libigl/libigl
Libigl
libigl 是一个 C++ 几何处理库，用于分析和操作 3D 三角形和四面体网格。它充当数值线性代数套件和网格操作框架，集成了几何变形引擎以实现刚性和多调和变换。
该项目以其仅头文件的库设计以及对专门变形技术的实现而著称，包括尽可能刚性 (rigid-as-possible) 和多调和形状变形。它还提供了一个可视化工具，用于通过交互式场景控制和网格拾取来渲染表面和标量场。
该库涵盖了广泛的功能，包括用于曲率和测地距离的几何分析、通过等值面提取和三角剖分进行的网格生成，以及通过各向异性变形进行的网格重构。它还支持布尔网格操作、表面参数化以及用于求解拉普拉斯方程和二次规划的数值优化。
该工具包包括用于导入和导出各种 3D 几何格式的实用程序，并支持与 Matlab 的互操作性，以便执行脚本和共享矩阵。
Features
- Geometry Processing Libraries - A collection of tools for analyzing and manipulating 3D triangle and tetrahedral meshes using linear algebra.
- Surface and Volume Meshes - The product creates 3D tetrahedralizations of a given volume or point set.
- Finite Element Operators - The product builds sparse operators and finite-element matrices for mesh analysis.
- Boolean Mesh Operations - Computes unions, intersections, and differences of triangle meshes using robust mesh arrangements.
- Constrained Delaunay Triangulations - Generates high-quality 2D or 3D meshes while preserving specified boundary edges.
- Rigid-As-Possible Deformations - The product implements deformation by optimizing local rotations and global positions to maintain surface structure.
- Mesh Exporters - Reads and writes 3D geometry across various industry formats including OBJ, OFF, STL, and PLY.
- Mesh Manipulation Toolkits - A toolkit for performing boolean operations, decimation, remeshing, and surface parameterization on 3D geometry.
- Triangle Mesh Data Structures - The product organizes and accesses facets and edges within a triangle mesh using specialized data structures.
- Volumetric Mesh Extraction - The product generates triangle meshes from 3D scalar fields using Marching Cubes or Marching Tetrahedra.
- PDE-Based Mesh Deformations - Solves partial differential equations to propagate handle transformations and maintain surface continuity during deformation.
- Surface Normal Computations - Calculates and visualizes vertex or face normals for rendering and geometric analysis.
- Laplace-Beltrami Operators - Computes surface curvature and smoothing using cotangent-based discretization of the Laplace-Beltrami operator.
- Linear Algebra Libraries - Implements high-performance numerical operations and sparse system solving using a template-based matrix library.
- Linear Algebra Routines - Performs high-level linear algebra operations on vertex and face matrices.
- Sparse Matrix Manipulations - Implements sparse matrix operations including the removal of diagonals and repetition of matrix patterns.
- Iterative Constraint Projection - The product projects points onto non-linear constraints using a local-global iterative framework.
- Header-Only Libraries - Provides source code primarily in headers to simplify integration and enable compiler optimizations.
- Mesh Subdivision - The product increases mesh resolution using in-plane upsampling, Loop smoothing, or barycentric subdivision.
- 3D Mesh Quality Analysis - Computes face angles and areas to evaluate mesh regularity and isometry.
- Interactive Mesh Viewers - A viewer for rendering surfaces and scalar fields with interactive camera controls and mesh picking.
- CSG Engines - Represents complex shapes as a hierarchy of boolean operations to maintain precision.
- Dual Quaternion Skinning - The product deforms meshes using dual quaternion blending to avoid joint collapse artifacts.
- Field-Aligned Remeshing - The product generates non-uniform quad meshes by warping the surface according to a frame field.
- Tangent Field Generation - The product generates rotationally symmetric vector fields to guide quadrilateral and hexahedral remeshing.
- Generalized Winding Numbers - Determines if a point is inside a non-manifold mesh by calculating the generalized winding number.
- Skinning Optimizations - The product accelerates non-linear deformation by optimizing over a low-dimensional subspace of weights.
- Smoothing Algorithms - The product removes artifacts from piecewise-constant weights using precomputed Laplacian deltas.
- Mesh Simplification - The product simplifies meshes by iteratively collapsing edges based on cost and placement criteria.
- Laplacian Surface Smoothing - Flows a surface along its mean curvature normal to minimize area using the cotangent operator.
- Detail Restoration - The product restores high-frequency detail to smoothed deformations using precomputed local coordinate frames.
- Mesh Planarization - The product transforms a quadrilateral mesh into a planar one using a local-global iterative approach.
- Ray-Mesh Intersection Tests - The product performs high-performance intersection tests between rays and 3D geometry.
- Dynamic AABB Trees - Uses axis-aligned bounding box hierarchies to accelerate distance queries and ray-mesh intersections.
- Surface Curvature Analysis - Computes Gaussian and mean curvature and determines principal directions using quadric fitting.
- Surface Parametrizations - The product maps 3D meshes to 2D UV planes using harmonic or as-rigid-as-possible algorithms.
- Sparse Matrix Diagonal Operations - Retrieves the main diagonal of sparse matrices as vectors or constructs square matrices from diagonals.
- Barycentric Coordinate Generation - The product generates generalized barycentric coordinates that retain affine precision for cage-based deformation.
- Biharmonic Weight Computations - The product calculates weights for mesh processing using biharmonic operators to ensure smooth transitions.
- Signed Distance Fields - The product performs accelerated distance and inclusion queries using an axis-aligned bounding box hierarchy.
- Geodesic Distance Computations - Calculates the shortest path distance between points on a surface using exact or heat-method algorithms.
- Index Mapping - Reorders or selects matrix elements using an index map column vector.
- Extrema Identification - Locates the maximum or minimum coefficients within a matrix and identifies their subscripts.
- Matrix Slicing - Enables reading or writing non-contiguous sub-matrices using index lists or boolean masks.
- Mesh Spectral Analysis - Extracts eigen pairs of the generalized eigenvalue problem to analyze low-frequency modes.
- Partial Differential Equation Solvers - The product computes vertex values for the Laplace equation using sparse linear systems.
- Quadratic Programming Solvers - The product minimizes quadratic energy subject to constraints using an active set solver.
- Scalar Field Visualization - Visualizes scalar data on mesh vertices and faces using interpolating fragment shaders and colormaps.
- Winding Number Inclusion Tests - Distinguishes the inside from the outside of non-manifold meshes using generalized winding numbers.
- Geometry Processing - Simple library for geometry processing.
- Graphics and Rendering - Simple library for geometry processing tasks.
- Graphics Rendering - Simple library for geometry processing.
- Media & Communication - Geometry processing library
