# CGAL — Computational Geometry Algorithms Library

> CGAL provides reliable and efficient geometric algorithms in C++ for applications in meshing, point cloud processing, shape analysis, and scientific computing.

## Install

Save in your project root:

# CGAL — Computational Geometry Algorithms Library

## Quick Use
```bash
# Install via package manager
sudo apt install libcgal-dev   # Debian/Ubuntu
brew install cgal              # macOS
vcpkg install cgal             # vcpkg
# Compile: g++ -std=c++17 my_app.cpp -lCGAL -lgmp -lmpfr
```

## Introduction
CGAL is an open-source C++ library that provides robust, efficient implementations of geometric algorithms. Used across academia and industry for meshing, shape reconstruction, geometry processing, and spatial indexing, it emphasizes exact computation to avoid floating-point failures.

## What CGAL Does
- Computes Delaunay triangulations, Voronoi diagrams, and convex hulls in 2D and 3D
- Generates surface and volume meshes with quality guarantees for simulation workflows
- Processes point clouds with reconstruction, simplification, and normal estimation
- Performs Boolean operations on polygonal meshes (union, intersection, difference)
- Provides spatial search structures including kd-trees and range trees

## Architecture Overview
CGAL is organized as a collection of packages, each implementing a family of geometric algorithms. It uses exact arithmetic kernels (via GMP/MPFR) to guarantee correct geometric predicates, avoiding robustness issues that plague floating-point geometry. A traits-based design lets users swap kernels for performance vs. exactness tradeoffs.

## Self-Hosting & Configuration
- Install headers and link against CGAL, GMP, and MPFR libraries
- Available through apt, Homebrew, vcpkg, Conan, and conda-forge
- Header-only for many packages; only a few require compiled library components
- Choose between exact (Exact_predicates_exact_constructions_kernel) and fast (Exact_predicates_inexact_constructions_kernel) computation kernels
- Integrates with CMake via find_package(CGAL)

## Key Features
- Exact geometric computation prevents robustness failures in degenerate cases
- Comprehensive coverage: triangulations, meshes, arrangements, Boolean ops, and more
- Industrial-grade mesh generation for FEM, CFD, and 3D printing applications
- Extensive point cloud processing for LiDAR and photogrammetry pipelines
- Active development with regular releases and long-term maintenance

## Comparison with Similar Tools
- **Boost.Geometry** — Boost.Geometry covers basic 2D operations; CGAL provides deeper algorithms including 3D meshing and exact computation
- **Open3D** — Open3D focuses on 3D data visualization and learning; CGAL specializes in rigorous computational geometry
- **libigl** — libigl targets geometry processing research with Eigen integration; CGAL offers broader algorithm coverage with exactness guarantees
- **VTK** — VTK is a visualization toolkit; CGAL provides the underlying geometric computation that VTK can display

## FAQ
**Q: Why does CGAL use exact arithmetic?**
A: Floating-point errors can cause geometric predicates to return wrong results, leading to crashes or invalid output. Exact arithmetic eliminates this class of bugs.

**Q: Is CGAL fast despite exact arithmetic?**
A: Yes. CGAL uses lazy evaluation and filtered kernels that fall back to exact arithmetic only when needed, keeping most computations fast.

**Q: What license does CGAL use?**
A: CGAL uses a dual license: GPL for open-source projects and a commercial license for proprietary use.

**Q: Can CGAL process large point clouds?**
A: Yes. CGAL's point cloud packages handle millions of points with spatial indexing and stream processing.

## Sources
- https://github.com/CGAL/cgal
- https://doc.cgal.org/

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Author: AI Open Source