Luiz Velhos Legacy on Geometry Processing Prof. Afonso Paiva - - PowerPoint PPT Presentation
Luiz Velhos Legacy on Geometry Processing Prof. Afonso Paiva ICMC-USP, S ao Carlos, SP, Brazil apneto@icmc.usp.br Prof. Marcelo Ferreira Siqueira DMAT-UFRN, Natal, RN, Brazil mfsiqueira@mat.ufrn.br Outline The 80's The 90's
ICMC-USP, S˜ ao Carlos, SP, Brazil apneto@icmc.usp.br
DMAT-UFRN, Natal, RN, Brazil mfsiqueira@mat.ufrn.br
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Geometry processing ≈ geometric modeling + computational geometry
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Geometry processing ≈ geometric modeling + computational geometry
ezier and B-spline surfaces, NURBS).
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Geometry processing ≈ geometric modeling + computational geometry
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Geometry processing ≈ geometric modeling + computational geometry
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Luiz Velho was involved with the animation industry and started working with geometric modeling in the late 80’s and early 90’s. More precisely, he got inter- ested in a yet unexplored mathematical model for curves, surfaces, and solids:
[Velho, Gomes and de Figueiredo, 2002]
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How to tessellate implicit surfaces?
[Lorensen and Cline, SIGGRAPH, 1987]
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How to tessellate implicit surfaces?
[Lorensen and Cline, SIGGRAPH, 1987]
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How to tessellate implicit surfaces?
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How to tessellate implicit surfaces?
Velho. Adaptive polygonization of implicit surfaces using simplicial decomposition and boundary constraints. Proceedings of the Eurographics’90, pages 125-136, September 1990.
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First Brazilian to publish a paper in the prestigious Eurographics conference!
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How to tessellate implicit surfaces?
[Velho, JGT, 1996]
ing conformal triangle meshes more difficult. But, what if you sole purpose is render- ing?
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How to tessellate implicit surfaces?
[Velho, JGT, 1996]
ple algorithm: Luiz Velho. Simple and efficient polygonization of implicit surfaces. Journal
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Revisiting the tessellation problem for parametric surfaces...
tessellating parametric surfaces: L. Velho and L. H. de Figueiredo. Optimal adaptive ap- proximation of parametric surfaces. Proceedings of SIBGRAPI’96, pages 127-133, October 1996.
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What if the purpose is representation conversion?
representation: L. Velho and J. Gomes. Approximate conversion of parametric to implicit
Misha Kazhdan (Jonhs Hopkins University) adopted a similar idea for Poisson surface reconstruction from point cloud more than 10 years later (SGP 2006).
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Luiz Velho received his Ph.D. degree from the University of Toronto in 1994, but he was already a established researcher and world-renowned expert in computer animation before starting his Ph.D. studies. His Ph.D. advisor, Dimetri Terzopoulos, was a pioneer in com- bining techniques from computer graphics, image processing, and computer vision to solve problems in each of these areas. Luiz Velho is likely to have inherited the same holistic view from him!
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Tessellating both implicit and parametric surfaces with a single algorithm:
both implicit and parametric surfaces: L. Velho, L. H. de Figueiredo and J. Gomes. A Unified Approach for Hierarchical Adaptive Tessellation of Surfaces. ACM ToG, 18(4): 329- 360, 1999.
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Mesh processing demanded efficient data structures and mesh operators. Luiz Velho was
and adaptive meshes, which combined elements from combinatorial topology and graph theory.
At this point in time the graphics community started focusing on polygonal meshes, and what we mean today by geometry processing did not exist back then. The Stanford’s Digital Michelangelo Project opened up a huge window of research opportunities. It was time to solve problems such as mesh simplification, mesh compression, mesh transmission, and mesh smoothing, mesh reconstruction from point cloud, and noise removal in the graphics context.
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The mesh processing work developed by Luiz Velho from the late 90’s until 2004 was influ- enced by some ideas from another hot research topic in the graphics community: subdivision surfaces.
Catmull-Clark, 1978 Loop, 1987 Pixar, 1997
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The mesh processing work developed by Luiz Velho from the late 90’s until 2004 was influ- enced by some ideas from another hot research topic in the graphics community: subdivision surfaces.
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The paper co-authored with Jonas Gomes in 1999, (L. Velho and J. Gomes. Quasi 4-8 Subdivi- sion Surfaces, Proceedings of SIBGRAPI ’99, pages 7-19, Campinas, SP, Brazil), introduced the 4-8 meshes:
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and a refinement scheme:
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The previous regular refinement scheme was modified to give rise to a semi-regular and hier- archical scheme, which allowed for the extraction of conformal variable-resolution meshes based on spatially varying adaptation functions (see paper L. Velho. Semi-regular 4-8 refine- ment and box spline surfaces. Proceedings of the SIBGRAPI 2000, pages 131-138, Gramado, RS, Brazil).
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The implementation of the algorithms in the papers showed before was made possible by the use of a powerful data structure for representing multi-triangulations (the so-called 4-k meshes).
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In 2001, Luiz Velho described an algorithm for mesh simplification which is significantly influenced by the 4-8 meshes. Simplification can be seen as the inverse of the refinement
First Brazilian to publish a paper in the SMI conference!
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The A48 data structure constitutes an improvement over all data structures available back
algorithms for mesh simplification and mesh refinement (such as QEM and progressive meshes). Most research work developed at IMPA from 2000 on were based on the A48 data structure. The original data structure was later modified to give rise to the so-called A48 data structure. The latter need not explicitly store the local operations that dynamically modify an initial mesh.
2004.
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Stellar operations: simplicity and completeness
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Stellar operations: simplicity and completeness
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First Brazilian to publish a paper in the prestigious Symposium on Geometry Processing!
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Revisiting the mesh simplification problem...
Using Probabilistic Optimization. Computer Graphics Forum, 23(4): 825-838, 2004.
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A paper from 2001 gave a proof that 4-8 subdivision surfaces are C4- continuous everywhere, except at extraordinary vertices where they are C1- continuous: L. Velho and D. Zorin. 4-8 Subdivision. CAGD, 18(5):397–427, 2001.
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In this moment, discrete differential geometry and spectral mesh processing become popular in computer graphics, and a modern book about geometry processing is released .
[L´ evy and Zhang, SIGGRAPH, 2010] [Grinspun et al., SIGGRAPH, 2005]
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From 2005 to 2010, Luiz Velho worked on a variety of important problems in geometry processing: surface reconstruction from point cloud, discrete geodesics, mesh compression, adapted dynamic meshes, mesh segmentation, and geometry sam- pling. A remarkable fact is that most papers published in the above period resulted from the work of his PhD students and from collaborations with other re- searchers from Brazilian institutions, such UFRJ, PUC-Rio, Unicamp, and USP. Luiz Velho also kept alive his fruitful collaboration with his IMPA peers (Jonas Gomes, Luiz Henrique de Figueiredo, and Paulo Cezar Carvalho), and their students.
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Surface Reconstruction from Point Cloud
tion for Noisy Point Clouds”. Proceedings of the SGP, Vienna, Austria, July 4-6, 2005.
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Mesh Compression
¸a, and L. Velho. Adaptive multi- resolution triangulations based on physical compression. CNME, 21(10): 571- 580, 2005.
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Discrete Geodesics
Geodesic Curves”. The Visual Computer, 24(12): 1025-1037, 2008 (extended from SIBGRAPI 2007).
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Dynamic Meshes
to Adapt Dynamic Meshes. Computer & Graphics, 32(2): 141-149, April 2008 (extended from SIBGRAPI 2006).
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Mesh Segmentation
ticulated Bodies. Computer Graphics Forum, 27(5): 1349-1356, 2008 (in SGP 2008).
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Surface Reconstruction from Hermite Data
its”. Computer Graphics Forum, 30(1): 27-42, 2011 (extended from SIBGRAPI 2010).
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Geometry Sampling
On 2D Solid Alpha- Complexes of Poisson Disc Samplings. International Journal of Shape Mod- eling, 2010.
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Finally, Luiz is an invited speaker at SIBGRAPI!
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Simplicial Diffeomorphisms
2010.
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First Brazilian to give a lecture as keynote speaker of the Symposium on Geometry Processing!
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In 2010, Luiz receives the medal of Ordem Nacional do M´ erito Cient´ ıfico!
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Luiz Velho organized the Trimester Program on Computational Manifolds, which featured a seminar with world-renowned researchers on geometry pro- cessing.
Computational Manifolds and Applications - 2011
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Luiz Velho organized the Trimester Program on Computational Manifolds, which featured a seminar with world-renowned researchers on geometry pro- cessing.
Computational Manifolds and Applications - 2011
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The event, which took place in 2011, was driven by a collaborative work from 2009:
New Construction of Smooth Surfaces from Triangle Meshes using Parametric Pseudo-Surfaces. Computer & Graphics, 33(3): 331-340, July 2009 (from SMI ’09).
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tion Mesh Representation. Computer & Graphics, 38: 332-340, 2014.
Multiresolution in GPU
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Texture Synthesis
[Zonenschein, Gomes, Velho, de Figueiredo, Tigges and Wyvill, SIBGRAPI 1998] [Zhang, Zhou, Velho, Guo and Shum, SIGGRAPH 2003]
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Sketch-based Modeling
[Paiva, Amorin, Velho and Sousa, SIBGRAPI 2011] [Brazil, Amorin, Sousa, Velho and de Figueiredo, Computers & Graphics, 2015]
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Warping and Morphing
[Gomes, Darsa, Costa and Velho, 1997]
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Dithering
The first paper of a Brazilian institution published in SIGGRAPH!