Journal for Geometry and Graphics 08 (2004), No. 1, 001--016
Copyright Heldermann Verlag 2004
Optimal Rational Circles of Degrees Five and Six
Helmut E. Bez
Dept. of Computer Science, Loughborough University, Loughborough, Leicestershire, LE11 3TU, U.K.
h.e.bez@lboro.ac.uk
Thomas J. Wetzel
Wetzel Associates Inc., 4022 E. Greenway Road, Ste. 11 PMB 189, Phoenix, AZ 85032-4760, U.S.A.
tjwetzel@compuserve.com
This paper presents new low degree, complete Bézier circles with positive weights. Specifically: two symmetric, quintic parametrizations - optimized towards arc-length parametrization in L2 and Linfinity norms - are developed and a new degree six circle with a symmetric, near arc-length parametrization is presented. Properties of the parametrizations are discussed and compared.
Keywords: Rational paths, circle parametrization, optimization.
MSC: 68U05; 53A04
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