Explicit construction of W-system over triangular domain

In digital geometry, triangular mesh models have been widely used recently to represent an object. To process triangular mesh models orthogonal function systems over triangular domain have become more and more important. The W-system of degree k is a new hybrid orthogonal function system consisting of piecewise polynomials of degree k. Univariate W-system has been constructed in direct way, whereas bivariate W-system over triangular domains has been constructed recursively. In this paper, we introduce an alternative method for constructing the W-system over triangular domain directly, which is more easily understood and less time consuming. As an example, the concrete expression of W-system of degree 2 is presented. Illustrative example is included to demonstrate the validity and applicability of this new system. It is because W-system is a hybrid orthogonal function system with both smooth functions and functions with jumps that the surfaces or a group of surfaces can be accurately reconstructed via corresponding W-series without Gibbs phenomenon.