Interactive construction and analysis of planar quintic Pythagorean-hodograph curves with MFC and OpenGL.

摘要

An interactive implementation for the construction and analysis of planar quintic Pythagorean-hodograph (PH) curves has been developed, based on the Microsoft Foundation Class (MFC) Library, and the Open Graphics Library (OpenGL). The special algebraic structure of PH curves allows key properties, such as the arc length, elastic bending energy, and offset curves, to be exactly calculated. The algorithms used to construct planar PH curves, and to compute their key properties, have been implemented as C functions. Use of the complex representation for planar PH curves greatly facilitates these implementations. The interactive construction and analysis capability has been developed using C++ in the Windows environment. The point data input from the user can be used to define a single planar PH quintic segments as first-order Hermite interpolants, or open or closed C2 PH quintic splines interpolating a sequence of N+1 points in the plane.