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.

翻译：在过去几十年中,与Pythagorean Hodlog(短PH曲线)的多球曲线在过去几十年中由于在CAA/CAM、制造、数字控制机械和机器人等不同领域、制造、数字控制机械和机器人的有用性而得到了相当的注意。这项工作涉及PH曲线的类别,这些曲线是按指数-极极极极极球空间(用于短期EPH曲线)建造的指数指数-极极极极极极极化空间。特别是,对于两个最经常遇到的极极极极极极极多空间,我们首先提供了必要和充分的条件,以便用B\'{e}类似曲线的控制多边形来满足这些曲线,以便满足PH特性。随后,对于这类EPH曲线,讨论了参数速度或累积和总弧长度等基本特征,以展示出与众所周知的多球系相对等(短的EHPH曲线曲线曲线)空间。在讨论应用问题的解决办法时,例如一级赫米特数据内部调时,通常PH值数据等两个最常见的曲线的差别和优点值得称赞。最后,我们提出并展示了一个新的评价算方法,并显示这种评价算方法与最近提出的Cast-Cast-HAVAL-H和Charl和Charwa-Charwa-HAll和C-H 和CHR-H 和CL-HM-H 以及两个拟议方法和方法。