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Yohei Nakajima 介绍并发布了一种名为 "Hardening"（软到硬的形状延续）的新型打包搜索方法，在 188 个实例上与退火、增长等基线对比，发现它虽非默认更优，但能到达其他方法错过的最优打包（如正方形 n=17、n=26）。研究由 Claude (Anthropic) 协助开发实验、代码与验证。
A CMU graphics professor used Astra to craft a highly detailed 3D dragon from just 27 KB of code after roughly 25 hours of AI calls, while graphics researchers showed the same underlying mathematical 3D modeling technique can deliver up to 629× faster rendering and 1,000× faster geometry evaluation.
Yohei Nakajima shares 'Soft-to-Rigid' (Hardening), a shape-continuation search method for congruent shape packing that deforms inscribed disks into target shapes, finding packings other methods miss on squares, though it is not a better overall default. The study is fully reproducible with an open paper, repository, and replayable experiments.
A website collecting the best-known point configurations for the Heilbronn problem—maximizing the smallest triangle area among n points in unit-area regions (square, triangle, and optimal convex regions)—with exact coordinates, proofs, and an in-browser rational arithmetic verifier.
This paper presents a reinforcement learning agent trained to generate provably optimal quadrilateral block decompositions for planar domains, demonstrating superior performance over existing tools like Gmsh in terms of usability and optimality.
The article explains a method for creating fractal boundaries in Voronoi partitions using a jittered grid approach, efficient for applications like coastline simulation.
This article presents a fast algorithm for computing the volume of a simple, closed, triangulated 3D mesh using the divergence theorem.
A blog post describes computing the Pole of Inaccessibility in the San Gabriel Mountains using a Voronoi diagram approach with OpenStreetMap road and trail data, and shares the resulting code in a GitHub repository.
Delaunay32 is a fast, parallel C++17 library for exact 2D Delaunay triangulation with integer predicates, supporting int32 coordinates and direct float input, and is significantly faster than existing triangulators.
Discusses a 2014 paper that refutes the 3SUM conjecture by presenting subquadratic algorithms for the 3SUM problem, with implications for computational geometry and graph algorithms.
A detailed thinking trace from the AI model Claude Fable as it designs a comprehensive computational geometry and physics simulation framework in Rust, incorporating advanced mathematical concepts like conformal geometric algebra and sheaf cohomology.
This paper from the 2008 Canadian Conference on Computational Geometry introduces the theory of balloon polyhedra, examining how balloon twisting can be modeled computationally to create geometric shapes.
Developer releases `exact-poly`, a 2D geometry library using exact integer arithmetic instead of floats to eliminate cross-platform reproducibility issues caused by IEEE 754 implementation differences.