Abstract
In a previous work we introduced a construction designed 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 introduces diagrams and diagram
interactions to replace matricies and matrix multiplication. The diagrams we
use are patterns of value-labeled nodes, one type of diagram corresponding to
each row or column of one of the matricies of a biorthogonal system. All types
of diagrams used in the construction are defined on a common mesh of the
multiresolution.
Notes
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