Applet for Subdivision Triangle Patch That Models a Sphere
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 for this applet are original
giving at points on a sphere. 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.


