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Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
This paper proposed a method to judge whether the point is inside or outside of the simple convex polygon by the intersection of the vertical line. It determined the point to an area enclosed by two straight lines, then convert the problem…
High-quality quadrilateral mesh generation is a fundamental challenge in computer graphics. Traditional optimization-based methods are often constrained by the topological quality of input meshes and suffer from severe efficiency…
We construct a converging geometric iterated function system on the moduli space of ordered triangles, for which the involved functions have geometric meanings and contain a non-contraction map under the natural metric.
The handling of topology changes in two-phase flows, such as breakup or coalescence of interfaces, with front tracking is a well-known problem that requires an additional effort to perform explicit manipulations of the Lagrangian front. In…
We discuss ways in which tools from topology can be used to derive lower bounds for the circuit complexity of Boolean functions.
The goal of this paper is to exhibit and analyze an algorithm that takes a given closed orientable hyperbolic surface and outputs an explicit Dirichlet domain. The input is a fundamental polygon with side pairings. While grounded in…
This paper focuses on the challenging task of learning 3D object surface reconstructions from single RGB images. Existing methods achieve varying degrees of success by using different geometric representations. However, they all have their…
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…
A new algorithm for computing a point on a polynomial or rational curve in B\'{e}zier form is proposed. The method has a geometric interpretation and uses only convex combinations of control points. The new algorithm's computational…
A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical…
We present a new and general framework for convolutional neural network operations on spherical (or omnidirectional) images. Our approach represents the surface as a graph of connected points that doesn't rely on a particular sampling…
We present the winning implementation of the Seventh Computational Geometry Challenge (CG:SHOP 2025). The task in this challenge was to find non-obtuse triangulations for given planar regions, respecting a given set of constraints…
Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly…
This paper presents a real-time solution for collision detection between objects based on the physics properties. Traditional approaches on collision detection often rely on the geometric relationships that computing the intersections…
We examine implicit representations of parametric or point cloud models, based on interpolation matrices, which are not sensitive to base points. We show how interpolation matrices can be used for ray shooting of a parametric ray with a…
In this article, we devise a concise algorithm for computing BOCP. Our method is simple, easy-to-implement but without loss of efficiency. Given two circular-arc polygons with $m$ and $n$ edges respectively, our method runs in…
We present a numerical method for computing the single layer (Stokeslet) and double layer (stresslet) integrals in Stokes flow. The method applies to smooth, closed surfaces in three dimensions, and achieves high accuracy both on and near…
Given a system of triangles in the plane $\mathbb{R}^2$ along with given data of function and gradient values at the vertices, we describe the general pattern of local linear methods invoving only four smooth standard shape functions which…
We present subquadratic algorithms in the algebraic decision-tree model for several \textsc{3Sum}-hard geometric problems, all of which can be reduced to the following question: Given two sets $A$, $B$, each consisting of $n$ pairwise…