270 lines
15 KiB
Markdown
270 lines
15 KiB
Markdown
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>
|
|
<link rel="stylesheet" href="http://yandex.st/highlightjs/7.3/styles/default.min.css">
|
|
<script src="http://yandex.st/highlightjs/7.3/highlight.min.js"></script>
|
|
<script>hljs.initHighlightingOnLoad();</script>
|
|
|
|
# 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](#chapter1:introductiontolibigl)
|
|
* [Libigl design principles](#libigldesignprinciples)
|
|
* [101 Mesh representation](#meshrepresentation)
|
|
* [102 Visualizing surfaces](#visualizingsurfaces)
|
|
* [103 Interaction with keyboard and mouse](#interactionwithkeyboardandmouse)
|
|
* [104 Scalar field visualization](#scalarfieldvisualization)
|
|
* [105 Overlays](#overlays)
|
|
* [106 Viewer Menu](#viewermenu)
|
|
* [107 Multiple Meshes](#multiplemeshes)
|
|
* [Chapter 2: Discrete Geometric Quantities and Operators](#chapter2:discretegeometricquantitiesandoperators)
|
|
* [201 Normals](#normals)
|
|
* [Per-face](#per-face)
|
|
* [Per-vertex](#per-vertex)
|
|
* [Per-corner](#per-corner)
|
|
* [202 Gaussian Curvature](#gaussiancurvature)
|
|
* [203 Curvature Directions](#curvaturedirections)
|
|
* [204 Gradient](#gradient)
|
|
* [205 Laplacian](#laplacian)
|
|
* [Mass matrix](#massmatrix)
|
|
* [Alternative construction of
|
|
Laplacian](#alternativeconstructionoflaplacian)
|
|
* [206 Geodesic Distance](#geodesic)
|
|
* [Chapter 3: Matrices and Linear Algebra](#chapter3:matricesandlinearalgebra)
|
|
* [301 Slice](#slice)
|
|
* [302 Sort](#sort)
|
|
* [Other Matlab-style functions](#othermatlab-stylefunctions)
|
|
* [303 Laplace Equation](#laplaceequation)
|
|
* [Quadratic energy minimization](#quadraticenergyminimization)
|
|
* [304 Linear Equality Constraints](#linearequalityconstraints)
|
|
* [305 Quadratic Programming](#quadraticprogramming)
|
|
* [306 Eigen Decomposition](#eigendecomposition)
|
|
* [Chapter 4: Shape Deformation](#chapter4:shapedeformation)
|
|
* [401 Biharmonic Deformation](#biharmonicdeformation)
|
|
* [402 Polyharmonic Deformation](#polyharmonicdeformation)
|
|
* [403 Bounded Biharmonic Weights](#boundedbiharmonicweights)
|
|
* [404 Dual Quaternion Skinning](#dualquaternionskinning)
|
|
* [405 As-rigid-as-possible](#as-rigid-as-possible)
|
|
* [406 Fast automatic skinning
|
|
transformations](#fastautomaticskinningtransformations)
|
|
* [ARAP with grouped edge-sets](#arapwithgroupededge-sets)
|
|
* [407 Biharmonic Coordinates](#biharmoniccoordinates)
|
|
* [Chapter 5: Parametrization](#chapter5:parametrization)
|
|
* [501 Harmonic parametrization](#harmonicparametrization)
|
|
* [502 Least-Square Conformal Maps](#leastsquareconformalmaps)
|
|
* [503 As-Rigid-As-Possible](#asrigidaspossible)
|
|
* [504 N-Rotationally symmetric tangent fields](#nrotationallysymmetrictangetfields)
|
|
* [505 Global, seamless integer-grid parametrization](#globalseamlessintegergridparametrization)
|
|
* [506 Anisotropic remeshing using frame fields](#anisotropicremeshingusingframefields)
|
|
* [507 Planarization](#planarization)
|
|
* [Chapter 6: External libraries](#chapter6:externallibraries)
|
|
* [601 State serialization](#stateserialization)
|
|
* [602 Mixing Matlab code](#mixingmatlabcode)
|
|
* [Saving a Matlab workspace](#savingamatlabworkspace)
|
|
* [Dumping Eigen matrices to copy and paste into Matlab](#dumpingeigenmatricestocopyandpasteintomatlab)
|
|
* [603 Calling libigl functions from Matlab](#callinglibiglfunctionsfrommatlab)
|
|
* [604 Triangulation of closed polygons](#triangulationofclosedpolygons)
|
|
* [605 Tetrahedralization of closed surfaces](#tetrahedralizationofclosedsurfaces)
|
|
* [606 Baking ambient occlusion](#bakingambientocclusion)
|
|
* [607 Screen Capture](#screencapture)
|
|
* [608 Locally Injective Maps](#locallyinjectivemaps)
|
|
* [609 Boolean Operations on Meshes](#booleanoperationsonmeshes)
|
|
* [610 CSG Tree](#csgtree)
|
|
* [Chapter 7: Miscellaneous](#chapter7:miscellaneous)
|
|
* [701 Mesh Statistics](#meshstatistics)
|
|
* [702 Generalized Winding Number](#generalizedwindingnumber)
|
|
* [703 Mesh Decimation](#meshdecimation)
|
|
* [704 Signed Distances](#signeddistances)
|
|
* [705 Marching Cubes](#marchingcubes)
|
|
* [706 Facet Orientation](#facetorientation)
|
|
* [707 Swept Volume](#sweptvolume)
|
|
* [708 Picking Vertices and Faces](#pickingverticesandfaces)
|
|
* [709 Vector Field Visualization](#vectorfieldvisualizer)
|
|
* [710 Scalable Locally Injective Maps](#slim)
|
|
* [711 Subdivision surfaces](#subdivision)
|
|
* [712 Data smoothing](#datasmoothing)
|
|
* [713 ShapeUp projection](#shapeup)
|
|
* [Chapter 8: Outlook for continuing development](#future)
|
|
|
|
|
|
|
|
|
|
[#attene_2014]: Marco Attene.
|
|
[Direct repair of self-intersecting
|
|
meshes](https://www.google.com/search?q=Direct+repair+of+self-intersecting+meshes),
|
|
2014.
|
|
[#baerentzen_2005]: J Andreas Baerentzen and Henrik Aanaes.
|
|
[Signed distance computation using the angle weighted
|
|
pseudonormal](https://www.google.com/search?q=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](https://www.google.com/search?q=Real-Time+Subspace+Integration+for+St.Venant-Kirchhoff+Deformable+Models),
|
|
2005.
|
|
[#bommes_2009]: David Bommes, Henrik Zimmer, Leif Kobbelt.
|
|
[Mixed-integer
|
|
quadrangulation](http://www-sop.inria.fr/members/David.Bommes/publications/miq.pdf),
|
|
2009.
|
|
[#botsch_2004]: Matrio Botsch and Leif Kobbelt.
|
|
[An Intuitive Framework for Real-Time Freeform
|
|
Modeling](https://www.google.com/search?q=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](http://lgg.epfl.ch/publications/2012/shapeup.pdf), 2012
|
|
[#chao_2010]: Isaac Chao, Ulrich Pinkall, Patrick Sanan, Peter Schröder.
|
|
[A Simple Geometric Model for Elastic
|
|
Deformations](https://www.google.com/search?q=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](http://igl.ethz.ch/projects/complex-roots/), 2014
|
|
[#diamanti_2015]: Olga Diamanti, Amir Vaxman, Daniele Panozzo, Olga
|
|
Sorkine-Hornung. [Integrable PolyVector Fields](http://igl.ethz.ch/projects/integrable/), 2015
|
|
[#eck_2005]: Matthias Eck, Tony DeRose, Tom Duchamp, Hugues Hoppe, Michael Lounsbery, Werner
|
|
Stuetzle. [Multiresolution Analysis of Arbitrary
|
|
Meshes](http://research.microsoft.com/en-us/um/people/hoppe/mra.pdf), 2005.
|
|
[#garg_2016]: Akash Garg, Alec Jacobson, Eitan Grinspun. [Computational Design
|
|
of
|
|
Reconfigurables](https://www.google.com/search?q=Computational+Design+of+Reconfigurables),
|
|
2016
|
|
[#hildebrandt_2011]: Klaus Hildebrandt, Christian Schulz, Christoph von
|
|
Tycowicz, and Konrad Polthier. [Interactive Surface Modeling using Modal
|
|
Analysis](https://www.google.com/search?q=Interactive+Surface+Modeling+using+Modal+Analysis),
|
|
2011.
|
|
[#hoppe_1996]: Hugues Hoppe. [Progressive
|
|
Meshes](https://www.google.com/search?q=Progressive+meshes), 1996
|
|
[#jacobson_skinning_course_2014]: Alec Jacobson, Zhigang Deng, Ladislav Kavan,
|
|
J.P. Lewis. [_Skinning: Real-Time Shape
|
|
Deformation_](https://www.google.com/search?q=Skinning+Real-Time+Shape+Deformation),
|
|
2014.
|
|
[#jacobson_thesis_2013]: Alec Jacobson,
|
|
[_Algorithms and Interfaces for Real-Time Deformation of 2D and 3D
|
|
Shapes_](https://www.google.com/search?q=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](https://www.google.com/search?q=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](https://www.google.com/search?q=Fast+Automatic+Skinning+Transformations),
|
|
2012.
|
|
[#jacobson_2011]: Alec Jacobson, Ilya Baran, Jovan Popović, and Olga Sorkine.
|
|
[Bounded Biharmonic Weights for Real-Time
|
|
Deformation](https://www.google.com/search?q=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](https://www.google.com/search?q=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](https://www.google.com/search?q=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](https://www.google.com/search?q=Can+Mean-Curvature+Flow+Be+Made+Non-Singular),
|
|
2012.
|
|
[#knoppel_2013]: Felix Knöppel, Keenan Crane, Ulrich Pinkall, and Peter
|
|
Schröder. [Globally Optimal Direction
|
|
Fields](http://www.cs.columbia.edu/~keenan/Projects/GloballyOptimalDirectionFields/paper.pdf),
|
|
2013.
|
|
[#levy_2002]: Bruno Lévy, Sylvain Petitjean, Nicolas Ray, Jérome Maillot.
|
|
[Least Squares Conformal Maps, for Automatic Texture Atlas
|
|
Generation,](http://www.cs.jhu.edu/~misha/Fall09/Levy02.pdf), 2002.
|
|
[#levy_2008]: Nicolas Ray, Bruno Vallet, Wan Chiu Li, Bruno Lévy.
|
|
[N-Symmetry Direction Field
|
|
Design](http://alice.loria.fr/publications/papers/2008/DGF/NSDFD-TOG.pdf),
|
|
2008.
|
|
[#liu_2008]: Ligang Liu, Lei Zhang, Yin Xu, Craig Gotsman, Steven J. Gortler.
|
|
[A Local/Global Approach to Mesh
|
|
Parameterization](http://cs.harvard.edu/~sjg/papers/arap.pdf), 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](http://research.microsoft.com/en-us/um/people/yangliu/publication/cdf.pdf),
|
|
2008.
|
|
[#loop_1987]: Charles Loop. [Smooth Subdivision Surfaces Based on
|
|
Triangles](https://www.google.com/search?q=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](https://www.google.com/search?q=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](https://www.google.com/search?q=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](https://www.google.com/search?q=Discrete+Differential-Geometry+Operators+for+Triangulated+2-Manifolds),
|
|
2003.
|
|
[#mullen_2008]: Patrick Mullen, Yiying Tong, Pierre Alliez, Mathieu Desbrun.
|
|
[Spectral Conformal
|
|
Parameterization](http://www.geometry.caltech.edu/pubs/MTAD08.pdf), 2008.
|
|
[#panozzo_2010]: Daniele Panozzo, Enrico Puppo, Luigi Rocca, [Efficient
|
|
Multi-scale Curvature and Crease
|
|
Estimation](https://www.google.com/search?q=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](http://cs.nyu.edu/~panozzo/papers/frame-fields-2014.pdf),
|
|
2014.
|
|
[#rabinovich_2016]: Michael Rabinovich, Roi Poranne, Daniele Panozzo, Olga
|
|
Sorkine-Hornung. [Scalable Locally Injective
|
|
Mappings](http://cs.nyu.edu/~panozzo/papers/SLIM-2016.pdf), 2016.
|
|
[#rustamov_2011]: Raid M. Rustamov, [Multiscale Biharmonic
|
|
Kernels](https://www.google.com/search?q=Multiscale+Biharmonic+Kernels), 2011.
|
|
[#schroeder_1994]: William J. Schroeder, William E. Lorensen, and Steve
|
|
Linthicum. [Implicit Modeling of Swept Surfaces and
|
|
Volumes](https://www.google.com/search?q=implicit+modeling+of+swept+surfaces+and+volumes),
|
|
1994.
|
|
[#schuller_2013]: Christian Schüller, Ladislav Kavan, Daniele Panozzo, Olga
|
|
Sorkine-Hornung. [Locally Injective
|
|
Mappings](http://igl.ethz.ch/projects/LIM/), 2013.
|
|
[#sharf_2007]: Andrei Sharf, Thomas Lewiner, Gil Shklarski, Sivan Toledo, and
|
|
Daniel Cohen-Or. [Interactive topology-aware surface
|
|
reconstruction](https://www.google.com/search?q=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](https://www.google.com/search?q=Laplacian+Surface+Editing), 2004.
|
|
[#sorkine_2007]: Olga Sorkine and Marc Alexa. [As-rigid-as-possible Surface
|
|
Modeling](https://www.google.com/search?q=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](https://arxiv.org/abs/1707.04348),
|
|
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](https://www.google.com/search?q=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](https://www.google.com/search?q=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](https://www.google.com/search?q=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](https://www.google.com/search?q=Linear+Subspace+Design+for+Real-Time+Shape+Deformation),
|
|
2015
|
|
[#zhou_2016]: Qingnan Zhou, Eitan Grinspun, Denis Zorin. [Mesh Arrangements for
|
|
Solid
|
|
Geometry](https://www.google.com/search?q=Mesh+Arrangements+for+Solid+Geometry),
|
|
2016
|
|
[#mitchell_1987]: Joseph S. B. Mitchell, David M. Mount, Christos H. Papadimitriou. [The Discrete Geodesic Problem](https://www.google.com/search?q=The+Discrete+Geodesic+Problem), 1987
|