Gaussian Curvature
Surface:
Torus
Monkey saddle
Bumpy sphere
Horn torus
Hyperbolic paraboloid
Rotation speed:
0.4
Mesh density:
40
K<0
K>0
Gaussian curvature K = κ₁·κ₂ (product of principal curvatures). Blue = negative (saddle/hyperbolic), red = positive (elliptic/dome), black = zero (flat/parabolic). Gauss's Theorema Egregium: K is intrinsic — preserved by isometry.