Design Nomenclature / Form & Geometry
Mean curvature
Also called h, average curvature
This entry has not been translated yet and is shown in English.
The average of the two principal curvatures, H = (κ₁ + κ₂) / 2. Unlike Gaussian curvature it depends on how the surface sits in space rather than on its intrinsic metric alone: a plane and a cylinder share K = 0 but not H. Surfaces with H = 0 everywhere are minimal — soap films, catenoids, tensile roofs.
In practice
The curvature you read as 'how much is this bulging', and the one smoothing drives toward zero. Laplacian smooth is mean-curvature flow, which is exactly why it shrinks a model and eats the detail along with the noise.