Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
A multisided generalization of Bézier surfaces
ACM Transactions on Graphics (TOG)
Necessary and sufficient conditions for tangent plane continuity of Be´zier surfaces
Computer Aided Geometric Design
Base points, resultants, and the implicit representation of rational surfaces
Base points, resultants, and the implicit representation of rational surfaces
Functional composition algorithms via blossoming
ACM Transactions on Graphics (TOG)
Scattered Data Techniques for Surfaces
Dagstuhl '97, Scientific Visualization
Triangulation and display of rational parametric surfaces
VIS '94 Proceedings of the conference on Visualization '94
Multisided arrays of control points for multisided Bézier patches
Computer Aided Geometric Design
Spherical manifolds for adaptive resolution surface modeling
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Polyhedral vertex blending with setbacks using rational S-patches
Computer Aided Geometric Design
The Bernstein polynomial basis: A centennial retrospective
Computer Aided Geometric Design
Mathematical and Computer Modelling: An International Journal
| Hi-index | 0.00 |
Rational Be´zier surfaces provide an effective tool for geometric design. One aspect of the theory of rational surfaces that is not well understood is what happens when a rational parameterization takes on the value (0/0, 0/0, 0/0) for some parameter value. Such parameter values are called base points of the parameterization. Base points can be introduced into a rational parameterization in Be´zier form by setting weights of appropriate control points to zero. By judiciously introducing base points, one can create parameterizations of four-, five- and six-sided surface patches using rational Be´zier surfaces defined over triangular domains. Subdivision techniques allow rendering and smooth meshing of such surfaces. Properties of base points also lead to a new understanding of incompatible edge twist methods such as Gregory's patch.