Approximate Subdivision Surface Evaluation in the Language of Linear Algebra

Michael Driscoll
Computer Science Division, UC Berkeley
UC Berkeley Report, 2012


   title={Approximate Subdivision Surface Evaluation in the Language of Linear Algebra},

   author={Driscoll, M. and others},



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We present an interpretation of approximate subdivision surface evaluation in the language of linear algebra. Specifically, vertices in the refined mesh can be computed by left-multiplying the vector of control vertices by a sparse matrix we call the subdivision operator. This interpretation is rather general: it applies to any level of subdivision, it holds for many common subdivision schemes (including Catmull-Clark and Loop), it can be extended to support hierarchical edit operations, and it subsumes sharpness and feature-adaptive schemes. Furthermore, our interpretation encourages high-performance implementations built on numerical linear algebra libraries. It is most applicable to subdivision of static control meshes undergoing deformation, i.e. animation, in which case it allows users to trade-off time-to-first-frame and framerate. We implemented our strategy as an extension to Pixar’s production subdivision code and observed speedups of 2x to 14x using both multicore CPUs and GPUs.
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