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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.

Thomas J. Wetzel
Wetzel Associates Inc., 4022 E. Greenway Road, Ste. 11 PMB 189, Phoenix, AZ 85032-4760, U.S.A.

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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