title: libigl Tutorial
author: Daniele Panozzo and Alec Jacobson
date: 07 November 2015
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# libigl tutorial notes

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

![](images/libigl-logo.jpg)

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)




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[#panozzo_2014]: Daniele Panozzo, Enrico Puppo, Marco Tarini, Olga
  Sorkine-Hornung.  [Frame Fields: Anisotropic and Non-Orthogonal Cross
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[#rabinovich_2016]: Michael Rabinovich, Roi Poranne, Daniele Panozzo, Olga
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