This paper - http://ivizlab.sfu.c...PEG-4 Faces.pdf - Feature Point Based Deformation for MPEG-4 Facial Animation, describes on pages 4 and 5 how to do what I want, I believe.

If I am understanding it right, that algorithm finds the closest control point for a vertex, then the two that flank that vertex. The weight for each control point (Feature Point in the paper) is proportional to the distance to each of these points, relative to the others.

Therefore, the weights sum should be 1 and the vertex will move with the plane defined by the control points.

There are a couple of things I do not understand though:

1.

**In equation (2), what are d12 and d13**, these are not defined in figure (1). Are they equivalent to d2 and d3? Or d1 - d2, d1 - d3?

2.

**When you have the inverted proportional distance, what is the purpose of taking the Sine of it**? (Equation (4))

Finally, in equation (5) on page (6), why is the deformation of the vertex calculated in that way?

**Why is the displacement not simply**:

SUM( controlpoint_0_displacement * controlpoint_0_weight, ..., controlpoint_n_displacement * controlpoint_n_weight )

Could anyone who knows whats going on explain? Thanks!

SJ