Fundamentals of interactive computer graphics
Fundamentals of interactive computer graphics
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
The complexity of robot motion planning
The complexity of robot motion planning
Computer Aided Geometric Design
Automatic parameterization of rational curves and surfaces III: algebraic plane curves
Computer Aided Geometric Design
Polygonization of implicit surfaces
Computer Aided Geometric Design
Real-time rendering of trimmed surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Applications of surface networks to sampling problems in computer graphics
Applications of surface networks to sampling problems in computer graphics
Geometric computations with algebraic varieties of bounded degree
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Efficient techniques for multipolynomial resultant algorithms
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Creating multisided rational Bézier surfaces using base points
ACM Transactions on Graphics (TOG)
Degree, multiplicity, and inversion formulas for rational surfaces using u-resultants
Computer Aided Geometric Design
Factoring rational polynomials over the complex numbers
SIAM Journal on Computing
Algebraic and numeric techniques in modeling and robotics
Algebraic and numeric techniques in modeling and robotics
Adaptive Polygonalization of Implicitly Defined Surfaces
IEEE Computer Graphics and Applications
The GANITH algebraic geometry toolkit
DISCO '90 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
Base points, resultants, and the implicit representation of rational surfaces
Base points, resultants, and the implicit representation of rational surfaces
Interactive display of large-scale NURBS models
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
Drawing closed rational surfaces
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Rational parametrizations of nonsingular real cubic surfaces
ACM Transactions on Graphics (TOG)
A mapping-independent primitive for the triangulation of parametric surfaces
Graphical Models - Special issue on SMI 2002
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We present a comprehensive algorithm to construct a topologically correct triangulation of the real affine part of a rational parametric surface with few restrictions on the defining rational functions. The rational functions are allowed to be undefined on domain curves (pole curves) and at certain special points (base points), and the surface is allowed to have nodal or cuspidal self-intersections. We also recognize that for a complete display some real points on the parametric surface may be generated only by complex parameter values, and that some finite points on the surface may be generated only by infinite parameter values; we show how to compensate for these conditions. Our techniques for handling these problems have applications in scientific visualization, rendering non-standard NURBS, and in finite-element mesh generation.