An algebraic approach to curves and surfaces on the sphere and on other quadrics
Selected papers of the international symposium on Free-form curves and free-form surfaces
On the lower degree intersections of two natural quadrics
ACM Transactions on Graphics (TOG)
Pipe surfaces with rational spine curve are rational
Computer Aided Geometric Design
Computing rational parametrizations of canal surfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Constraints in constructive solid geometry
I3D '86 Proceedings of the 1986 workshop on Interactive 3D graphics
The parametrization of canal surfaces and the decomposition of polynomials into a sum of two squares
Journal of Symbolic Computation - Special issue on computer algebra and mechanized reasoning: selected St. Andrews' ISSAC/Calculemus 2000 contributions
Using Tangent Balls to Find Plane Sections of Natural Quadrics
IEEE Computer Graphics and Applications
Clifford algebra, Lorentzian geometry, and rational parametrization of canal surfaces
Computer Aided Geometric Design
Minimal rational parametrizations of canal surfaces
Computing - Special issue on Geometric Modeling (Dagstuhl 2005)
Isogeometric Analysis: Toward Integration of CAD and FEA
Isogeometric Analysis: Toward Integration of CAD and FEA
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By applying results on canal surfaces, we study exact rational parametrizations of fixed radius rolling ball blends of pairs of natural quadrics. We classify all configurations where this kind of rational parametrization is possible, and describe a general algorithm for parametrizing fixed radius rolling ball blends. The algorithm is then applied to parametrize the fixed radius rolling ball blends of pairs of natural quadrics.