GLOBAL CONSTRAINED PARAMETERIZATION OF TRIANGULATED SURFACES

Methods and apparatus for mapping a feature onto a simulated surface having contoured portions, the surface being definable by a plurality of generally adjacent triangulations, the surface being further definable by a plurality of intersecting isoparametric curves linking identified values of the feature to identified points on the surface. In one embodiment, the isoparametric curves are characterized in that when the surface is flat, the isoparametric curves intersect one another in a perpendicular manner, and the perpendicularity of the intersections on the contoured portions of the surface is maintained. In another embodiment, the isoparametric curves are characterized in that when the surface is flat. The isoparametric curves are spaced a predetermined distance apart, and the spacing of the intersections on the contoured portions of the surface is maintained. In a third embodiment of the invention, the isoparametric curves are characterized by defined mathematical relationships having a plurality of variables associated with at least the topology of the surface, and at least one of the variables is held constant between isoparametric curves. Preferably, each of the triangulations are characterized by vertices terminating at points on the surface, and the method further includes using the vertices to define a gradient of a mathematical function associated with the feature, which function is interpolated over the triangulated surface.