Application of Orthogonal Polynomial in Orthogonal Projection of Algebraic Surface

Point orthogonal projection onto an algebraic surface is a very important topic in computer-aided geometric design and other fields. However, implementing this method currently extremely challenging difficult because it to achieve desired degree of robustness. Therefore, we construct polynomial, which the ninth formula, after inner product eighth formula itself. Additionally, use Newton iterative for iteration. In order ensure maximum convergence, two techniques are used before iteration: (1) Newton’s gradient descent method, make initial iteration point fall on surface, (2) computation foot-point moving close position surface. Theoretical analysis experimental results show that proposed algorithm can accurately, efficiently, robustly converge test points different spatial positions.