Pythagorean-hodograph ovals of constant width

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Abstract

A constructive geometric approach to rational ovals and rosettes of constant width formed by piecewise rational PH curves is presented. We propose two main constructions. The first construction, models with rational PH curves of algebraic class 3 (T-quartics) and is based on the fact that T-quartics are exactly the involutes of T-cubic curves. The second construction, models with rational PH curves of algebraic class m>4 and is based on the dual control structure of offsets of rational PH curves.

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