8.5.4.1 Gaussian curvature

Color Plate A.3 shows a color map of the Gaussian curvature . Since the surface is anti-symmetric with respect to , the Gaussian curvature which is the product of maximum and minimum principal curvatures is symmetric with respect to . The range of the curvature is . The global maximum Gaussian curvature occurs at two stationary points within the domain , . The global minimum curvature is located at two corners and . There is also a saddle point inside the domain at , with value , which is a flat point of the surface. There are six local maxima and two local minima along the domain boundaries. Local maxima at , , , , , with all values , and local minima at with and at with . Since the two local maxima inside the domain have the same coordinate, we subdivide the surface into two sub-domains along the iso-parametric line . In this picture, we avoid the curvature level so as not to deal with the self-intersecting contour at the saddle point.