Interpolation-Based Animation - Computer Animation: Algorithms and Techniques - page 140

Slice from Object 1 showing
reconstructed polygon
Slice from Object 2 showing
reconstructed polygon
Point from Object 1
Point from Object 2
Interpolated point
Superimposed slices showing interpolated points
Slice reconstructed from
interpolated points
FIGURE 4.35
Interpolating slices taken from two objects along each respective central axis.
each of the original shapes, but the new models now have the same topologies. These new definitions
for the objects can then be transformed by a vertex-by-vertex interpolation.
There are several different ways to map an object to a sphere. No one way has been found to work
for all objects, but, taken together, most of the genus 0 objects can be successfully mapped to a sphere.
The most obvious way is to project each vertex and edge of the object away from a center point of the
object onto the sphere. This, of course, works fine for star-shaped polyhedra but fails for others.