p]M, which is the vector space formed by the set of all

tangent vectors to M at P; it is determined by its basis vectors on [T.

If the model is not rendered with diffuse, specular and normal maps there is usually no need to calculate normal and

tangent vectors at vertex positions.

5), we have the following equation between the

tangent vectors of the curves (c), ([c.

2])], which defines the

tangent vectors as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], with i = 1, 2.

X, Y) is treated as a derivation of the tensor algebra for any

tangent vectors X, Y.

Quantized flow: The quantized flow vectors derived from the smooth

tangent vectors is used to build stroke directions for the pixels inside a region.

Conversely, if the submanifold is totally geodesic, then h(Y, W) = 0, for arbitrary

tangent vectors Y and W.

When we move all unit

tangent vectors T of a curve [?

This differential gives the change of the

tangent vectors throughout the function.

A parametric surface w(u, v) is called smooth if the

tangent vectors in the u and v directions satisfy

ij] is the Gram matrix corresponding to the pair of

tangent vectors ([dx'.

However, to describe the deformation in the direction perpendicular to the thin structure's mid-surface, the information on the

tangent vectors ([G.