Diagrammatic tools for generating biorthogonal multiresolutions


Elsewhere we have introduced a construction to produce biorthogonal multiresolutions 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 presents the construction for regular meshes using diagrams (stencils, masks) and interactions between diagrams to replace matrices and matrix multiplication. Regular triangular meshes with butterfly subdivision and a variant of Loop subdivision due to Litke, et al. are used as examples.

International Journal of Shape Modeling (World Scientific Publishing Company)
Faramarz F. Samavati

My research interests include Computer Graphics, Geometric Modeling, Visualization, and Digital Earth.