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