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

Table 1

Time cost of the algorithms.

	Degree	Algorithm 2	Algorithm 3	Algorithm 4	Redundancy
EX1	(1, 0, 1, 0)	0.016 s	0.016 s	0.001 s	N
EX2	(2, 0, 1, 0)	0.188 s	0.063 s	0.001 s	N
EX3	(3, 0, 1, 0)	0.032 s	0.468 s	0.016 s	N
EX4	(4, 0, 1, 0)	0.734 s	2.671 s	0.001 s	N
EX5	(2, 0, 2, 0)	0.203 s	0.031 s	0.001 s	N
EX6	(3, 0, 2, 0)	596.797 s	0.047 s	0.001 s	N
EX7	(1, 1, 1, 1)	0.078 s	0.016 s	0.001 s	Y
EX8	(2, 1, 2, 1)	0.891 s	0.297 s	0.016 s	Y
EX9	(2, 2, 2, 1)	0.078 s	0.015 s	0.032 s	Y
EX10	(2, 2, 2, 2)	1.515 s	0.984 s	0.016 s	Y
EX11	(3, 1, 2, 1)	NA	113.938 s	0.016 s	Y