Related papers: Simplification of Multi-Scale Geometry using Adapt…
Reducing the triangle count in complex 3D models is a basic geometry preprocessing step in graphics pipelines such as efficient rendering and interactive editing. However, most existing mesh simplification methods exhibit a few issues.…
Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…
We consider the task of generating realistic 3D shapes, which is useful for a variety of applications such as automatic scene generation and physical simulation. Compared to other 3D representations like voxels and point clouds, meshes are…
We introduce an algorithm to remesh triangle meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips that are aligned to principal curvature…
Triangles are everywhere in the virtual world. The surface of nearly every graphical object is saved as a triangular mesh on a computer. Light effects and movements of virtual objects are computed on the basis of triangulations. Besides…
Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have…
This paper tackles the challenging problem of constrained hexahedral meshing. An algorithm is introduced to build combinatorial hexahedral meshes whose boundary facets exactly match a given quadrangulation of the topological sphere. This…
This work proposes a new formulation to the long-standing problem of convex decomposition through learning feature fields, enabling the first feed-forward model for open-world convex decomposition. Our method produces high-quality…
Algorithms for minimal enclosing ball problems are often geometric in nature. To highlight the metric ingredients underlying their efficiency, we focus here on a particularly simple geodesic-based method. A recent subgradient-based study…
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…
The recent developments in neural fields have brought phenomenal capabilities to the field of shape generation, but they lack crucial properties, such as incremental control - a fundamental requirement for artistic work. Triangular meshes,…
Neural Radiance Fields (NeRF) have constituted a remarkable breakthrough in image-based 3D reconstruction. However, their implicit volumetric representations differ significantly from the widely-adopted polygonal meshes and lack support…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra,…
Adaptive methods do not have a direct generalization to manifolds as the adaptive term is not invariant. Momentum methods on manifolds suffer from efficiency problems stemming from the curvature of the manifold. We introduce a framework to…
Streamline-based quad meshing algorithms use smooth cross fields to partition surfaces into quadrilateral regions by tracing cross field separatrices. In practice, re-entrant corners and misalignment of singularities lead to small regions…
The analysis of curves has been routinely dealt with using tools from functional data analysis. However its extension to multi-dimensional curves poses a new challenge due to its inherent geometric features that are difficult to capture…
In this paper, we present a surface remeshing method with high approximation quality based on Principal Component Analysis. Given a triangular mesh and a user assigned polygon/vertex budget, traditional methods usually require the extra…
Mesh simplification is the process of reducing the number of vertices, edges and triangles in a three-dimensional (3D) mesh while preserving the overall shape and salient features of the mesh. A popular strategy for this is edge collapse,…
We propose a deep learning strategy to estimate the mean curvature of two-dimensional implicit interfaces in the level-set method. Our approach is based on fitting feed-forward neural networks to synthetic data sets constructed from…