| OCR Text |
Show 44 The X scan proceeds similarly to the polygonal case. The edges are sorted in X order in the active curve list but now must be explicitly linked together according to which pairs have surface between them. As the scan ray passes an edge on the left side of a curve a new active point must be created. The Z coordinate of the point is determined by solving a quadratic equation. The direction of the normal vector to the surface is however, linear in X,Y,Z and so can be computed incrementally. The inclusion of curved surfaces into the algorithm has therefore necessitated the addition of another type of edge needing to be tracked, the silhouette edge. The intersection of a silhouette edge with the scan plane represents the extrema of the surface in the X direction, knowledge of which is necessary for the X scan to work properly. Parametric Surface Algorithm (Introduction) The basic difference between algorithms which operate on algebraic surfaces and those which operate on parametric surfaces is that the latter do all their computations in parametric space. That is, the intersection of a given surface with the scan plane will be generated by all values of u and v which satisfy the equation Y(u,v) Yscan All values of (u,v) which satisfy this equation may then be |
