Cyclides in computer aided geometric design
Computer Aided Geometric Design
Canal surfaces and inversive geometry
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Computer Aided Geometric Design
Cyclides and the guiding circle
Mathematics and Computers in Simulation - Special issue: Applied and computational mathematics - selected papers of the fifth PanAmerican workshop - June 21-25, 2004, Tegucigalpa, Honduras
Path splines with circle envelopes
Computer Aided Geometric Design
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Envelopes of monoparametric families of spheres determine canal surfaces. In the particular case of a quadratic family of spheres the envelope is an algebraic surface of degree four that is composed of circles. We are interested in the construction of smooth tubular splines with pieces of envelopes of quadratic families of spheres. We present a scheme for the construction of a tubular spline that interpolates a sequence of circles in 3D. We control the shape near each circle by prescribing a sphere that contains it and is tangent to the spline. We offer further shape handles for local control through weights that are assigned to the controlling spheres.