An Algorithm for Curve Orthogonal Projections onto Implicit Surfaces

In this paper a second order iteration algorithm for projecting a space parametric curve perpendicularly onto an implicit surface is presented.First, the first and second derivatives of the coordinate points of the orthogonal projection curve with respect to the parameter of the space parametric curve are obtained by using the orthogonal conditions possessed jointly by points of the space parametric curve and of the orthogonal projection curve.A marching approach based on second-order Taylor approximation is further proposed to compute the coordinate points of the orthogonal projection curve and two methods for controlling the iteration step are also given.Finally, a first-order technique is put forward to correct the iteration errors introduced by the truncated higher-order terms in the second-order Taylor's formula.Simulations indicate that the presented algorithm has good accuracy and efficiency.