The article blends a personal dilemma about relocating for a partner with a detailed guide on computing a point’s mirror across a line using geometry formulas and Java code, offering step‑by‑step calculations, common pitfalls, and a complete implementation.
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.
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.
This article explains the concepts of polygons, including simple, convex, and concave types, describes vertex visibility, ear clipping, and various algorithms for polygon triangulation and convex decomposition, discussing their complexities and practical considerations.
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.
This article presents an interview case about finding the minimum enclosing circle of a planar point set, explains the geometric concepts, outlines a randomized incremental algorithm with correctness proof and complexity analysis, and provides a complete C implementation.
