Ben Chambers wrote:
> 
> Hmm, seems just a little bit messy.  Where on the triangle are the
> control points placed?  (One thing I wanted to achieve with mine is
> that it uses no more data than the original triangle - three points,
> and three normals, so control points don't have to be generated).

There is a site that has a PDF describing how to get the control
points for a cubic Bezier triangular patch, derived from the corners
and normals of that corner.  It's here:

  http://www-courses.cs.uiuc.edu/~cs319/subdiv.pdf

It won't handle sharp edges (which are important for most work). Note
that this is for CUBIC patches, whereas the code I gave above is for
quartic patches.  For cubic patches, you'd need this macro:

// start of macro code
#macro CubicTriPatch(A,B,C,D,E,F,G,H,I,J,cD)

#if(cD<1)
  smooth_triangle { A,vcross(C-A,B-A),
    G,vcross(D-G,H-G),J,vcross(I-J,F-J) }
#else
  CubicTriPatch(A,(A+B)/2,(A+C)/2,(A+2*B+D)/4,(A+B+C+E)/4,(A+2*C+F)/4,
    (A+3*B+3*D+G)/8,(A+2*B+D+C+2*E+H)/8,(A+B+2*C+2*E+F+I)/8,
    (A+3*C+3*F+J)/8,cD-1 )

  CubicTriPatch(G,(G+H)/2,(D+G)/2,(G+2*H+I)/4,(D+E+G+H)/4,(B+2*D+G)/4,
    (G+3*H+3*I+J)/8,(D+2*E+F+G+2*H+I)/8,(G+H+2*D+2*E+B+C)/8,
    (A+3*B+3*D+G)/8,cD-1 )

  CubicTriPatch(J,(J+F)/2,(I+J)/2,(J+2*F+C)/4,(E+F+I+J)/4,(H+2*I+J)/4,
    (A+3*C+3*F+J)/8,(I+2*E+B+J+2*F+C)/8,(J+F+2*I+2*E+H+D)/8,
    (G+3*H+3*I+J)/8,cD-1 )

  CubicTriPatch((A+3*B+3*D+G)/8,(A+2*B+D+C+2*E+H)/8,
    (A+B+2*C+2*E+F+I)/8,(A+3*C+3*F+J)/8,(G+H+2*D+2*E+B+C)/8,
    (B+C+D+2*E+F+H+I)/8,(I+2*E+B+J+2*F+C)/8,(D+2*E+F+G+2*H+I)/8,
    (D+2*E+F+H+2*I+J)/8,(G+3*H+3*I+J)/8,cD-1 )
#end
#end

// end of macro code

Regards,
John

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