A New Approach to the Construction of Subdivision Algorithms: The MATLAB Software Package
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Date
2025-07-15
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This software package creates subdivision matrices for generalized quadratic and cubic B-spline subdivision. The algorithms produce subdivision matrices for subdivision surfaces as well as subdivision volumes. The subdivision matrices define refinement rules for arbitrary combinatorial structures. Irregular points and edges are supported in all cases.
All generated subdivision matrices have a valid eigenstructure: they have a subdominant eigenvalue of 1/2 with multiplicity two (for subdivision surfaces) and multiplicity three (for subdivision volumes). Moreover the central part of the structure forms a convex polytope (or in the cubic case, a set of cubes whose outer faces form a central polytope).
The software package also includes a number of additional functions, such as plotting the evaluated B-spline elements or uniformly refining structures of any size.
Keywords
subdivision, matrix, refinement, software, Matlab, cubic, quadratic, initial element, bivariate, trivariate, Doo-Sabin, Catmull-Clark, B-spline, uniform, subdominant eigenvalue 1/2, polyhedron, polytope, convex, prism, trapezohedron, irregular, extraordinary vertex, planar, 3-connected, Steinitz, Koebe-Andreev-Thurston, plot, package, manual, volumetric, surface, cube, lattice, arbitrary mesh, free form, CAD, subdivision algorithms, B-spline subdivision, geometric modeling, applied mathematics, mesh refinement, quadratic B-splines, cubic B-splines, convex polytopes, Colin-de-Verdière matrices, matrix exponentials, characteristic map, refinement rules, tensor-product structure, subdivision surfaces, subdivision volumes, computer-aided geometric design, volumetric meshing, hexahedral meshes, algorithmic construction, open source software, CC-BY licensed code, Alexander Dietz, TU Darmstadt, new subdivision method, generalized B-spline algorithm, Catmull-Clark alternative, volumetric subdivision theory, eigenvalue-based mesh refinement, geometric structure preservation, smooth surface generation, smooth volume generation
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Except where otherwise noted, this license is described as CC BY 4.0 - Attribution 4.0 International