
The gaussian curvature of a surface at a point is the product of the principal curvatures at that point. The tangent plane of any point with positive gaussian curvature touches the surface at a single point, whereas the tangent plane of any point with negative gaussian curvature cuts the surface. Any point with zero mean curvature has negative or zero gaussian curvature.
Mean and gaussian curvature of selected level surfaces are compared using color to indicate curvature.