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.