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

Algorithm 2

Exact parametric loci of orthogonal projection: .

Input  ,

Output  .

Step 1. Generate the polynomial system .

Step 2. Decompose in to the union of regular systems, Let .

Step 3. Let

Step 4. .

Step 5. Return .