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Efficient, fair interpolation using Catmull-Clark surfaces
Abstract
We describe an efficient method for constructing a smooth surface that interpolates the vertices of a mesh of arbitrary topological type. Normal vectors can also be interpolated at an arbitrary subset of the vertices. The method improves on existing interpolation techniques in that it is fast, robust and general. Our approach is to compute a control mesh whose Catmull-Clark subdivision surface interpolates the given data and minimizes a smoothness or "fairness" measure of the surface. Following Celniker and Gossard, the norm we use is based on a linear combination of thin-plate and membrane energies. Even though Catmull-Clark surfaces do not possess closed-form parametrizations, we show that the relevant properties of the surfaces can be computed efficiently and without approximation. In particular, we show that (1) simple, exact interpolation conditions can be derived, and (2) the fairness norm and its derivatives can be computed exactly, without resort to numerical integration.
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Cites
Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505
Cited by
Multiresolution analysis for surfaces of arbitrary topological type
Lounsbery, M., DeRose, T. D., & Warren, J. (1997) · ACM Transactions on Graphics · doi:10.1145/237748.237750 · Cited by 760
Self-citationInterpolating Subdivision for meshes with arbitrary topology
Zorin, D., Schröder, P., & Sweldens, W. (1996) · Proceedings of the 23rd annual conference on Computer graphics and interactive techniques · doi:10.1145/237170.237254 · Cited by 537
Curve and surface smoothing without shrinkage
Taubin, G. (2002) · Proceedings of IEEE International Conference on Computer Vision · doi:10.1109/iccv.1995.466848 · Cited by 420
An anthropometric face model using variational techniques
DeCarlo, D., Metaxas, D., & Stone, M. (1998) · Proceedings of the 25th annual conference on Computer graphics and interactive techniques - SIGGRAPH '98 · doi:10.1145/280814.280823 · Cited by 327
Metadata
- Authors
- Halstead, M., Kass, M., & DeRose, T.
- Venue
- Proceedings of the 20th annual conference on Computer graphics and interactive techniques
- Publisher
- ACM
- Published
- 1993-09
- Pages
- 35-44
- OpenAlex
- W2056816721
- Cited by
- 393
- References
- 1
- FWCI
- 20.95
- Type
- conference paper
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Efficient, fair interpolation using Catmull-Clark surfaces. https://app.cochat.ai/papers/10.1145/166117.166121
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- Halstead, M., Kass, M., & DeRose, T. (1993). Efficient, fair interpolation using Catmull-Clark surfaces. Proceedings of the 20th annual conference on Computer graphics and interactive techniques. https://doi.org/10.1145/166117.166121
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