computational modeling for non-planar {3D} printing},
  year = {2019}
}

@misc{kazerounian2015knee,
  author = {Kazerounian, Kazem and Huber, Martin and Ilies, Horea and Eschbach, Matthew},
  note = {US Patent App. 14/319,149},
  title = {Knee Orthosis Device and Associated Methods},
  year = {2015}
}

@misc{ilies2014geometric,
  author = {Ilies, Horea T},
  date-modified = {2023-10-11 22:02:56 -0400},
  month = sep,
  note = {US Patent 8,849,617},
  title = {Geometric singularity detection},
  year = {2014}
}

@misc{ilies2012method,
  author = {Ilies, Horea and Eftekharian, Ata A},
  month = mar,
  note = {US Patent App. 13/172,824},
  title = {Method and system for constructing geometric skeletons and medial zones of rigid and non-rigid shapes},
  year = {2012}
}

@misc{rankin2006handheld,
  author = {Rankin, II James and Stewart, Paul and Buttolo, Pietro and Marsan, Anne and Ilies, Horea},
  date-added = {2023-10-27 12:46:59 -0400},
  date-modified = {2023-10-27 12:46:59 -0400},
  month = nov,
  note = {US Patent 7,141,963},
  publisher = {Google Patents},
  title = {Handheld switch measurement system},
  year = {2006}
}

@misc{shapiro2000methods,
  author = {Shapiro, Vadim and Ilies, Horea T},
  month = mar,
  note = {US Patent 6,044,306},
  title = {Methods and apparatus for shaping moving geometric shapes},
  year = {2000}
}

@phdthesis{ilies2000phd,
  author = {Ilies, Horea T},
  date-added = {2023-10-27 12:43:24 -0400},
  date-modified = {2023-10-27 12:44:18 -0400},
  school = {University of Wisconsin, Madison},
  title = {On Shaping Moving Mechanical Parts, University of Wisconsin, Madison, June 2000},
  year = {2000}
}

Broadly, mechanical design is the transformation, or mapping, from a functional description of a device to a form, or structural description. In general there are many shapes satisfying the same functional description, which implies that any systematic approach to mechanical design would require the construction and exploration of the space of design solutions corresponding to a given functional description. Thus, both generating and searching this space for solutions to a given problem must rely on an appropriate characterization of the design space.

In this work we propose a characterization of the design space of solutions for the class of problems of moving parts subjected to spatial containment and contact constraints. Cams, latches, and other mechanisms involving higher kinematic pairs are examples of parts whose shapes are subjected to such spatial constraints. Our design space characterization relies on the concept of the largest part satisfying given spatial constraints, and is used as a basis for the formulation of a new set-theoretic approach to designing moving parts based on a ‘material shrinking’ paradigm. Within this formulation, the design proceeds by eliminating only the material whose presence would violate given spatial constraints, and results in the largest part satisfying containment and contact constraints. To determine and reason about the shape of this largest part, we have developed a set of specific tools that are aimed at constructing and exploring the space of design solutions for the class of problems of interest.

The approach proposed in this thesis results in a family of parts satisfying the same spatial constraints. The presented approach does not impose arbitrary restrictions on the geometry of the shape, but it identifies the largest shape satisfying the specified constraints. Consequently, any other shape satisfying the same constraints must be a subset of this largest shape. We illustrate the viability of our approach by applying our experimental implementation of the concepts and tools developed in this thesis to the shape design of parts belonging to four different application domains.