Grasshopper mesh
Matthias Nießner, Charles Loop, Mark Meyer, Tony DeRose, " Feature Adaptive GPU Rendering of Catmull-Clark Subdivision Surfaces", ACM Transactions on Graphics Volume 31 Issue 1, January 2012, doi: 10.1145/2077341.2077347, demo.Remesh to quad-dominant meshes from your surfaces, solids, meshes. IEEE Transactions on Visualization and Computer Graphics. The power of Rhino and Grasshopper in the Autodesk Revit environment. "Real-Time Creased Approximate Subdivision Surfaces with Displacements" (PDF). "Approximating Catmull-Clark subdivision surfaces with bicubic patches" (PDF). Proceedings of the 25th annual conference on Computer graphics and interactive techniques - SIGGRAPH '98. "Subdivision surfaces in character animation" (PDF). ^ "Pixar's OpenSubdiv V2: A detailed look".In Martin Watt Erwin Coumans George ElKoura et al. "OpenSubdiv: Interoperating GPU Compute and Drawing". CS1 maint: archived copy as title ( link) "Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values" (PDF). "Recursively generated B-spline surfaces on arbitrary topological meshes" (PDF). This method reformulates the recursive refinement process into a matrix exponential problem, which can be solved directly by means of matrix diagonalization.
This can be accomplished by means of the technique of Jos Stam (1998). The limit surface of Catmull–Clark subdivision surfaces can also be evaluated directly, without any recursive refinement. After one iteration, the number of extraordinary points on the surface remains constant. It can be shown that the limit surface obtained by this refinement process is at least C 1 continuity). The arbitrary-looking barycenter formula was chosen by Catmull and Clark based on the aesthetic appearance of the resulting surfaces rather than on a mathematical derivation, although they do go to great lengths to rigorously show that the method converges to bicubic B-spline surfaces. Repeated subdivision results in meshes that are more and more rounded. less "jagged" or "pointy") than the old mesh. The new mesh will generally look "smoother" (i.e. The new mesh will consist only of quadrilaterals, which in general will not be planar.