相关论文: Square-Domain Area-Preserving Parameterization for…

We propose a patchwise local Fourier extension method for approximating smooth functions on general two dimensional domains with curved boundaries. The domain is embedded into a Cartesian background grid and decomposed into rectangular…

We present an automated technique for computing a map between two genus-zero shapes, which matches semantically corresponding regions to one another. Lack of annotated data prohibits direct inference of 3D semantic priors; instead, current…

Existing approaches for classifying dynamic graphs either lift graph kernels to the temporal domain, or use graph neural networks (GNNs). However, current baselines have scalability issues, cannot handle a changing node set, or do not take…

Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…

We present an algorithm that covers any given rational ruled surface with two rational parametrizations. In addition, we present an algorithm that transforms any rational surface parametrization into a new rational surface parametrization…

We present a unified approach for characterizing the boundary of a possibly nonconvex domain. Motivated by the well-known Pascoletti--Serafini method of scalarization, we recast the boundary characterization as a multi-criteria optimization…

We introduce a fully-corrective generalized conditional gradient method for convex minimization problems involving total variation regularization on multidimensional domains. It relies on alternatively updating an active set of subsets of…

We develop and analyze a nonlinear reduced basis (RB) method for parametrized elliptic partial differential equations based on a binary-tree partition of the parameter domain into tensor-product structured subdomains. Each subdomain is…

We present new methods for uniformly sampling the solid angle subtended by a disk. To achieve this, we devise two novel area-preserving mappings from the unit square $[0,1]^2$ to a spherical ellipse (i.e. the projection of the disk onto the…

Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…

Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…

We develop and assess an optimization-based approach to parametric geometry reduction. Given a family of parametric domains, we aim to determine a parametric diffeomorphism $\Phi$ that maps a fixed reference domain $\Omega$ into each…

In this work, we propose a detailed computational framework for modelling the envelope of the swept volume, that is the boundary of the volume obtained by sweeping an input solid along a trajectory of rigid motions. Our framework is adapted…

The notions of discrete conformality on triangle meshes have rich mathematical theories and wide applications. The related notions of discrete uniformizations on triangle meshes, suggest efficient methods for computing the uniformizations…

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,…

We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…

A pair of pants is a genus zero orientable surface with three boundary components. A pants decomposition of a surface is a finite collection of unordered pairwise disjoint simple closed curves embedded in the surface that decompose the…

This paper further develops the Method of Matched Sections (MMS), a robust numerical framework for the solution of boundary value problems governed by partial differential equations. It demonstrates its unique applicability to the…

Signed distance fields (SDFs) are a widely used implicit surface representation, with broad applications in computer graphics, computer vision, and applied mathematics. To reconstruct an explicit triangle mesh surface corresponding to an…

Surface parameterization is a fundamental geometry processing problem with rich downstream applications. Traditional approaches are designed to operate on well-behaved mesh models with high-quality triangulations that are laboriously…