Identification and reverse engineering of Pythagorean-hodograph curves ?
Methods to identify whether or not given control points define a Pythagorean-hodograph (PH) curve are formulated. The methods are based on the satisfaction of control-point constraints or saturation of quadrature arc-length estimates, and apply equally to planar and spatial PH curves. For identified PH curves, algorithms to reconstruct the complex or quaternion pre-image polynomials are developed. The proposed methods allow existing CAD systems to fully exploit the advantageous properties of PH curves within the context of prevailing CAD geometry representations.
reverse engineering pythagorean-hodograph curves bzier control points arc length parametric speed numerical quadrature