A constructive approach to triangular trigonometric patches

09/18/2013
by   Ágoston Róth, et al.
0

We construct a constrained trivariate extension of the univariate normalized B-basis of the vector space of trigonometric polynomials of arbitrary (finite) order n defined on any compact interval [0,α], where α is a fixed (shape) parameter in (0,π). Our triangular extension is a normalized linearly independent constrained trivariate trigonometric function system of dimension 3n(n+1)+1 that spans the same vector space of functions as the constrained trivariate extension of the canonical basis of truncated Fourier series of order n over [0,α]. Although the explicit general basis transformation is yet unknown, the coincidence of these vector spaces is proved by means of an appropriate equivalence relation. As a possible application of our triangular extension, we introduce the notion of (rational) triangular trigonometric patches of order n and of singularity free parametrization that could be used as control point based modeling tools in CAGD.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset