Tuned Ternary Quad Subdivision
نویسندگان
چکیده
A well-documented problem of Catmull and Clark subdivision is that, in the neighborhood of extraordinary point, the curvature is unbounded and fluctuates. In fact, since one of the eigenvalues that determines elliptic shape is too small, the limit surface can have a saddle point when the designer’s input mesh suggests a convex shape. Here, we replace, near the extraordinary point, CatmullClark subdivision by another set of rules derived by refining each bi-cubic Bspline into nine. This provides many localized degrees of freedom for special rules so that we need not reach out to, possibly irregular, neighbor vertices when trying to improve, or tune the behavior. We illustrate a strategy how to sensibly set such degrees of freedom and exhibit tuned ternary quad subdivision that yields surfaces with bounded curvature, nonnegative weights and full contribution of elliptic and hyperbolic shape components.
منابع مشابه
Ternary subdivision for quadrilateral meshes
Abstract. A well-documented problem of Catmull and Clark subdivision surfaces is that, in the neighborhood of extraordinary points, the curvature is unbounded and fluctuates. In fact, since one of the eigenvalues that determines elliptic shape is too small, the limit surface can have a saddle point when the designer’s input mesh suggests a convex shape. Here, we replace, near the extraordinary ...
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