Game Development Reference
In-Depth Information
Figure 10.5. Simulation examples. The top row shows the rest positions, and the bottom
row shows the deformed positions (see Color Plate XI).
Let us now define the deformation gradient F as
∂T ( p ) x
∂x
∂T ( p ) x
∂y
∂T ( p ) x
∂z
∂T ( p ) y
∂x
∂T ( p ) y
∂y
∂T ( p ) y
∂z
T ( p )=
,
F =
(10.20)
∂T ( p ) z
∂x
∂T ( p ) z
∂y
∂T ( p ) z
∂z
where T ( p ) is the transformation applied to the homogeneous coordinates p of a
point. The deformation gradient is used to compute the rotation of the tetrahedron.
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