- Author:
- Jean Elaine Schweitzer,
- Chairperson:
- Anthony D. Derose
Subdivision surfaces are a convenient representation for modeling objects of arbitrary topological type. In this dissertation, we investigate the analysis of a piecewise smooth subdivision scheme, and we apply the scheme to reconstruct objects from non-uniformly sampled data points.
Defined as the limit of repeated refinement of a mesh of 3D control points, subdivision surfaces require analysis to establish convergence to a well-defined, tangent plane smooth $(G\sp1)$ surface. Recent research has focused on analyzing smooth surface schemes in which the rules are symmetrical about each vertex and edge. However, a scheme for creating surfaces with sharp features has rules that do not exhibit this symmetry. In this dissertation, we extend the use of eigenanalysis and characteristic maps to analyze a piecewise smooth subdivision scheme that generalizes quartic triangular B-spline surfaces.
Subdivision surfaces are suitable for optimized surface fitting and have been used in the reconstruction of objects from 3D data. Previous methods have created accurate representations of objects from dense and uniform data samples. As a practical low cost alternative, we present an algorithm for creating a subdivision surface from data sampled uniformly along closed curves and non-uniformly within the regions they enclose.
Cited By
DeRose T, Kass M and Truong T Subdivision Surfaces in Character Animation Seminal Graphics Papers: Pushing the Boundaries, Volume 2, (801-810)- Altenhofen C, Müller J, Weber D, Stork A and Fellner D Direct limit volumes Proceedings of the 26th Pacific Conference on Computer Graphics and Applications: Short Papers, (77-80)
- Abbas A A less-constrained solution to curve interpolation by Catmull-Clark subdivision surfaces Proceedings of the 2009 Computer Graphics International Conference, (63-72)
- Cheng F, Fan F, Lai S, Huang C, Wang J and Yong J (2009). Loop subdivision surface based progressive interpolation, Journal of Computer Science and Technology, 24:1, (39-46), Online publication date: 1-Jan-2009.
- Ling R, Wang W and Yan D Fitting sharp features with loop subdivision surfaces Proceedings of the Symposium on Geometry Processing, (1383-1391)
- Thomaszewski B, Wacker M and Straßer W A consistent bending model for cloth simulation with corotational subdivision finite elements Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation, (107-116)
- Zorin D Modeling with multiresolution subdivision surfaces ACM SIGGRAPH 2006 Courses, (30-50)
- Lanquetin S, Raffin R and Neveu M Generalized SCODEF deformations on subdivision surfaces Proceedings of the 4th international conference on Articulated Motion and Deformable Objects, (132-142)
- Severn A and Samavati F Fast intersections for subdivision surfaces Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I, (91-100)
- Levin A The importance of polynomial reproduction in piecewise-uniform subdivision Proceedings of the 11th IMA international conference on Mathematics of Surfaces, (272-307)
- Nasri A, Abbas A and Hasbini I Skinning Catmull-Clark Subdivision Surfaces with Incompatible Cross-Sectional Curves Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
- Loch B, Belward J and Hanan J Boundary treatment for virtual leaf surfaces Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia, (261-262)
- Litke N, Levin A and Schröder P Fitting subdivision surfaces Proceedings of the conference on Visualization '01, (319-324)
- DeRose T Subdivision surfaces in feature films Mathematical Methods for Curves and Surfaces, (73-79)
- Biermann H, Levin A and Zorin D Piecewise smooth subdivision surfaces with normal control Proceedings of the 27th annual conference on Computer graphics and interactive techniques, (113-120)
- Mandal C, Qin H and Vemuri B (2000). Dynamic Modeling of Butterfly Subdivision Surfaces, IEEE Transactions on Visualization and Computer Graphics, 6:3, (265-287), Online publication date: 1-Jul-2000.
- Gregory A, Ehmann S and Lin M inTouch Proceedings of the IEEE Virtual Reality 2000 Conference
- Schröder P Opportunities for Subdivision-Based Multiresolution Modeling Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
- Qin K and Wang H Eigenanalysis and Continuity of Non-Uniform Doo-Sabin Surfaces Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
- Markosian L, Cohen J, Crulli T and Hughes J Skin Proceedings of the 26th annual conference on Computer graphics and interactive techniques, (393-400)
- Levin A Interpolating nets of curves by smooth subdivision surfaces Proceedings of the 26th annual conference on Computer graphics and interactive techniques, (57-64)
- Khodakovsky A and Schröder P Fine level feature editing for subdivision surfaces Proceedings of the fifth ACM symposium on Solid modeling and applications, (203-211)
- Mandal C, Qin H and Vemuri B A novel FEM-based dynamic framework for subdivision surfaces Proceedings of the fifth ACM symposium on Solid modeling and applications, (191-202)
- Lee A, Sweldens W, Schröder P, Cowsar L and Dobkin D MAPS Proceedings of the 25th annual conference on Computer graphics and interactive techniques, (95-104)
- DeRose T, Kass M and Truong T Subdivision surfaces in character animation Proceedings of the 25th annual conference on Computer graphics and interactive techniques, (85-94)
- Qin H, Mandal C and Vemuri B (1998). Dynamic Catmull-Clark Subdivision Surfaces, IEEE Transactions on Visualization and Computer Graphics, 4:3, (215-229), Online publication date: 1-Jul-1998.
- Zorin D, Schröder P and Sweldens W Interactive multiresolution mesh editing Proceedings of the 24th annual conference on Computer graphics and interactive techniques, (259-268)
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