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Extended Chebyshev spaces that also comprise the constants represent largefamilies of functions that can be used in real-life modeling or engineeringapplications that also involve important (e.g. transcendental) integral orrational curves and surfaces. Concerning computer aided geometric design, theunique normalized B-bases of such vector spaces ensure optimal shape preservingproperties, important evaluation or subdivision algorithms and useful shapeparameters. Therefore, we propose global explicit formulas for the entries ofthose transformation matrices that map these normalized B-bases to thetraditional (or ordinary) bases of the underlying vector spaces. Then, we alsodescribe general and ready to use control point configurations for the exactrepresentation of those traditional integral parametric curves and (hybrid)surfaces that are specified by coordinate functions given as (products ofseparable) linear combinations of ordinary basis functions. The obtainedresults are also extended to the control point and weight based exactdescription of the rational counterpart of these integral parametric curves andsurfaces. The universal applicability of our methods is presented throughpolynomial, trigonometric, hyperbolic or mixed extended Chebyshev vectorspaces.

Control point based exact description of curves and surfaces in extended Chebyshev spaces