When a finger is close to a CG object, this system calculates a tangent plane
slope angles on the surface which the finger is close to.
Similarly the tangent plane
equation of the pipe at the point Q is expressed as
The tangent plane
at any point in the equatorial plane is parallel to the x-axis so the d[p.sub.ik] at these points lie in the tangent plane
Caption: Figure 5: The vectors [r.sub.[epsilon]] and [r.sub.[epsilon]] in the local tangent plane
to the surface.
The properties of the function f show that this surface does not remain, round the point a, on the same side of the tangent plane
, though each parametrized curve [alpha] [member of] [[GAMMA].sup.m.sub.F] (a) stays, around the point a, on the same side of the tangent plane
constitute the contravariant basis at the point [theta](y), where [[delta].sup.i.sub.j] is the Kronecker symbol (note that [mathematical expression not reproducible] and the vector [[??].sup.[alpha]](y) is also in the tangent plane
to S at [??](y)) (cf.
where [U.sup.[??]] is the projection of U on the tangent plane
The tangent plane
to w at the point [X.sub.0] = (x([u.sub.0], [v.sub.0]), y([u.sub.0], [v.sub.0]), z([u.sub.0], [v.sub.0]) on w is the plane that contains the tangent vectors [w.sub.u], [w.sub.v] and the point [X.sub.0], and therefore [w.sub.u] x [w.sub.v] is a normal vector of the tangent plane
a) Sliding type, when the displace is produced in the tangent plane
The reflection model known as the ray method, is based on the assumption that incident light is specularly reflected by the local tangent plane
on the surface.
In particular, this construction guarantees tangent plane
continuity, the strong convex hull property, locality and affine invariance.
Because 3D facial animation is composed of various different expression models, the tangent plane
and normal vector of the same vertex point also vary with changes in expressions, as shown in Figure 6.