LAUSR

This paper deals with Pythagorean hodograph curves of the spaces of algebraic trigonometric functions and trigonometric polynomials, span 1 , t , cos k t , sin k t k = 1 m $\text {span}\left \{1,t,\left \{{\cos \limits } \left ({kt}\right ), {\sin \limits } \left ({kt}\right )\right \}_{k=1}^{m}\right \} $ and span 1 , cos k t , sin k t k = 1 m , $ \text {span}\left \{1,\left \{{\cos \limits } \left ({kt}\right ), {\sin \limits } \left ({kt}\right )\right \}_{k=1}^{m}\right \}, $ respectively. First, we propose a general characterization of planar PH curves in these spaces. Next, we consider the particular cases m = 1 and m = 2. For each of them, we give the general form of the control polygon of the PH curves, the implicit relations defining these curves, and their geometrical interpretations. Some examples and particular cases complete this study.