| OCR Text |
Show The operation of finding entering edges for a 45 substituted into the parametric functions for X and Z to generate the cross section curve. There is a one to one correspondance between points on the (u,v) curve and points on the (X,Z) curve although their shapes may be quite different. The cross section curve in X,Z does not in general have an explicit formulation: it is neither parametric nor algebraic (except in the sense of an infinite Taylor series). The only feasible way of solving for the location of points on this curve is by numerical means. parametrically defined surface is effectively that of finding the local maxima of the Y definition function. As with quadratics these could be at corners, in the middle of edges or in the middle of the patch. The location of these maxima must be done explicitly in terms of the u and v values at the local maxima. For a given position of the scan plane there is no explicit X and Z. way of representing the the cross section curve in We can however explicitly represent certain points curve and use numerical techniques to move on the incrementally along the curve to get to other points. The minimal set of points we must keep track of are, as in the quadric case, the intersection of the boundary edges of the patch with the current scan plane and the intersection of the silhouette edge with the current scan plane. The boundary edges are defined in this case as those space |
