eloraiby / subdivexacteval

Exact Evaluation of Catmull-Clark Subdivision limit surface

This repo is a simple implementation of the algorithm implemented by Jos Stam in his paper:

Exact Evaluation of Catmull-Clark Subdivision Surfaces at Arbitrary Parameter Values, Jos Stam, SIGGRAPH 98 Conference Proceedings, Annual Conference Series, July 1998

http://www.dgp.toronto.edu/people/stam/reality/Research/pdf/sig98.pdf

This implementation loads the precomputed eigen structures downloaded from here.

Usage

This is implemented as a C# Class Library project, which when compiled produces a DLL. The evaluation of the limit surface patches can be done by calling the method EigenEvalStructure.EvaluateSurface.

Parameters:
* double[] controlPointCoords: 
Array of 2*N+8 control points where N is the valence of
this patch, sorted in the order described in the Stam's paper. The
coordinates of the control points should be packed into the flat array
in the form - [x1, x2, x3, x4, ... y1, y2, y3, y4, ... z1, z2, z3, z4 ...]
* double[][] uvParams:
This should be a nested array, representing the u,v coordinates of the
points to be evalutated. The inner arrays are expected to be of length 2.
* EvaluationType evalType:
This enumeration tells the function what property to evaluate at the
given parameters. See the documentation of this enumeration for more details.
* double uvTolerance:
This will be used as the minimum value of u and v since the evaluation
at an extraordinary points is not possible (see the paper). If not
supplied, then the default value is used defined as a const member
variable (1e-12).

Return Value:
If the evalType is set to evaluate the position (or tangent or
normal), then a flat array of coordinates of the evaluated points (or
normal vectors or tangent vectors) is returned in the form - [x1, y1,
z1, x2, y2, z2 ...].

The image below shows the results of this method, when tested on an extraordinary patch near the vertex of a cube (valence 3, and visualized in Rhinoceros 6).It shows the points and normals of the patch in green, and the limit surface (generated using the Subdivision command of Rhino) for reference in red.

Acknowledgements

All thanks to Jos Stam, obviously for the original paper, but also for helping me with some details of this implementation.