Matrix analysis
Computer-Aided Design
On algebraic surfaces meeting with geometric continuity
On algebraic surfaces meeting with geometric continuity
Automatic parameterization of rational curves and surfaces III: algebraic plane curves
Computer Aided Geometric Design
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Automatic parameterization of rational curves and surfaces IV: algebraic space curves
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Computer Aided Geometric Design
Symbolic parametrization of curves
Journal of Symbolic Computation
Higher-order interpolation and least-squares approximation using implicit algebraic surfaces
ACM Transactions on Graphics (TOG)
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
GCn continuity conditions for adjacent rational parametric surfaces
Computer Aided Geometric Design
Blending an implicit with a parametric surface
Computer Aided Geometric Design
Parametrization of algebraic curves over optimal field extensions
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Rational blending surfaces between quadrics
Computer Aided Geometric Design
Rational parametrization of surfaces
Journal of Symbolic Computation
Numerical implicitization for intersection and Gn-continuous blending of surfaces
Computer Aided Geometric Design
Gn-continous connections between normal ringed surfaces
Computer Aided Geometric Design
Geometric continuity: a parametrization independent measure of continuity for computer aided geometric design (curves, surfaces, splines)
Blending canal surfaces based on PH curves
Journal of Computer Science and Technology
| Hi-index | 0.00 |
In this paper we prove that, for a given set of parametric primary surfaces and parametric clipping curves, all parametric blending solutions can be expressed as the addition of a particular parametric solution and a generic linear combination of the basis of a free module of rank 3. As a consequence, we present an algorithm that outputs a generic expression for all the parametric solutions for the blending problem. In addition, we also prove that the set of all polynomial parametric solutions (i.e. solutions that have polynomial parametrizations) for a parametric blending problem can also be expressed in terms of the basis of a free module of rank 3, and we prove an algorithmic criterion to decide whether there exist parametric polynomial solutions. As a consequence we also present an algorithm that decides the existence of polynomial solutions, and that outputs (if this type of solution exists) a generic expression for all polynomial parametric solutions for the problem.