Applet for Single Subdivision Triangle Patch
DIRECTIONS: In this applet, you create a surface by prescribing
points on the surface and normal vectors for the surface at these points. The points
are larger points forming the base of the line segments (which represent
the normal vectors) drawn automatically in perspective. You can manipulate the base point
and the end point of the vector as normal, with the conventions that (1) when moving the base
point the vector is translated to start at the point to which it is moved, (2) the normal
vector is rescaled to have a unit length.
The surface is created by a subdivision scheme
and approximated in an iterative fashion. Starting with a triangle formed from the
three given points, new points are defined along the edge curves by a Hermite type
interpolation. A normal vector is then defined at this point, we then have generated
four smaller triangles for each initial triangle,
with the same structure (points and normal vectors). The
surface is then defined as the limiting surface obtained by an iteration.