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Repetitive patterns are ubiquitous in natural and human-made objects, and can be created with a variety of tools and methods. Manual authoring provides unmatched degree of freedom and control, but can require significant artistic expertise…
This paper describes a novel framework for computing geodesic paths in shape spaces of spherical surfaces under an elastic Riemannian metric. The novelty lies in defining this Riemannian metric directly on the quotient (shape) space, rather…
As 3D models become critical in today's manufacturing and product design, conventional 3D modeling approaches based on Computer-Aided Design (CAD) are labor-intensive, time-consuming, and have high demands on the creators. This work aims to…
In this article, we propose a shape optimization algorithm which is able to handle large deformations while maintaining a high level of mesh quality. Based on the method of mappings we introduce a nonlinear extension operator, which links a…
Computing the Euler genus of a graph is a fundamental problem in graph theory and topology. It has been shown to be NP-hard by [Thomassen '89] and a linear-time fixed-parameter algorithm has been obtained by [Mohar '99]. Despite extensive…
Molecule generation is a very important practical problem, with uses in drug discovery and material design, and AI methods promise to provide useful solutions. However, existing methods for molecule generation focus either on 2D graph…
Modular manipulators composed of pre-manufactured and interchangeable modules offer high adaptability across diverse tasks. However, their deployment requires generating feasible motions while jointly optimizing morphology and mounted pose…
3D shape generation aims to produce innovative 3D content adhering to specific conditions and constraints. Existing methods often decompose 3D shapes into a sequence of localized components, treating each element in isolation without…
Boundary incompleteness raises great challenges to automatic prostate segmentation in ultrasound images. Shape prior can provide strong guidance in estimating the missing boundary, but traditional shape models often suffer from hand-crafted…
This paper introduces a novel, robust, and computationally efficient framework for high-quality quadrilateral mesh generation on general two-dimensional domains. The core of the proposed approach is a novel method for computing cross fields…
We propose a computational framework, Hetero-EUCLID, for segmentation and parameter identification to characterize the full hyperelastic behavior of all constituents of a heterogeneous material. In this work, we leverage the Bayesian-EUCLID…
Recent work of Jonathan Campbell and Inna Zakharevich has focused on building machinery for studying scissors congruence problems via algebraic $K$-theory, and applying these tools to studying the Grothendieck ring of varieties. In this…
High-level synthesis, source-to-source compilers, and various Design Space Exploration techniques for pragma insertion have significantly improved the Quality of Results of generated designs. These tools offer benefits such as reduced…
We formulate mold filling in metal casting as a 2D neural operator learning problem that maps geometry and boundary data on an unstructured mesh to time resolved flow quantities, replacing expensive transient CFD. In the proposed method, a…
Deep generative models of 3D shapes have received a great deal of research interest. Yet, almost all of them generate discrete shape representations, such as voxels, point clouds, and polygon meshes. We present the first 3D generative model…
Generative AI has emerged as a transformative paradigm in engineering design, enabling automated synthesis and reconstruction of complex 3D geometries while preserving feasibility and performance relevance. This paper introduces a…
Selective Laser Melting (SLM) is a powder-bed additive manufacturing technique whose part quality depends critically on feedstock morphology. However, conventional powder characterization methods are low-throughput and qualitative, failing…
The latest sheet stamping processes enable efficient manufacturing of complex shape structural components that have high stiffness to weight ratios, but these processes can introduce defects. To assist component design for stamping…
We present an algorithm for producing Delaunay triangulations of manifolds. The algorithm can accommodate abstract manifolds that are not presented as submanifolds of Euclidean space. Given a set of sample points and an atlas on a compact…
In computer-aided design (CAD), the ability to "reverse engineer" the modeling steps used to create 3D shapes is a long-sought-after goal. This process can be decomposed into two sub-problems: converting an input mesh or point cloud into a…