An OpenGL and C++ based function library for curve and surface modeling in a large class of extended Chebyshev spaces
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Applying original and existing theoretical results, we propose a platform-independent multi-threaded function library that provides data structures to generate, differentiate and render both the ordinary basis and the non-negative normalized B-basis of an arbitrary extended Chebyshev (EC) space that comprises the constants and can be identified with the solution space of a user-defined constant-coefficient homogeneous linear differential equation. Using the obtained non-negative 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 general order elevation, to subdivide B-curves and B-surfaces by means of general de Casteljau-like B-algorithms, and to generate general basis transformations for the control point based exact description 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.
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