Mathematical elements for computer graphics (2nd ed.)
Mathematical elements for computer graphics (2nd ed.)
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Cyclides in computer aided geometric design
Computer Aided Geometric Design
On cyclides in geometric modeling
Computer Aided Geometric Design
Computers in Industry - Special issue: modeling in computer graphics
Cyclides in Surface and Solid Modeling
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Rational parametric representation of parabolic cyclide: formulation and applications
Computer Aided Geometric Design
Blending with affine and projective Dupin cyclides
Neural, Parallel & Scientific Computations - computer aided geometric design
Computer Aided Geometric Design
Computer Aided Geometric Design
Quartic supercyclides I: basic theory
Computer Aided Geometric Design
Blending two cones with Dupin cyclides
Computer Aided Geometric Design
Computer Aided Geometric Design
Do blending and offsetting commute for Dupin cyclides?
Computer Aided Geometric Design
Quartic supercyclides for geometric design
From geometric modeling to shape modeling
Dupin Cyclides as Blending Surfaces Cones
Proceedings of the 5th IMA Conference on the Mathematics of Surfaces
Dupin Cyclides and Supercyclides
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
Blending Between Right Circular Cylinders with Parabolic Cyclides
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
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The use of Dupin cyclides and supercyclides in CAGD applications has been the subject of many publications in the last decade. Dupin cyclides are low degree algebraic surfaces having both parametric and implicit representations. In this paper, we aim to give the necessary expansions to derive implicit equations of supercyclides in the affine as well as in the projective space, starting from equations of the Dupin cyclide and the transformation matrix. We introduce a particular subfamily of supercyclides, called elliptic supercyclides, and show how to use them for the blending of elliptic quadratic primitives. We also show how one can convert an elliptic supercyclide into a set of rational biquadratic Bézier patches.