Reconstruction
Flow complex based shape reconstruction from 3D curves
Bardia Sadri and Karan Singh
We address the problem of shape reconstruction from a sparse unorganized collection of 3D curves, typically generated by increasingly popular 3D curve sketching applications. Experimentally, we observe that human understanding of shape from connected 3D curves is largely consistent, and informed by both topological connectivity and geometry of the curves. We thus employ the flow complex, a structure that captures aspects of input topology and geometry, in a novel algorithm to produce an intersection-free 3D triangulated shape that interpolates the input 3D curves. Our approach is able to triangulate highly non-planar and concave curve cycles, providing a robust 3D mesh and parametric embedding for challenging 3D curve input. Our evaluation is four-fold: we show our algorithm to match designer selected curve cycles for surfacing; we produce user acceptable shapes for a wide range of curve inputs; we show our approach to be predictable and robust to curve addition and deletion; we compare our results to prior art.
ACM Transactions on Graphics (TOG), to appear [PDF]
We address the problem of shape reconstruction from a sparse unorganized collection of 3D curves, typically generated by increasingly popular 3D curve sketching applications. Experimentally, we observe that human understanding of shape from connected 3D curves is largely consistent, and informed by both topological connectivity and geometry of the curves. We thus employ the flow complex, a structure that captures aspects of input topology and geometry, in a novel algorithm to produce an intersection-free 3D triangulated shape that interpolates the input 3D curves. Our approach is able to triangulate highly non-planar and concave curve cycles, providing a robust 3D mesh and parametric embedding for challenging 3D curve input. Our evaluation is four-fold: we show our algorithm to match designer selected curve cycles for surfacing; we produce user acceptable shapes for a wide range of curve inputs; we show our approach to be predictable and robust to curve addition and deletion; we compare our results to prior art.
ACM Transactions on Graphics (TOG), to appear [PDF]
Manifold Homotopy via the Flow Complex
Bardia Sadri
Symposium on Geometry Processing (SGP), special issue of Computer Graphics Forum, 28(5), 2009 [PDF]
Short version in proceedings of EuroCG’08 [PDF]
EuroCG Presentation Slides [PDF]
Slides from an invited talk in the SIAM Conference on Discrete Mathematics ’08 [PDF]
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Symposium on Geometry Processing (SGP), special issue of Computer Graphics Forum, 28(5), 2009 [PDF]
Short version in proceedings of EuroCG’08 [PDF]
EuroCG Presentation Slides [PDF]
Slides from an invited talk in the SIAM Conference on Discrete Mathematics ’08 [PDF]
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Geometric and Topological Guarantees for the WRAP Reconstruction Algorithm
Edgar A. Ramos and Bardia Sadri
ACM-SIAM Symposium on Discrete Mathematics (SODA), 2007 [PDF]
SODA presentation slides [PDF]
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ACM-SIAM Symposium on Discrete Mathematics (SODA), 2007 [PDF]
SODA presentation slides [PDF]
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Medial Axis Approximation and Unstable Flow Complex
Edgar A. Ramos, Joachim Giesen, and Bardia Sadri
Symposium on Computational Geometry (SoCG), 2006. [PDF]
Journal version in the SoCG’06 special issue of International Journal of Computational Geometry and Applications (IJCGA). Volume 18, Issue 6, 2009 [PDF]
SoCG presentation slides [PDF]
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Symposium on Computational Geometry (SoCG), 2006. [PDF]
Journal version in the SoCG’06 special issue of International Journal of Computational Geometry and Applications (IJCGA). Volume 18, Issue 6, 2009 [PDF]
SoCG presentation slides [PDF]
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Surface and Medial Axis Topology Through Distance Flows Induced by Discrete Samples
Bardia Sadri
PhD thesis, Department of Computer Science, University of Illinois at Urbana-Champaign, Edgar A. Ramos, Adviser, 2006 [PDF]
PhD defense slides [PDF]
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PhD thesis, Department of Computer Science, University of Illinois at Urbana-Champaign, Edgar A. Ramos, Adviser, 2006 [PDF]
PhD defense slides [PDF]
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Critical Point of the Distance to an ε-Sampling of a Surface and Flow-Complex-Based Surface Reconstruction
Tamal K. Dey, Joachim Giesen, Edgar A. Ramos, and Bardia Sadri
Symposium on Computational Geometry (SoCG), 2005 [PDF] Journal version in the SoCG’05 special issue of International Journal of Computational Geometry and Applications (IJCGA) (2008) 18(1/2) 29-61 [PDF]
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Symposium on Computational Geometry (SoCG), 2005 [PDF] Journal version in the SoCG’05 special issue of International Journal of Computational Geometry and Applications (IJCGA) (2008) 18(1/2) 29-61 [PDF]
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