phQuinticHermite
fun phQuinticHermite(start: Vector2, startDerivative: Vector2, end: Vector2, endDerivative: Vector2): PHQuintic(source)
The PH quintic from start to end with derivatives startDerivative and endDerivative at its ends, after Farouki and Neff, "Hermite interpolation by Pythagorean hodograph quintics" (Mathematics of Computation, 1995). With w0 = √d0 and w2 = ±√d1 the end condition ∫w² = end - start is a quadratic in w1, 2·w1² + 3(w0 + w2)·w1 + 3w0² + w0w2 + 3w2² - 15(end - start) = 0, so there are four interpolants. The one with the smallest absolute rotation of its tangent is returned, which is the one without loops for reasonable data.