ICLR 2021 Challenge for Computational Geometry & Topology: Design and Results

ICLR 2022 Challenge for Computational Geometry and Topology: Design and Results

This paper presents the computational challenge on differential geometry and topology that was hosted within the ICLR 2022 workshop ``Geometric and Topological Representation Learning". The competition asked participants to provide implementations of machine learning algorithms on manifolds that would respect the API of the open-source software Geomstats (manifold part) and Scikit-Learn (machine learning part) or PyTorch. The challenge attracted seven teams in its two month duration. This paper describes the design of the challenge and summarizes its main findings.

A robust direct modeling method for quadric B-rep models based on geometry-topology inconsistency tracking

Boundary representation (B-rep) model editing plays an essential role in computer-aided design and motivates the very recent direct modeling paradigm, which features intuitive push-pull manipulation of the model geometry. In mechanical design, a substantial part of B-rep models being used are quadric models (composed of linear and quadric surfaces). However, push-pulling such models is not trivial due to the possible smooth face-face connections in the models. The major issue is that, during push-pull moves, it is often desirable to preserve these connections for functional, manufacturing, or …

Introduction to Periodic Geometry and Topology

This monograph introduces key concepts and problems in the new research area of Periodic Geometry and Topology for materials applications.Periodic structures such as solid crystalline materials or textiles were previously classified in discrete and coarse ways that depend on manual choices or are unstable under perturbations. Since crystal structures are determined in a rigid form, their finest natural equivalence is defined by rigid motion or isometry, which preserves inter-point distances. Due to atomic vibrations, isometry classes of periodic point sets form a continuous space whose geometr…

TG-Diff：耦合离散拓扑扩散与拓扑条件几何扩散用于边界表示生成

TG-Diff: Coupling Discrete Topology Diffusion and Topology-conditioned Geometry Diffusions for B-Rep Generation

研究提出TG-Diff框架，通过解耦拓扑与几何建模生成B-rep。基于以曲面为中心的表示开发两个扩散模型，拓扑扩散用离散扩散模型，曲面隐变量生成用条件隐变量扩散模型，经后处理形成封闭B-rep，计算量小且性能优越。

Algorithmic Semi-algebraic Geometry and Topology -- Recent Progress and Open Problems

We give a survey of algorithms for computing topological invariants of semi-algebraic sets with special emphasis on the more recent developments in designing algorithms for computing the Betti numbers of semi-algebraic sets. Aside from describing these results, we discuss briefly the background as well as the importance of these problems, and also describe the main tools from algorithmic semi-algebraic geometry, as well as algebraic topology, which make these advances possible. We end with a list of open problems.

Collection of abstracts of the Workshop on Triangulations in Geometry and Topology at CG Week 2014 in Kyoto

This workshop about triangulations of manifolds in computational geometry and topology was held at the 2014 CG-Week in Kyoto, Japan. It focussed on computational and combinatorial questions regarding triangulations, with the goal of bringing together researchers working on various aspects of triangulations and of fostering a closer collaboration within the computational geometry and topology community. Triangulations are highly suitable for computations due to their clear combinatorial structure. As a consequence, they have been successfully employed in discrete algorithms to solve purely theo…