Symbolic Computation of the Orthogonal Projection of Rational Curves onto Rational Parameterized Surfaces

Algorithm 4

Parametric loci of orthogonal projection: .

Input  , , where .

Output A variety that contains .

Step 1. Generate the polynomial system .

Step 2. Compute .

Step 3. Factorize , is a irreducible factor of in .

Step 4.

 Let ;

 For to do

  ;

  If , .

  Else .

 End for

Step 5. Return .

// [21] returns the parametric presetations of in parameters .