January 29, 2026
Orange slices, hot takes
Cutting Up Curved Things (With Math)
Pretty math vs sharp triangles: fans swoon, “ackchually” crew pounces
TLDR: The post shows how curved shapes get turned into triangles so GPUs can draw them. Comments split between praise for the clear explainer and pushback that ray tracing and distance fields can skip triangles, with warnings about tricky cases like cones—why it matters: choosing the right method affects speed and quality.
The post claims your graphics card only speaks triangles, so smooth curves get chopped into tiny slices called tessellation. Cue the crowd: Team Swoon arrived first, with aanet gushing “beautiful website” vibes and hearts. Then Team Ackchually crashed the party. joefourier argued modern GPUs don’t need triangle soup at all—they can draw cylinders straight from math using ray tracing (tracing light paths) or SDFs (signed distance fields), linking to these formulas like it’s a mic drop. Meanwhile, OgsyedIE waved a caution flag: naive triangulation breaks when “spiky” shapes meet curves—think cones—and you need real, grown‑up algorithms to avoid a visual trainwreck.
Fans loved the orange‑slice analogy for spheres, the clever “bridge the hole” trick, and the clean, friendly code snippets. But the drama brewed over whether triangles are the one true shape of the render kingdom or just the old default. Team Triangles says meshes are fast, simple, and everywhere—from games to Pixar—while Team Math flexes with “no tessellation needed” wizardry. Memes flew: “Triangles all the way down,” “feed your GPU fruit salad,” and a chorus of affectionate “<3”s for the site’s vibe. Verdict: gorgeous explainer, spicy debate, and a reminder that the future might be more math-y than mesh-y.
Key Points
- •GPUs render triangles, so curved surfaces must be tessellated into triangle meshes using vertices and indices.
- •Parametric surfaces (e.g., a cylinder defined by u and v) are sampled over a UV grid to create mesh vertices and triangles.
- •Planar convex polygons can be triangulated via fan triangulation, producing n−2 triangles for an n-gon.
- •Cylindrical surfaces are sampled by determining v_min and v_max from boundary projections onto the axis and sweeping u around 0–2π.
- •Spherical surfaces use lat/long sampling, replacing quads near poles with triangle fans; holes are handled by bridging loops and using ear clipping.