Algorithm 952: PHquintic: A Library of Basic Functions for the Construction and Analysis of Planar Quintic Pythagorean-Hodograph Curves

作者：Dong Bohan^*; Farouki Rida T

来源：ACM Transactions on Mathematical Software, 2015, 41(4): 28.

DOI：10.1145/2699467

• Geometric Design
• Free-Form Curves
• Algorithms
• Pythagorean-hodograph curves
• Hermite and spline interpolation
• computer-aided geometric design
• Newton-Raphson method
• arc length
• bending energy
• offset curves

The implementation of a library of basic functions for the construction and analysis of planar quintic Pythagorean-hodograph (PH) curves is presented using the complex representation. The special algebraic structure of PH curves permits exact algorithms for the computation of key properties, such as arc length, elastic bending energy, and offset (parallel) curves. Single planar PH quintic segments are constructed as interpolants to first-order Hermite data (end points and derivatives), and this construction is then extended to open or closed C-2 PH quintic spline curves interpolating a sequence of points in the plane. The nonlinear nature of PH curves incurs a multiplicity of formal solutions to such interpolation problems, and a key aspect of the algorithms is to efficiently single out the unique "good" interpolant among them.

• 出版日期2015-10