Classification of planar Pythagorean hodograph curves

Abstract

We classify planar polynomial Pythagorean-hodograph curves of any degree with respect to Euclidean similarities. We also analyze possible global shapes of the Pythagorean-hodograph curves of degree four and five and describe all possible configurations of their singular points.

This description results in a classification of Pythagorean-hodograph quartics and quintics with respect to the homeomorphisms of the plane. We also describe all the Pythagorean-hodograph curves of any degree up to five which exhibit central or axial symmetry. (C) 2020 Elsevier B.V.

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Keywords

• Pythagorean-hodograph curves
• Euclidean similarity
• Algebraic curves
• Singular points