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T-splines. Speaker : 周 联 2007.12.12. Mian works. Sederberg,T.W., Zheng,J.M., Bakenov,A., Nasri,A., T-splines and T-NURCCS . SIGGRAPH 2003. Sederberg,T.W., David L. C., Zheng, J.M., Lyche,T., T-spline Simplication and Local Refinement. SIGGRAPH 2004. Authors. Tom Lyche ,
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T-splines Speaker: 周 联 2007.12.12
Mian works • Sederberg,T.W., Zheng,J.M., Bakenov,A., Nasri,A., T-splines and T-NURCCS. SIGGRAPH 2003. • Sederberg,T.W., David L. C., Zheng, J.M., Lyche,T., T-spline Simplication and Local Refinement. SIGGRAPH 2004
Authors • Tom Lyche, University of Oslo • David L. Cardon, Brigham Young University • Thomas W. Sederberg, Brigham Young University • Jianmin Zheng, Nanyang Technological University • Almaz Bakenov, Embassy of Kyrgyz Republic Washington, D.C. • Ahmad Nasri, American University of Beirut
Other works • Song W.H., Yang X.N., Free-form deformation with weighted T-spline, The Visual Computer 2005 • Xin Li, Jiansong Deng, Falai Chen, Dimensions of Spline Spaces Over 3D Hierarchical T-Meshes, Journal of Information and Computational Science, Vol.3, No.3, 487--501, 2006. (EI) • Zhangjing Huang, Jiansong Deng, Yuyu Feng, and Falai Chen, New Proof of Dimension Formula of Spline Spaces over T-meshes via Smoothing Cofactors, Journal of Computational Mathematics, Vol.24, No.4, 501--514, 2006 • Jiansong Deng, Falai Chen, Yuyu Feng, Dimensions of spline spaces over T-meshes, Journal of Computational and Applied Mathematics, Vol.194, No.2, 267--283, 2006. • Xin Li, Jiansong Deng, Falai Chen, Surface Modeling with Polynomial Splines over Hierarchical T-meshes, accepted by CAD/CG'2007, and published on The Visual Computer, 2007. • Jiansong Deng, Falai Chen, etal., Polynomial splines over hierarchical T-meshes, submitted to Graphical Models, 2006.10
What are T-Splines? • T-Splines: a generalization of non-uniform B-spline surfaces "T-Splines are the next thing...They have opened up possibilities to work with surfaces that were simply impossible before." -- Eric Allen, Production Manager, DAZ http://www.daz3d.com/
Why use T-Splines? • Add detail only where you need it • Create even the most complex shapes as a single, editable surface • Create natural edge flow and non-rectangular topology www.tsplines.com
Why use T-Splines? • Fits into your Workflow
T-Splines vs. NURBS • Reduce the number of superfluous control points.
T-Splines vs. NURBS • Remove unwanted ripples.
T-Splines vs. NURBS • Remove gap
Other methods • hierarchical B splines • D. Forsey, R.H. Bartels, Hierarchical B-spline refinement, Comput. Graphics 22 (4) (1988) 205–212 • a spline space over a more general T-mesh, where crossing, T-junctional, and L-junctional vertices are allowed. • F. Weller, H. Hagen, Tensor-product spline spaces with knot segments, in: M. Dalen, T. Lyche, L.L. Schumaker (Eds.), Mathematical Methods for Curves and Surfaces, Vanderbilt University Press, Nashville, TN, 1995, pp. 563–572.
Polar Form Definition: Examples:
Polar Form Definition: Ramshaw, L. 1989. Blossoms are polar forms. Computer Aided Geometric Design 6, 323-358.
PB-splines • whose control points have no topological relationship with each other • it is point based instead of grid based
T-mesh • A T-spline is a PB-spline by means of a control grid called a T-mesh.
T-mesh • Infer knot vectors from T-grid
Merge B-splines into a T-spline • Traditional way • Use cubic NURSSes (SIGGRAPH 98)
A problem • A local knot insertion sometimes requires that other local knot insertions must be performed. Are there cases in which these prerequisites cannot all be satisfied?
T-spline Spaces • T-spline Spaces : the set of all T-splines that have the same T-mesh topology, knot intervals, and knot coordinate system.
Compared with old one • always work • requires far fewer unrequested control point insertions
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