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

🍩 Torus & Genus (2D)

Same topology as the 3D version, rendered with a hand-written Canvas2D pipeline: manual rotation matrices, perspective projection and painter's-algorithm depth sorting instead of WebGL.

🔭 Surface

🎛 View Mode

⚙️ Parameters

Major radius R 2.0 Minor radius r 0.70 Rotation speed 1.0× Mesh resolution 24

📐 Topological Invariants

Genus g

Euler χ

Orientable

Yes

π₁ (fund. group)

ℤ × ℤ

ℹ️ Theory

Euler characteristic χ = V − E + F is a topological invariant. For a closed orientable surface of genus g: χ = 2 − 2g.

Drag the canvas to rotate manually; release to resume auto-spin.