Demonstrating Whitney fold by the normal bundle to a parabola curve The critical distance points between two surfaces. The red-colored pairs of points are of minimal distances.
degenerate (formally A_3) maximal and minimal distances to an ellipse The Surface-Surface Intersection computed from a nonlinear constraint system, i.e. the zero set of a map from a 4-space to 3-space.
The flecnodal curve. Note that the base surface has two C1and one C0breakings. The critical distance points between two planar curves.
Computing the evolute of an ellipse using a dramatic degree reduction stragety as prensented in one of our papers. The extended evolute of a C^1 curve with 8 breaks.
Evolute of a C^2 curve and its curvature plot curvature critical points
computing zeros of curvature derivative: tranditional approach computing zeros of curvature derivative: our approach.
Tracking intersection curves of two deforming surfaces. Tracking critical distances between a moving point and a C^ curve.