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

Algorithm 1

.

INPUT  

OUTPUT  ,

where , and .

Step 1.

 , , , .

 For in do

  If , then

   For in do . end do;

   .

  Else .

 End do;

Step 2.

 For in do

  ;

  For in do

   If such that

    then delete from ; ;

   Else if such that ,

    then delete from ;

    ;

   Else if such that ,

    then ;

  End do;

  If then ;

  Else .

 End do;

Step 3.

 For in do

  For in do

   If ,

   then ; ; break;

  End do;

 End do;

Step 4. Return .

// returns all the irreducible factors of