  In the past few decades polynomial curves with Pythagorean Hodograph (for
short PH curves) have received considerable attention due to their usefulness
in various CAD/CAM areas, manufacturing, numerical control machining and
robotics. This work deals with classes of PH curves built-upon
exponential-polynomial spaces (for short EPH curves). In particular, for the
two most frequently encountered exponential-polynomial spaces, we first provide
necessary and sufficient conditions to be satisfied by the control polygon of
the B\'{e}zier-like curve in order to fulfill the PH property. Then, for such
EPH curves, fundamental characteristics like parametric speed or cumulative and
total arc length are discussed to show the interesting analogies with their
well-known polynomial counterparts. Differences and advantages with respect to
ordinary PH curves become commendable when discussing the solutions to
application problems like the interpolation of first-order Hermite data.
Finally, a new evaluation algorithm for EPH curves is proposed and shown to
compare favorably with the celebrated de Casteljau-like algorithm and two
recently proposed methods: Wo\'zny and Chudy's algorithm and the dynamic
evaluation procedure by Yang and Hong.
