一种基于OpenGL和C++的函数库，用于在一大类扩展Chebyshev空间中进行曲线和曲面建模
An OpenGL and C++ based function library for curve and surface modeling in a large class of extended Chebyshev spaces
AI总结：
本文提出了一种平台无关的多线程函数库，能够生成、求导和渲染用户指定的扩展Chebyshev空间的普通基和标准化B基，同时支持生成和可视化多种B曲线和张量积B曲面，并实现维度提升、B曲线和曲面的细分以及基变换方法。
摘要：
我们提出了一种平台无关的多线程函数库，提供数据结构以生成、求导和渲染用户指定的扩展Chebyshev（EC）空间的普通基和标准化B基。该EC空间包含常数且可与常系数齐次线性微分方程的解空间相一致，定义在足够小的区间上。利用获得的标准化B基，该库还能生成、（部分）求导、修改和可视化大量所谓的B曲线和张量积B曲面。此外，该库还实现了用于执行维度提升、通过类似于de Casteljau的B算法进行B曲线和B曲面细分，以及通过普通基生成任意积分曲线和曲面的B表示的基变换方法。无论所用EC空间的代数、指数、三角或混合类型，所提出的库在数值上都稳定且高效，直到合理的维度数，并可能对近似理论、计算机辅助几何设计、计算机图形学、等参数化分析和数值分析领域的学者和工程师有帮助。
英文摘要：
We propose a platform-independent multi-threaded function library that provides data structures to generate, differentiate and render both the ordinary basis and the normalized B-basis of a user-specified extended Chebyshev (EC) space that comprises the constants and can be identified with the solution space of a constant-coefficient homogeneous linear differential equation defined on a sufficiently small interval. Using the obtained normalized B-bases, our library can also generate, (partially) differentiate, modify and visualize a large family of so-called B-curves and tensor product B-surfaces. Moreover, the library also implements methods that can be used to perform dimension elevation, to subdivide B-curves and B-surfaces by means of de Casteljau-like B-algorithms, and to generate basis transformations for the B-representation of arbitrary integral curves and surfaces that are described in traditional parametric form by means of the ordinary bases of the underlying EC spaces. Independently of the algebraic, exponential, trigonometric or mixed type of the applied EC space, the proposed library is numerically stable and efficient up to a reasonable dimension number and may be useful for academics and engineers in the fields of Approximation Theory, Computer Aided Geometric Design, Computer Graphics, Isogeometric and Numerical Analysis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
