摘要
In this paper, a new algorithm with extrapolation process for computingthe ray/surface intersection is presented. Also, a ray is defined to be the in-tersection of two planes, which are nonorthogonal in general, in such a waythat the number of multiplication operations is reduced. In the preprocessingstep, NURBS surfaces are subdivided adaptively into rational Bezier patches.Parallelepipeds are used to enclose the respective patches as tightly as possible.Therefore, for each ray that hits the enclosure (i.e., parallelepiped) of a patchthe intersection points with the parallelepiped's faces can be used to vield agood starting poiat for the following iteration. The improved Newton iterationwith extrapolation process saves CPU time by reducing the number of iterationsteps. The intersection scheme is faster than previous methods for which published performance data allow reliable comparison. The method may also beused to speed up tracing the intersection of two parametric surfaces and otheroperations that need Newton iteration.
In this paper, a new algorithm with extrapolation process for computingthe ray/surface intersection is presented. Also, a ray is defined to be the in-tersection of two planes, which are nonorthogonal in general, in such a waythat the number of multiplication operations is reduced. In the preprocessingstep, NURBS surfaces are subdivided adaptively into rational Bezier patches.Parallelepipeds are used to enclose the respective patches as tightly as possible.Therefore, for each ray that hits the enclosure (i.e., parallelepiped) of a patchthe intersection points with the parallelepiped's faces can be used to vield agood starting poiat for the following iteration. The improved Newton iterationwith extrapolation process saves CPU time by reducing the number of iterationsteps. The intersection scheme is faster than previous methods for which published performance data allow reliable comparison. The method may also beused to speed up tracing the intersection of two parametric surfaces and otheroperations that need Newton iteration.
