  Extended Chebyshev spaces that also comprise the constants represent large
families of functions that can be used in real-life modeling or engineering
applications that also involve important (e.g. transcendental) integral or
rational curves and surfaces. Concerning computer aided geometric design, the
unique normalized B-bases of such vector spaces ensure optimal shape preserving
properties, important evaluation or subdivision algorithms and useful shape
parameters. Therefore, we propose global explicit formulas for the entries of
those transformation matrices that map these normalized B-bases to the
traditional (or ordinary) bases of the underlying vector spaces. Then, we also
describe general and ready to use control point configurations for the exact
representation of those traditional integral parametric curves and (hybrid)
surfaces that are specified by coordinate functions given as (products of
separable) linear combinations of ordinary basis functions. The obtained
results are also extended to the control point and weight based exact
description of the rational counterpart of these integral parametric curves and
surfaces. The universal applicability of our methods is presented through
polynomial, trigonometric, hyperbolic or mixed extended Chebyshev vector
spaces.
