Much work has been done in finding duals and wavelets for a single scaling function on a triangulation (see , ,  among others). The CBC algorithm allows the construction of duals with arbitrary approximation order at the expense of a larger support. This is an independent approach to the construction of a dual mask to the piecewise linear "hat" function on a uniform triangulation with a focus on maintaining the same hexagonal support. The associated wavelet masks are also constructed with only slightly larger supports.
A Short-support Dual Mask to the Piecewise Linears on a Uniform TriangulationApproximation Theory X: Wavelets, Splines, and Applications (2002)
Citation InformationBruce Kessler, "A Short-support Dual Mask to the Piecewise Linears on a Uniform Triangulation", Approximation Theory X: Wavelets, Splines, and Applications, edited by C. K. Chui, L. L. Schumaker, and J. Stockler, Vanderbilt University Press, 323-332 (2002).