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

Algorithm 3

Minimal variety that contains the parametric loci of orthogonal projection: .

Input  ,

Output  .

Step 1. Generate the polynomial system .

Step 2. Compute the Gröebner basis of under the term order such that .

Step 3. Let . Let to be the dimension of .

Step 4. If , then return .

Step 5. If , then decompose into the intersection of prime ideals: .

 Return .

Step 6. If , return .