igl/docs/tutorial/index.md

title: libigl Tutorial author: Daniele Panozzo and Alec Jacobson date: 07 November 2015 css: style.css html header: <script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>

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libigl tutorial notes

originally presented by Daniele Panozzo and Alec Jacobson at SGP Graduate School 2014

Libigl is an open source C++ library for geometry processing research and development. Dropping the heavy data structures of tradition geometry libraries, libigl is a simple header-only library of encapsulated functions. This combines the rapid prototyping familiar to Matlab or Python programmers with the performance and versatility of C++. The tutorial is a self-contained, hands-on introduction to libigl. Via interactive, step-by-step examples, we demonstrate how to accomplish common geometry processing tasks such as computation of differential quantities and operators, real-time deformation, parametrization, numerical optimization and remeshing. Each section of the lecture notes links to a cross-platform example application.

Table of contents

• Chapter 1: Introduction to libigl
  • Libigl design principles
  • 101 Mesh representation
  • 102 Visualizing surfaces
  • 103 Interaction with keyboard and mouse
  • 104 Scalar field visualization
  • 105 Overlays
  • 106 Viewer Menu
  • 107 Multiple Meshes
• Chapter 2: Discrete Geometric Quantities and Operators
  • 201 Normals
    • Per-face
    • Per-vertex
    • Per-corner
  • 202 Gaussian Curvature
  • 203 Curvature Directions
  • 204 Gradient
  • 205 Laplacian
    • Mass matrix
    • Alternative construction of Laplacian
  • 206 Geodesic Distance
• Chapter 3: Matrices and Linear Algebra
  • 301 Slice
  • 302 Sort
    • Other Matlab-style functions
  • 303 Laplace Equation
    • Quadratic energy minimization
  • 304 Linear Equality Constraints
  • 305 Quadratic Programming
  • 306 Eigen Decomposition
• Chapter 4: Shape Deformation
  • 401 Biharmonic Deformation
  • 402 Polyharmonic Deformation
  • 403 Bounded Biharmonic Weights
  • 404 Dual Quaternion Skinning
  • 405 As-rigid-as-possible
  • 406 Fast automatic skinning transformations
    • ARAP with grouped edge-sets
  • 407 Biharmonic Coordinates
• Chapter 5: Parametrization
  • 501 Harmonic parametrization
  • 502 Least-Square Conformal Maps
  • 503 As-Rigid-As-Possible
  • 504 N-Rotationally symmetric tangent fields
  • 505 Global, seamless integer-grid parametrization
  • 506 Anisotropic remeshing using frame fields
  • 507 Planarization
• Chapter 6: External libraries
  • 601 State serialization
  • 602 Mixing Matlab code
    • Saving a Matlab workspace
    • Dumping Eigen matrices to copy and paste into Matlab
  • 603 Calling libigl functions from Matlab
  • 604 Triangulation of closed polygons
  • 605 Tetrahedralization of closed surfaces
  • 606 Baking ambient occlusion
  • 607 Screen Capture
  • 608 Locally Injective Maps
  • 609 Boolean Operations on Meshes
  • 610 CSG Tree
• Chapter 7: Miscellaneous
  • 701 Mesh Statistics
  • 702 Generalized Winding Number
  • 703 Mesh Decimation
  • 704 Signed Distances
  • 705 Marching Cubes
  • 706 Facet Orientation
  • 707 Swept Volume
  • 708 Picking Vertices and Faces
  • 709 Vector Field Visualization
  • 710 Scalable Locally Injective Maps
  • 711 Subdivision surfaces
  • 712 Data smoothing
  • 713 ShapeUp projection
• Chapter 8: Outlook for continuing development

[#attene_2014]: Marco Attene. Direct repair of self-intersecting meshes, 2014. [#baerentzen_2005]: J Andreas Baerentzen and Henrik Aanaes. Signed distance computation using the angle weighted pseudonormal, 2005. [#barbic_2005]: Jernej Barbic and Doug James. Real-Time Subspace Integration for St.Venant-Kirchhoff Deformable Models, 2005. [#bommes_2009]: David Bommes, Henrik Zimmer, Leif Kobbelt. Mixed-integer quadrangulation, 2009. [#botsch_2004]: Matrio Botsch and Leif Kobbelt. An Intuitive Framework for Real-Time Freeform Modeling, 2004. [#bouaziz_2012]: Sofien Bouaziz, Mario Deuss, Yuliy Schwartzburg, Thibaut Weise, Mark Pauly Shape-Up: Shaping Discrete Geometry with Projections, 2012 [#chao_2010]: Isaac Chao, Ulrich Pinkall, Patrick Sanan, Peter Schröder. A Simple Geometric Model for Elastic Deformations, 2010. [#diamanti_2014]: Olga Diamanti, Amir Vaxman, Daniele Panozzo, Olga Sorkine-Hornung. Designing N-PolyVector Fields with Complex Polynomials, 2014 [#diamanti_2015]: Olga Diamanti, Amir Vaxman, Daniele Panozzo, Olga Sorkine-Hornung. Integrable PolyVector Fields, 2015 [#eck_2005]: Matthias Eck, Tony DeRose, Tom Duchamp, Hugues Hoppe, Michael Lounsbery, Werner Stuetzle. Multiresolution Analysis of Arbitrary Meshes, 2005. [#garg_2016]: Akash Garg, Alec Jacobson, Eitan Grinspun. Computational Design of Reconfigurables, 2016 [#hildebrandt_2011]: Klaus Hildebrandt, Christian Schulz, Christoph von Tycowicz, and Konrad Polthier. Interactive Surface Modeling using Modal Analysis, 2011. [#hoppe_1996]: Hugues Hoppe. Progressive Meshes, 1996 [#jacobson_skinning_course_2014]: Alec Jacobson, Zhigang Deng, Ladislav Kavan, J.P. Lewis. Skinning: Real-Time Shape Deformation, 2014. [#jacobson_thesis_2013]: Alec Jacobson, Algorithms and Interfaces for Real-Time Deformation of 2D and 3D Shapes, 2013. [#jacobson_2013]: Alec Jacobson, Ladislav Kavan, and Olga Sorkine. Robust Inside-Outside Segmentation using Generalized Winding Numbers, 2013. [#jacobson_2012]: Alec Jacobson, Ilya Baran, Ladislav Kavan, Jovan Popović, and Olga Sorkine. Fast Automatic Skinning Transformations, 2012. [#jacobson_2011]: Alec Jacobson, Ilya Baran, Jovan Popović, and Olga Sorkine. Bounded Biharmonic Weights for Real-Time Deformation, 2011. [#jacobson_mixed_2010]: Alec Jacobson, Elif Tosun, Olga Sorkine, and Denis Zorin. Mixed Finite Elements for Variational Surface Modeling, 2010. [#kavan_2008]: Ladislav Kavan, Steven Collins, Jiri Zara, and Carol O'Sullivan. Geometric Skinning with Approximate Dual Quaternion Blending, 2008. [#kazhdan_2012]: Michael Kazhdan, Jake Solomon, Mirela Ben-Chen, Can Mean-Curvature Flow Be Made Non-Singular, 2012. [#knoppel_2013]: Felix Knöppel, Keenan Crane, Ulrich Pinkall, and Peter Schröder. Globally Optimal Direction Fields, 2013. [#levy_2002]: Bruno Lévy, Sylvain Petitjean, Nicolas Ray, Jérome Maillot. Least Squares Conformal Maps, for Automatic Texture Atlas Generation,, 2002. [#levy_2008]: Nicolas Ray, Bruno Vallet, Wan Chiu Li, Bruno Lévy. N-Symmetry Direction Field Design, 2008. [#liu_2008]: Ligang Liu, Lei Zhang, Yin Xu, Craig Gotsman, Steven J. Gortler. A Local/Global Approach to Mesh Parameterization, 2008. [#liu_2011]: Yang Liu, Weiwei Xu, Jun Wang, Lifeng Zhu, Baining Guo, Falai Chen, Guoping Wang. General Planar Quadrilateral Mesh Design Using Conjugate Direction Field, 2008. [#loop_1987]: Charles Loop. Smooth Subdivision Surfaces Based on Triangles, 1987. [#lorensen_1987]: W.E. Lorensen and Harvey E. Cline. Marching cubes: A high resolution 3d surface construction algorithm, 1987. [#mcadams_2011]: Alexa McAdams, Andrew Selle, Rasmus Tamstorf, Joseph Teran, Eftychios Sifakis. Computing the Singular Value Decomposition of 3x3 matrices with minimal branching and elementary floating point operations, 2011. [#meyer_2003]: Mark Meyer, Mathieu Desbrun, Peter Schröder and Alan H. Barr, Discrete Differential-Geometry Operators for Triangulated 2-Manifolds, 2003. [#mullen_2008]: Patrick Mullen, Yiying Tong, Pierre Alliez, Mathieu Desbrun. Spectral Conformal Parameterization, 2008. [#panozzo_2010]: Daniele Panozzo, Enrico Puppo, Luigi Rocca, Efficient Multi-scale Curvature and Crease Estimation, 2010. [#panozzo_2014]: Daniele Panozzo, Enrico Puppo, Marco Tarini, Olga Sorkine-Hornung. Frame Fields: Anisotropic and Non-Orthogonal Cross Fields, 2014. [#rabinovich_2016]: Michael Rabinovich, Roi Poranne, Daniele Panozzo, Olga Sorkine-Hornung. Scalable Locally Injective Mappings, 2016. [#rustamov_2011]: Raid M. Rustamov, Multiscale Biharmonic Kernels, 2011. [#schroeder_1994]: William J. Schroeder, William E. Lorensen, and Steve Linthicum. Implicit Modeling of Swept Surfaces and Volumes, 1994. [#schuller_2013]: Christian Schüller, Ladislav Kavan, Daniele Panozzo, Olga Sorkine-Hornung. Locally Injective Mappings, 2013. [#sharf_2007]: Andrei Sharf, Thomas Lewiner, Gil Shklarski, Sivan Toledo, and Daniel Cohen-Or. Interactive topology-aware surface reconstruction, 2007. [#sorkine_2004]: Olga Sorkine, Yaron Lipman, Daniel Cohen-Or, Marc Alexa, Christian Rössl and Hans-Peter Seidel. Laplacian Surface Editing, 2004. [#sorkine_2007]: Olga Sorkine and Marc Alexa. As-rigid-as-possible Surface Modeling, 2007. [#stein_2017]: Oded Stein, Eitan Grinspun, Max Wardetzky, Alec Jacobson. Natural Boundary Conditions for Smoothing in Geometry Processing, 2017. [#takayama14]: Kenshi Takayama, Alec Jacobson, Ladislav Kavan, Olga Sorkine-Hornung. A Simple Method for Correcting Facet Orientations in Polygon Meshes Based on Ray Casting, 2014. [#vallet_2008]: Bruno Vallet and Bruno Lévy. Spectral Geometry Processing with Manifold Harmonics, 2008. [#vaxman_2016]: Amir Vaxman, Marcel Campen, Olga Diamanti, Daniele Panozzo, David Bommes, Klaus Hildebrandt, Mirela Ben-Chen. Directional Field Synthesis, Design, and Processing, 2016 [#wang_bc_2015]: Yu Wang, Alec Jacobson, Jernej Barbic, Ladislav Kavan. Linear Subspace Design for Real-Time Shape Deformation, 2015 [#zhou_2016]: Qingnan Zhou, Eitan Grinspun, Denis Zorin. Mesh Arrangements for Solid Geometry, 2016 [#mitchell_1987]: Joseph S. B. Mitchell, David M. Mount, Christos H. Papadimitriou. The Discrete Geodesic Problem, 1987