Research On Algorithm Of Parallel Projection Of Curve And Surface Intersection Based On Re-parameterization

The parallel projection of curves on surfaces and surface intersection are fundamental problems in computer aided design.In this paper,we study the parallel projection of curves onto surfaces and the intersection algorithm between Bézier surfaces,it is significant to improve the efficiency and stability of the related algorithm.The main research content is as follows:(1)Parallel projection algorithm of curve on surface based on reparameterizationFor the parallel projection of a curve onto a surface,the obtained projection curve does not fall completely on the surface,and a curve projection algorithm based on reparameterization is proposed.Firstly,a curve on the parametric surface is obtained using the reparameterization function;secondly,the distance between this curve and the given source curve is taken as the objective function;finally,a set of nonlinear equations is obtained by transformation and the optimized projection curve is solved by numerical iteration method.The experimental results show that the projection curve obtained by the algorithm in this paper falls strictly on the projection surface and has higher accuracy compared with the existing algorithms.(2)Bézier parametric surface intersection algorithm based on reparameterizationThe existing parametric surface intersection algorithms usually use B-spline curve to interpolate a series of intersection points and use them as the final approximate intersection line.The approximate intersection line is generally not guaranteed to fall precisely on any given surface.To solve this problem,this paper proposes a new algorithm for surface intersection based on reparameterization.Firstly,the control grid of the surface is encrypted by surface elevation,and then the intersection line between the control grid is found using triangular surface slices as an approximation of the exact intersection line and mapped to the respective parameter domains of the two surfaces.Then,the broken line segment on the parameter domain of the surface is fitted by a piecewise B-spline curve,and the fitting result is taken as the initial value of Newton iteration.Finally,the Newton iteration method is used to get a more accurate intersection line of the parameter domain.Compared with the traditional tracking intersection algorithm,this algorithm can directly obtain the rational polynomial representation of the intersection line,and the intersection line is strictly located on one of the surfaces,so it can obtain higher approximation accuracy with fewer control points of the intersection curve.Simulation results show that the algorithm is accurate and effective.