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computational geometry

7 articles · Page 1 of 1
Machine Learning Algorithms & Natural Language Processing
Machine Learning Algorithms & Natural Language Processing
Jun 30, 2026 · Artificial Intelligence

ChatGPT Overturns a 7‑Year Computational Geometry Challenge by Yao‑Class Legend Chen Lijie

A new arXiv paper shows that the farthest‑pair problem in arbitrary super‑constant dimensions requires near‑quadratic time, with the breakthrough proof generated by GPT‑5.5 Pro and built on Chen Lijie's seven‑year work and his recent contribution to disproving the Erdős unit‑distance conjecture.

AI-assisted proofErdős unit distance conjectureGPT-5.5
0 likes · 12 min read
ChatGPT Overturns a 7‑Year Computational Geometry Challenge by Yao‑Class Legend Chen Lijie
Bilibili Tech
Bilibili Tech
Mar 17, 2023 · Game Development

Triangulation of Vector Graphics: Polygon Decomposition and Monotone Polygon Algorithms

This article explains how to convert vector‑graphics paths into GPU‑ready triangles by approximating Bézier curves with poly‑lines, simplifying self‑intersecting polygons using the Bentley‑Ottmann sweep‑line algorithm, decomposing simple polygons into monotone pieces, and finally triangulating those monotone polygons.

Bézier curvesGPU renderingbentley-ottmann
0 likes · 21 min read
Triangulation of Vector Graphics: Polygon Decomposition and Monotone Polygon Algorithms
Model Perspective
Model Perspective
Mar 10, 2023 · Fundamentals

Unlocking the Shoelace Theorem: Fast Polygon Area Calculation Explained

This article explores the “push‑step aggregation” technique featured in the drama “Microscope under the Ming,” revealing that it is essentially the Shoelace Theorem for quickly computing polygon areas, complete with mathematical derivation, visual illustrations, and a Python implementation.

PythonShoelace theoremalgorithm
0 likes · 8 min read
Unlocking the Shoelace Theorem: Fast Polygon Area Calculation Explained
360 Tech Engineering
360 Tech Engineering
Jun 16, 2020 · Fundamentals

Delaunay Triangulation: Definition, Properties, and Divide‑and‑Conquer Algorithm Implementation in TypeScript

This article explains the Delaunay triangulation concept, its geometric properties such as empty circumcircles and maximal minimum angles, and presents a detailed divide‑and‑conquer algorithm with step‑by‑step merging logic and a complete TypeScript code implementation.

Delaunay triangulationTypeScriptalgorithm
0 likes · 10 min read
Delaunay Triangulation: Definition, Properties, and Divide‑and‑Conquer Algorithm Implementation in TypeScript