Animation

The animations are created by linear interpolation between the initial mesh and subdivided surface. Since the original mesh and the subdivided surface are not equivalent, we tessellate the original mesh without moving any vertex. After this step we have a mesh that looks exactly like the initial mesh, but it is also equivalent to the final surface and a mapping between the two is trivial.

Morphing

Morphing is a smooth transition from one object to another. It is a difficult problem that has more than one solution and the “quality” metric is hard to formalize.

The morphing problem can be split into two parts:

• Finding a mapping between the source and destination surfaces
• Find a curve to move the points from source to destination

A subdivided surface is usually a highly tessellated mesh while the control polygon is ideally the smallest polygon that can define the surface. We know from the above paragraph that we have a mapping between a control polygon and its subdivided surface, therefore the problem is reduced to finding a mapping between the control polygons.

Now we have to find a path to move the vertices from one position to the other.

For the smooth curve from source to destination I chose 2 solutions:

• Linear interpolation
• Cubic Bezier interpolation where the intermediate points are the pre-image of the subdivided surface on the original mesh.