Algorithms are presented for polygonalizing implicitly defined, quadric and cubic hypersurfaces in n ≥ 3 dimensional space and furthermore displaying their projections in 3D. The method relies on initially constructing the rational parametric equations of the implicitly defined hypersurfaces, and then polygonalizing these hypersurfaces by an adaptive generalized curvature dependent scheme. The number of hyperpolygons used are optimal, in that they are the order of the minimum number required for a smooth Gouraud like shading of the hypersurfaces. Such hypersurface projection displays should prove useful in scientific visualization applications. The curvature dependent polygonal meshes produced, should also prove very useful in finite difference and finite element analysis programs for multi-dimensional domains.

We describe an efficient parallel solution for the problem of finding the shortest Euclidean path between two points in three dimensional space in the presence of polyhedral obstacles. We consider the important case where the order in which the obstacles are encountered in this shortest path is known. In particular for this case we describe an efficient parallel numerical iterative method on a concurrent-read exclusive-write synchronous shared-memory model. The iterations are essentially convergent non-linear block Gauss-Seidel. For special relative orientations of the, say n, polyhedral obstacles, we further describe a direct method that gives the exact solution in O(log n) time using n processors.