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Torus & Surface Genus (2D) — Topology of Orientable Surfaces

Canvas2D topology lab: hand-rotated, hand-projected meshes for sphere, torus and double torus, with wireframe, painter's-algorithm shading and fundamental-polygon views, plus live genus and Euler characteristic readouts.

Mathematics2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

This 2D companion draws the exact same sphere/torus/double-torus meshes as the 3D version, but through a hand-written Canvas2D pipeline: manual rotation matrices, a simple perspective projection (scale = fov / (fov + z)), and painter's-algorithm depth sorting for the shaded view, instead of WebGL. The fundamental-polygon view and live genus/χ/π₁ readouts work identically to the 3D original.

⚙ Under the hood

Canvas2D topology lab with hand-rolled 3D rotation and perspective projection, wireframe/shaded/fundamental-polygon views, and live genus, Euler characteristic and fundamental-group readouts for sphere, torus and double torus.

torusgenustopologyeuler characteristicfundamental group

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install