An orthogonal basis for the hyperbolic hybrid polynomial space

Motivated by the wide usage of the Tchebyshev basis and Legendre basis in the algebra polynomial space, we construct an orthogonal basis with the properties of the H-Bezier basis in the hyperbolic hybrid polynomial space, which is similar to the Legendre basis and holds remarkable properties. Moreover, we derive the transformation matrices that map the H-Bezier basis and the orthogonal basis forms into each other. An example for approximating the degree reduction of the H-Bezier curves is sketched to illustrate the utility of the orthogonal basis.