| OCR Text |
Show 46 curves formed by fixing either the u or v parameter at 0 or 1 (for square patches). This yields a Y function of the form Y(O,v) Y(l,v) Yuo(v) YUl (v) etc. To intersect any of the boundary edges with the scan plane this (perhaps rational cubic) function must be solved for v in Yuo(v)-Yscan 0 The other set of edges necessary to track along, silhouette edges, are defined by the Z component of the normal being zero. This generates points in the parameter space defined by the two equations Xu(u,v) Yv(u,v) - Xv(u,v) Yu(u,v) 0 Y(u,v) - Yscan = 0 Thus, each type of edge defines a point in the parameter space which can be substituted into the X and Z functions to yield the X and Z of the edge on the current scan plane. In addition to following the position of these points in parameter space (and thus in XZ space) as the scan plane moves down the screen, it is also necessary to keep track of their connectivity. That is, which pairs of edges are connected by spans of curve which represent continuous regions of the patch. This is not so easy as for polygons |
