Higher dimensional PH curves

Abstract

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.