After R. T. Farouki introduced, there has been vast researches on Pythagorean Hodograph curves. By the nice property that its velocity function is polynomial/rational, it gives us simpler formulae in computing geometrically driven objects --- offset curve/surface, pipe/canal surface --- which are widely used in CAGD. We present a geometric method to construct PH curves in higher dimensional Euclidean spaces.
Gwang-Il Kim. "Higher dimensional PH curves." Proc. Japan Acad. Ser. A Math. Sci. 78 (10) 185 - 187, Dec. 2002. https://doi.org/10.3792/pjaa.78.185