Haar Wavelets Supported on Triangles and Tetrahedra: a Multiwavelet Approach

Abstract

The usual dyadic tiling D of R2 induces a natural triangular tiling of R2, just by dividing each 2-cube Q E D into two rectangular triangles. The only difficulty in leading with these
geometrical objects is that, even for triangles in the same level, we can not generally obtain any of them by integer translation of a fixed one. Our approach to this situation would be to introduce a new basic transform aside from the usual dilation and integer translation, namely, a "spin". Our aim in this note is to show that the multiwavelet approach solves the problem neatly using only the two traditional transforms.