Abstract:

The T-Bézier curve surfaces are all tensor form. In order to further study T-Bézier basis in non-polynomial space and perfect the theory of triangular domain, a kind of trigonometric basis for trigonometric polynomial space of order 4 over triangular domain was proposed. The constructed basis over triangular domain was  proved to have nice properties such as positivity, partition of unity, symmetry, boundary representation and linear independence and so on. Some properties of the corresponding surface are also proved. Finally, some applications of the proposed T-Bézier surface are shown.

Key words: computer aided geometric design; T-Bézier basis; trigonometric polynomial; triangular domain