Graphics Reference
In-Depth Information
Vertex skinning is a commonly used technique whereby the joins
between polygons are smoothed. This is implemented by applying
additional transform matrices with appropriate weights to each vertex.
The multiple matrices used to skin vertices are stored in a matrix palette.
The matrices' indices per vertex are used to refer to appropriate matrices
in the matrix palette that will be used to skin the vertex. Vertex skinning
is commonly used for character models in 3D games to ensure that they
appear smooth and realistic (as much as possible) without having to use
additional geometry. The number of matrices used to skin a vertex is
typically two to four.
The mathematics of vertex skinning is given by the following equations:
P
′
′
= ∑
w M P
×
×
i
i
N
= ∑
w M
×
−1
T
×
N
i
i
∑
w
=
1
,
i
=
1
to
n
i
where
n
is the number of matrices that will be used to transform the vertex
P
is the vertex position
P'
is the transformed (skinned) position
N
is the vertex normal
N'
is the transformed (skinned) normal
M
i
is the matrix associated with the
i
ith matrix per vertex and is
computed as
M
i
=
matrix_palette [ matrix_index[i] ]
with
n
matrix_index
values specified per vertex
M
i
-1
T
is the inverse transpose of matrix
M
i
W
i
is the weight associated with the matrix
We discuss how to implement vertex skinning with a matrix palette of
32 matrices and up to four matrices per vertex to generate a skinned
vertex. A matrix palette size of 32 matrices is quite common. The
matrices in the matrix palette typically are 4 × 3 column major matrices
(i.e., four
vec3
entries per matrix). If the matrices were to be stored
in column-major order, 128 uniform entries with 3 elements of each
uniform entry would be necessary to store a row. The minimum value of
