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Tensor Product Patches

Tensor Product Patches:

Subdivision, Recursion, Evaluation:

Partial Derivatives:
Ordinary derivative in each variable separately:

Each of the above is a tangent vector in a parametric direction
Surface is regular at each (s,t) where these two vectors are linearly independent
The (unnormalized) surface normal is given at any regular point by

(the sign dictates what is the outward pointing normal)

In particular, the cross-boundary tangent is given by
(e.g. for the s=0 boundary):

(and similarly for the other boundaries)

Smoothly Joined Patches:
Can be achieved by ensuring that

(and correspondingly for the other boundaries)


CS488/688: Introduction to Interactive Computer Graphics
University of Waterloo
Computer Graphics Lab