C2 interpolation of spatial data subject to arc-length constraints using Pythagorean-hodograph quintic splines

In order to reconstruct spatial curves from discrete electronic sensor data, two alternative C Pythagorean–hodograph (PH) quintic spline formulations are proposed, interpolating given spatial data subject to prescribed contraints on the arc length of each spline segment. The first approach is concerned with the interpolation of a sequence of points, while the second addresses the interpolation of derivatives only (without spatial localization). The special structure of PH curves allows the arc–length conditions to be expressed as algebraic constraints on the curve coefficients. The C PH quintic splines are thus defined through minimization of a quadratic function subject to quadratic constraints, and a close starting approximation to the desired solution is identified in order to facilitate efficient construction by iterative methods. The C PH spline constructions are illustrated by several computed examples. e–mail: [email protected], [email protected], [email protected], [email protected]