DISCRETE DIFFERENTIAL GEOMETRY

Angle defect K(v) = 2π−Σθ, cotangent Laplacian, mesh smoothing
Discrete Gaussian curvature at vertex v:
K(v) = 2π − Σ θᵢ (angle defect)

Gauss-Bonnet:
Σᵥ K(v) = 2π χ(M)

Cotangent Laplacian:
Δf(v) = Σ(cot αᵢ + cot βᵢ)(fⱼ−fᵢ)

Total K:
Euler χ:
Vertices: