Polynomiality vs. rationality of Pythagorean hodograph/normal curves and surfaces
Zbynek Sir  1@  
1 : Charles University Prague

We propose a new method for studying relation between polynomial a rational PH/PN objects. It is based on determining the corresponding motion polynomial. While the primal (rotation) component of the motion polynomial is arbitrary, the dual (translation) part is determined be a linear system of equations. This system is analysed and possible denominators of the resulting PH/PN curves and surfaces are discussed. Polynomial object in this approach appear as special cases of the polynomial ones. From a certain point of view however the polynomial objects appear to be the generic cases.

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