Diagrammatic Tools for Generating Biorthogonal Multiresolutions.

In a previous work (1) we introduced a construction designed to produce biorthogonal multiresolu- tions from given subdivisions. This construction was formulated in matrix terms, which is appropriate for curves and tensor-product surfaces. For mesh surfaces of non-tensor connectivity, however, matrix notation is inconvenient. This work introduces diagrams and diagram interactions to replace matrices and matrix multiplication for regular meshes. Regular triangular meshes are used as a model. The diagrams we use are patterns of value-labeled nodes, one type of diagram corresponding to each row or column of one of the matrices of a biorthogonal system. All types of diagrams used in the construc- tion are dened on a common mesh of the multiresolution.