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Topology optimization(TO) is widely used in engineering because of its ability to save material and optimize structural performance. Although prior work has explored 2D human-centered design tool for TO, the results are often limited in…
We present a novel construction of recursion operators for scalar second-order integrable multidimensional PDEs with isospectral Lax pairs written in terms of first-order scalar differential operators. Our approach is quite straightforward…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
The problem of polycube construction or deformation is an essential problem in computer graphics. In this paper, we present a robust, simple, efficient and automatic algorithm to deform the meshes of arbitrary shapes into their polycube…
Deep implicit surfaces excel at modeling generic shapes but do not always capture the regularities present in manufactured objects, which is something simple geometric primitives are particularly good at. In this paper, we propose a…
We reconstruct 3D deformable object through time, in the context of a live pottery making process where the crafter molds the object. Because the object suffers from heavy hand interaction, and is being deformed, classical techniques cannot…
The high-resolution visualization of atomic structures is significant for understanding the relationship between the microscopic configurations and macroscopic properties of materials. However, a rapid, accurate, and robust approach to…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
The synthesis of a metasurface exhibiting a specific set of desired scattering properties is a time-consuming and resource-demanding process, which conventionally relies on many cycles of full-wave simulations. It requires an experienced…
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface…
Key points, correspondences, projection matrices, point clouds and dense clouds are the skeletons in image-based 3D reconstruction, of which point clouds have the important role in generating a realistic and natural model for a 3D…
Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the…
We investigate the problem of learning to generate 3D parametric surface representations for novel object instances, as seen from one or more views. Previous work on learning shape reconstruction from multiple views uses discrete…
The emergence of 3D artificial intelligence-generated content (3D-AIGC) has enabled rapid synthesis of intricate geometries. However, a fundamental disconnect persists between AI-generated content and human-centric design paradigms, rooted…
Creating high-fidelity 3D meshes with arbitrary topology, including open surfaces and complex interiors, remains a significant challenge. Existing implicit field methods often require costly and detail-degrading watertight conversion, while…
In this article we describe an algorithm that can be applied for the generation of various classes of maps on orientable surfaces. It uses existing generators for abstract graphs and combines them with an efficient embedding and isomorphism…
This paper describes a method for fast simplification of surface meshes. Whereas past methods focus on visual appearance, our goal is to solve equations on the surface. Hence, rather than approximate the extrinsic geometry, we construct a…
The creation of a volumetric mesh representing the interior of an input polygonal mesh is a common requirement in graphics and computational mechanics applications. Most mesh creation techniques assume that the input surface is not…
Geometric Deep Learning has recently made striking progress with the advent of continuous Deep Implicit Fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid,…
Deformable surface tracking from monocular images is well-known to be under-constrained. Occlusions often make the task even more challenging, and can result in failure if the surface is not sufficiently textured. In this work, we…