Cyclides in computer aided geometric design
Computer Aided Geometric Design
Cyclides in computer aided geometric design II
Computer Aided Geometric Design
Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
Computer Aided Geometric Design
Quartic supercyclides I: basic theory
Computer Aided Geometric Design
Applications of Laguerre geometry in CAGD
Computer Aided Geometric Design
A Laguerre geometric approach to rational offsets
Computer Aided Geometric Design
Studying cyclides with Laguerre geometry
Computer Aided Geometric Design
Proceedings of the 5th IMA Conference on the Mathematics of Surfaces
Branching blend of natural quadrics based on surfaces with rational offsets
Computer Aided Geometric Design
Construction of rational surface patches bounded by lines of curvature
Computer Aided Geometric Design
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Dupin cyclides are algebraic surfaces of order three and four whose lines of curvature are circles. These surfaces have a variety of interesting properties and are aesthetic from a geometric and algebraic viewpoint. Besides their special property with respect to lines of curvature they appear as envelopes of one-parameter families of spheres in a twofold way. In the present article we study two families of canal surfaces with rational lines of curvature and rational principal curvatures, which contain the Dupin cyclides of order three and four as special instances in each family. The surfaces are constructed as anticaustics with respect to parallel illumination and reflection at tangent planes of curves on a cylinder of rotation.