Automatic parameterization of rational curves and surfaces 1: conics and conicoids
Computer-Aided Design
Automatic parametrization of rational curves and surfaces II: cubics and cubicoids
Computer-Aided Design
Automatic parameterization of rational curves and surfaces III: algebraic plane curves
Computer Aided Geometric Design
Parametrization of cubic algebraic surfaces
Proceedings on Mathematics of surfaces II
Automatic parameterization of rational curves and surfaces IV: algebraic space curves
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
A fast algorithm for rendering parametric surfaces
Tutorial: computer graphics; image synthesis
Bernstein-Bézier Methods for the Computer-Aided Design of Free-Form Curves and Surfaces
Journal of the ACM (JACM)
Scan line methods for displaying parametrically defined surfaces
Communications of the ACM
A computer technique for displaying n-dimensional hyperobjects
Communications of the ACM
Geometric Modeling with Algebraic Surfaces
Proceedings of the 3rd IMA Conference on the Mathematics of Surfaces
Geometric computations with algebraic varieties of bounded degree
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Dimension-independent modeling with simplicial complexes
ACM Transactions on Graphics (TOG)
Accelerated walkthrough of large spline models
Proceedings of the 1997 symposium on Interactive 3D graphics
Interactive Display of Large NURBS Models
IEEE Transactions on Visualization and Computer Graphics
Illuminating the Fourth Dimension
IEEE Computer Graphics and Applications
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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.