Computer Aided Geometric Design
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Dual contouring of hermite data
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
A realtime GPU subdivision kernel
ACM SIGGRAPH 2005 Papers
Integration of CAD and boundary element analysis through subdivision methods
Computers and Industrial Engineering
ACM Transactions on Graphics (TOG)
Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods
Computer Graphics Forum
Uniform interpolation curves and surfaces based on a family of symmetric splines
Computer Aided Geometric Design
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In this paper, we describe a method for exact evaluation of a limit mesh defined via subdivision and its associated tangent vectors on a uniform grid of any size. Other exact evaluation technique either restrict the grids to have subdivision sampling and are, hence, exponentially increasing in size or make assumptions about the underlying surface being piecewise polynomial (Stam's method is a widely used technique that makes this assumption). As opposed to Stam's technique, our method works for both polynomial and non-polynomial schemes. The values for this exact evaluation scheme can be computed via a simple system of linear equation derived from the scaling relations associated with the scheme or, equivalently, as the dominant left eigenvector of an upsampled subdivision matrix associated with the scheme. To illustrate one possible application of this method, we demonstrate how to generate adaptive polygonalizations of a non-polynomial quad-based subdivision surfaces using our exact evaluation method. Our tessellation method guarantees a water-tight tessellation no matter how the surface is sampled and is quite fast. We achieve tessellation rates of over 33.5 million triangles/second using a CPU implementation.