Abstract
Using the normalized B-bases of vector spaces of trigonometric and hyperbolic polynomials of finite order, we specify control point configurations for the exact description of the zeroth and higher order (mixed partial) derivatives of integral curves and (hybrid) multivariate surfaces determined by coordinate functions that are exclusively given either by traditional trigonometric or hyperbolic polynomials in each of their variables. Based on homogeneous coordinates and central projection, we also propose algorithms for the control point and weight based exact description of the zeroth order (partial) derivative of the rational counterpart of these integral curves and surfaces. The core of the proposed modeling methods relies on basis transformation matrices with entries that can be efficiently obtained by order elevation.
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