Quiz 5

Q1 Bind matrices

3 Points

Explain how to construct a bind matrix for each joint on a skeleton, and explain the space-to-space transformation each bind matrix applies to any mesh vertex. Your answer should be no more than two sentences.

Calculate the inverse of the joint's transformation matrix with respect to the world. This bind matrix, when applied to a mesh vertex, transforms the vertex from model space to the joint's local space.

Q2 Making a Bind Matrix

3 Points

Compute the bind matrix for the skeleton joint with the overall transform shown below (you should leave it written as a sequence of individual matrices). Then, apply that bind matrix to a vertex located at the world-space position (2, 2).

let the above matrix be R1, R2, R3, R4, R5, respectively

then the bind matrix

B=(R1*R2*R3*R4*R5)^(-1)=R5^(-1)*R4^(-1)*R3^(-1)*R2^(-1)*R1^(-1)$

then the world-space position:

p=B*(2,2)=R5^(-1)*R4^(-1)*R3^(-1)*R2^(-1)*R1^(-1)*(2,2)

Q3 Unmoving Mesh

3 Points

Adam has written a program that applies linear blend skinning to a mesh with a skeleton. However, when his skeleton moves its joints, the mesh does not move with them. Suggest one possible cause for this error in no more than one sentence.

The joint weights for the vertices might not be properly initialized or normalized, causing the mesh to ignore joint influences.