Project Note3

Skin surface

In computational geometry, skin surface is a tangent continuous curve or surface of a given set of balls. The steps to get the skin surface are as following:

1. Delaunay triangulation;

2. Voronoi Diagram;

3. Mixed cell;

4. For each mixed cell, there is a patch for the cell in the skin surface.

In total, there are just 3 types of patches: circle, hyperbola and invert-circle. (In 3D, sphere, hyperboloid and invert-sphere). The centre of these patches is the intersection of aff(d) and aff(v).

At first, I think the centre must be in the Delaunay cells, so I add this constrain in my program. Then I found many needed patches are not draw. When I turn back to my lecture notes, I found that the aff() function is not the conv() function, which represents the convex hull of the input. The affine function is just the linear combination of the given input set, which means the affine hull of a point, a segment, a triangle are all the whole planar.

Remember to make the concept clear before starting experiments!