Brown University School of Engineering

ENGN 2501 Digital Geometry Processing

Spring 2023

• Home
• Lectures
• References
• Assignments
• Core Mesh
• Core Scene Graph

References

Software Applications

1. MeshLab
   Open source system for processing and editing 3D triangular meshes. It provides a set of tools for editing, cleaning, healing, inspecting, rendering, texturing and converting meshes. It offers features for processing raw data produced by 3D digitization tools/devices and for preparing models for 3D printing.
2. OpenSCAD
   OpenSCAD is an open source application for creating solid 3D CAD objects.
3. MeshMixer
   A sort of "Swiss Army Knife" for 3D meshes.
4. CloudCompare
   Open source 3D point cloud and mesh processing software.
5. Blender
   Much more complex open source system for 3D modeling and animation.

Software Libraries

1. CGAL
   Sofware library that provides easy access to efficient and reliable geometric algorithms in the form of a C++ library.
2. OpenMesh
   OpenMesh is a C++ library which implements a generic and efficient data structure for representing and manipulating polygonal meshes.
3. Open3D
   Open3D is an open-source library that supports rapid development of software that deals with 3D data. The Open3D frontend exposes a set of carefully selected data structures and algorithms in both C++ and Python. The backend is highly optimized and is set up for parallelization.
4. Point Cloud Library (PCL)
   A standalone, large scale, open project for 2D/3D image and point cloud processing.

Algorithms and Data Structures

1. Introduction to Algorithms, Second Edition,
   by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.
   The MIT Press and McGraw-Hill, 2001.
2. Data Structures and Network Algorithms,
   by Robert Endre Tarjan.
   CBMS-NSF Regional Conference Series in Applied Mathematics,
   SIAM, 1983.
3. Graphics Gems Repository

File Formats

• ISO/IEC 14772-1:97 VRML'97
• VRML 2.0 - Cheat Sheat, by Jan Hardenbergh
• TECFA's VRML Pointers
• Web 3D Consortium
• The Annotated VRML97 Reference Manual,
  by Rikk Carey and Gavin Bell, 1997.
• PLY

Data Repositories

• Georgia Tech Large Geometric Models Archive
• The Stanford 3D Scanning Repository
• AIM@SHAPE Shape Repository v4.0

Courses and Tutorials

• Siggraph 2000 Course 23
  Subdivision for Modeling and Animation
• Geometric Modeling Based on Polygonal Meshes,
  by L. P. Kobbelt, S. Bishoff, M. Botsch, K. Kahler,
  C. Rossl, R. Schneider, and J. Vorsatz,
  Eurographics 2000 Tutorial, September 2000
• Siggraph 2006 Course 1
  Discrete Differential Geometry: An Applied Introduction
• Siggraph 2006 Course 2
  Interactive Shape Modeling
• Siggraph 2006 Course 13
  Surface Modeling and Parameterization with Manifolds
• Siggraph 2006 Course 29
  Geometric Modeling Based on Triangle Meshes

Surface Representations

1. Primitives for the manipulation of General Subdivisions
   and the Computation of Voronoi Diagrams
   by L. Guibas and J. Stolfi,
   in ACM Transactions on Graphics,
   Vol. 4, No. 2, April 1985, pp. 74-123
2. Geometry and Topology for Mesh Generation
   by H. Edelsbruner, Cambridge University Press, 2001
3. Using generic programming for designing a data structure for polyhedral surfaces,
   by Lutz Kettner, Computational Geometry: Theory and Applications, Volume 13, Issue 1, Pages: 65 - 90, May 1999.

Point Clouds

• Point Primitives for Interactive Modeling and Processing of 3D Geometry
  by M. Pauly, Ph.D. Thesis, Federal Institute of Technology (ETH) of Zurich, 2003
• A survey of point-based techniques in computer graphics ,
  by L. P. Kobbelt, and M. Botsch, Computers & Graphics 28 (2004) 801–814
• Uncertainty and Variability in Point Cloud Surface Data
  by M. Pauly, N. J. Mitra, and L. J. Guibas, in Proceedings of Eurographics Symposium on Point-Based Graphics,2004

Fixing Meshes

• Filling Holes in Complex Surfaces using Volumetric Diffusion
  by J. Davis, S. R. Marschner, M. Garr, and M. Levoy, in Proceedings of 3DPVT'02

Differential Geometry

• Notes on Differential Geometry
  by Michael Garland, UIUC 2004.
• Differential Geometry of Curves and Surfaces
  by Manfredo do Carmo, Birkhauser Verlag, 1994.
• Elementary Topics in Differential Geometry
  by J. A. Thorpe, Springer-Verlag 1979.
• Geometric Methods and Applications
  by Jean Gallier, Springer-Verlag 2001.
• Geomodelling
  by Jean-Laurent Mallet, Oxford University Press, 2002.

Isosurfaces

• Marching Cubes: A High Resolution 3d Surface Reconstruction Algorithm
  by W.E. Lorensen and H.E. Cline, in Proceedings of Siggraph'87.
• Feature Sensitive Surface Extraction from Volume Data
  by L. P. Kobbelt, M. Botsch, U. Schwanecke, and H.-P. Seidel, in Proceedings of Siggraph 2001

Surface Reconstruction

• Reconstruction and Representation of 3D Objects with Radial Basis Functions
  by J. C. Carr, R. K. Beatson, J. B. Cherrie, T. J. Mitchell, W. R. Fright, B. C. McCallum, and T. R. Evans, in Proceedings of Siggraph'2001.
• Geometric Surface Processing via Normal Maps
  by Tolga Tasdizen, Ross Whitaker, Paul Burchard, and Stanley Osher in ACM Transactions on Graphics, Vol. 22, No. 4, October 2003, Pages 1012–1033
• Multi-level Partition of Unity Implicits
  by Y. Ohtake, A. Belyaev, M. Alexa, G. Turk, H.-P. Seidel in Proceedings of Siggraph 2003.
• Vectorfield Isosurface-based Reconstruction from Oriented Points
  P. G. Sibley, and G. Taubin in Proceedings of Siggraph 2005 (sketch).
• Beyond Silhouettes: Surface Reconstruction using Multi-Flash Photography
  by D. Crispell, D. Lanman, P. G. Sibley, Y. Zhao, and G. Taubin, in Proceedings of 3DPVT'06
• Multi-Flash 3D Photography: Capturing Shape and Appearance
  by D. Lanman, P. G. Sibley, D. Crispell, Y. Zhao, and G. Taubin, in Proceedings of Siggraph 2006 (poster).
• Poisson Surface Reconstruction
  by M. Kazhdan, M. Bolitho and H. Hoppe
  Eurographics Symposium on Geometry Processing, SGP'2006.

Visual Hull / Volume carving

• Shape from Light Field Boundary,
  by Kutulakos, K.N., CVPR'97.
• A Theory of Shape by Space Carving,
  by Kutulakos, K.N. and Seitz, S.M., University of Rochester CS Technical Report #692.
• Automatic 3D Model Construction for Turn-Table Sequences,
  Andrew W. Fitzgibbon, Geoff Cross and Andrew Zisserman, Robotics Research Group, Department of Engineering Science, University of Oxford. PDF
• Photorealistic Scene Reconstruction by Voxel Coloring,
  by Seitz, S.M. and Dyer, C.R.

Smoothing

• Geometric Signal Processing on Polygonal Meshes
  by G. Taubin
  Eurographics 2000 State of The Art Report (STAR), September 2000
• A Signal Processing Approach to Fair Surface Design
  by G. Taubin,
  Siggraph 1995
• Optimal Surface Smoothing as Filter Design,
  by G. Taubin, T. Zhang, and G. Golub
  in Proceedings of Fourth European Conference on Computer Vision (ECCV'96)
  and IBM Technical Report RC-20404, March 1996
• Interactive Multi-Resolution Modeling on Arbitrary Meshes
  by L. P. Kobbelt, S. Campagna, J. Vorsatz, and H.-P. Seidel
  Siggraph 1998.
• Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow
  by M. Desbrun, M. Meyer, P. Schroder, and A. H. Barr
  Siggraph 1999.
• Polyhedral Surface Smoothing with Simultaneous Mesh Regularization
  by Y. Ohtake, A.G. Belyaev, and I.A. Bogaevski
  in Proceedings of the Geometric Modeling and Processing 2000, April 2000
• A Discrete Spring Model for Generating Fair Curves and Surfaces
  by A. Yamada, K. Shimada, T. Furuhata, and K.-H. Hou
  in Proceedings of Pacific Graphics 1999, October 1999
• Anisotropic Geometric Diffusion in Surface Processing
  by U. Clarenz, U. Diewald, and M. Rumpf
  in Proceedings of IEEE Visualization 2000, October 2000
• Bilateral mesh denoising
  by S. Fleishman, I. Drori, and D. Cohen-Or
  Siggraph 2003.
• Non-iterative, feature-preserving mesh smoothing
  by T. R. Jones, F. Durand, and Mathieu Desbrun,
  Siggraph 2003
• Anisotropic filtering of non-linear surface features
  by K. Hildebrandt and K. Polthier
  Eurographics 2004

Simplification

• Survey of Polygonal Surface Simplification Algorithms
  by P.S. Heckbert and M. Garland
  in Course Notes, Multiresolution Surface Modeling Course Siggraph'97
• A Developer's Survey of Polygonal Simplification Algorithms
  by D.P. Luebke
  University of Virginia TR 1999
• Surface Simplification Using Quadric Error Metrics
  by M. Garland, and P. Heckbert
  Siggraph'97
• Decimation of Triangle Meshes
  by W.J. Schroeder, J.A. Zarge, and W.E. Lorensen
  Siggraph'92
• Fast and Memory Efficient Polygonal Simplification
  by P. Lindstrom, and G. Turk
  IEEE Visualization 1998.
• Out-of-Core Simplification of Large Polygonal Models
  by P. Lindstrom
  Siggraph'2000.

Subdivision

• www.subdivision.org
  Subdivision Methods for Geometric Design: AConstructive Approach
  by J. Warren and H. Weimer
  Morgan-Kaufmann, 2002
• Stellar Subdivision Grammars
  by Luiz Velho
  Proccedings of Eurographics Symposium on Geometry Processing, 2003
• A Dynamic Adaptive Mesh Library Based on Stellar Operators
  by Luiz Velho
  Journal of Graphics Tools, Vol 9, No 2, pages 1-29, 2004
• A Survey of Subdivision-Based Tools for Surface Modeling
  by I. Martin, D. Zorin, and F. Bernardini
  in Geometric And Algorithmic Aspects Of Computer-aided Design And Manufacturing, (R. Janardan, M. Smid, and D. Dutta (eds.)), AMS 2005
• Embarrassingly Parallel Mesh Refinement by Edge Subdivision
  by David C. Thompson, and Philippe P. Pebay
  Engineering with Computers Vol 22, pages 75–93, 2006
  

Mesh Optimization

• Multiresolution Shape Deformations for Meshes with Dynamic Vertex Connectivity,
  by L. P. Kobbelt, T. Bareuther, and H.-P. Seidel
  Eurographics 2000
• Dynamic remeshing and applications,
  by J. Vorsatz, Ch. Rössl, and H.-P. Seidel
  ACM Symposium on Solid Modeling and Applications (SM'03)
• A Remeshing Approach to Multiresolution Modeling,
  by M. Botsch and L. Kobbelt
  Eurographics/ACM SIGGRAPH Symposium on Geometry Processing (SGP'04)

Remeshing

• Re-Tiling Polygonal Surfaces,
  by Greg Turk
  Siggraph 1992
• Interactive Geometry Remeshing
  by P. Alliez, M. Meyer, and M. Desbrun
  Siggraph 2002
• Anisotropic Polygonal Remeshing
  by P. Alliez, D. Cohen-Steiner, O. Devillers, B. Levy, and M. Desbrun
  Siggraph 2003
• Explicit surface remeshing
  by V. Surazhsky and C. Gotsman
  in Proceedings of the Symposium on Mesh Processing 2003
• Direct Anisotropic Quad-Dominant Remeshing
  by M. Marinov, and L. Kobbelt
  in Pacific Graphics 2004
• Spectral Surface Quadrangulation
  by S. Dong, P.T. Bremer, M. Garland, V. Pascucci, and J.C. Hart
  Siggraph 2006

Interactive Shape Editing and Surface Deformation

• As-rigid-as-possible shape interpolation
  by M. Alexa, D. Cohen-Or, and D. Levin
  Siggraph 2000
• Linear combination of transformations
  M. Alexa
  Siggraph 2002
• Differential Coordinates for Local Mesh Morphing and Deformation
  by M. Alexa
  The Visual Computer, 2003
• An Intuitive Framework for Real-Time Freeform Modeling
  by M. Botsch and L. Kobbelt
  Siggraph 2004
• Deformation Transfer for Triangle Meshes
  R. W. Sumner Jovan Popovic
  Siggraph 2004
• Mesh Editing With Poisson-Based Gradient Field Manipulation
  by Y. Yu, K. Zhou, D. Xu, X. Shi, H. Bao, B. Guo, and H.-Y. Shum
  Siggraph 2004
• Differential coordinates for interactive mesh editing
  by Y. Lipman, O. Sorkine, D. Cohen-Or, D. Levin, C. Rossi, and H.P. Seidel
  Shape Modeling International 2004
• Linear rotation-invariant coordinates for meshes
  by Y. Lipman, O. Sorkine, D. Levin, and D. Cohen-Or
  Siggraph 2005
• Real-Time Shape Editing using Radial Basis Functions
  by M. Botsch, and L. Kobbelt
  Eurographics 2005
• Laplacian Mesh Processing
  by O. Sorkine
  Eurographics 2005 Star Report
• Efficient linear system solvers for mesh processing
  by M Botsch, D Bommes, L Kobbelt
  IMA conference on Mathematics of Surfaces 2005
• A fast multigrid algorithm for mesh deformation
  by L. Shi, Y. Yu, N. Bell, and W.-W. Feng
  Siggraph 2006
• Vector Field Based Shape Deformations
  by W. von Funck, H. Theisel, and H.-P. Seidel
  Siggraph 2006
• Deformation Transfer for Detail-Preserving Surface Editing
  by M. Botsch, R.W. Sumner, M. Pauly, and M. Gross,
  Vision, Modeling, and Visualization 2006
• Differential Representations for Mesh Processing
  by O. Sorkine
  Computer Graphics Forum 2006
• Material-Aware Mesh Deformations
  T. Popa, D. Julius, and A. Sheffer
  Shape Modeling and Applications 2006 (SMI'06)
• Vector Field Design on Surfaces
  by E. Zhang, and K. Mischaikow, and G. Turk
  ACM Transactions on Graphics
  Volume 25, Issue 4, Pages 1294 - 1326, October 2006
• Volume and shape preservation via moving frame manipulation
  by Y. Lipman, D. Cohen-Or, G. Ran, and D. Levin
  ACM Transactions on Graphics, January 2007
• Design of Tangent Vector Fields
  by M. Fisher, P. Schröder, M. Desbrun, and H. Hoppe
  Siggraph 2007
• Implicit Boundary Control of Vector Field Based Shape Deformations
  by W. von Funck, H. Theisel, and H.-P. Seidel
  Mathematics of Surfaces XII, 2007
• On Linear Variational Surface Deformation Methods [Survey]
  by M. Botsch, and O. Sorkine,
  IEEE Transactions on Visualization and Computer Graphics, January 2008

Copyright © 2019 Gabriel Taubin