裁剪后二次曲面的光线跟踪

Ray Tracing Trimmed Quadric Surfaces

提出了一个对裁剪后二次曲面进行光线跟踪的新方法。在该方法中引进了一个易于由世界坐标求参数的辅助参数空间，通过预处理，事先将原参数域下的边界变换到新的参数空间。这样，光线与曲面的求交仍可按二次曲面的几何参数进行，求出交点后，再将交点变换到辅助参数空间，在新的参数域中判断交点是否在裁剪过的曲面上。

new algorithm on ray tracing trimmed quadric surfaces is described in this paper, in which an auxiliary parameter space is introduced. Through preprocessing, the boundary of NURBS can be transferred to that of the new auxiliary parameter space.Line-surface intersection can be treated according to surfaces' algebraic equations and their geometric parameters. Intersections are calculated in the local coordinate system of quadric surfaces, and then they are transferred to the auxiliary parameter space to judge whether the intersections are trimmed off.