https://github.com/zju-fast-lab/vertexenumeration3d

Fast Vertex Enumeration for 3D Polytopes
https://github.com/zju-fast-lab/vertexenumeration3d

computational-geometry convex-polyhedron polyhedron polytope

Last synced: 23 days ago
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Fast Vertex Enumeration for 3D Polytopes

• Host: GitHub
• URL: https://github.com/zju-fast-lab/vertexenumeration3d
• Owner: ZJU-FAST-Lab
• Created: 2020-12-14T03:52:53.000Z (over 4 years ago)
• Default Branch: master
• Last Pushed: 2022-03-11T07:46:39.000Z (about 3 years ago)
• Last Synced: 2025-04-04T11:46:40.149Z (about 1 month ago)
• Topics: computational-geometry, convex-polyhedron, polyhedron, polytope
• Language: C++
• Homepage:
• Size: 213 KB
• Stars: 58
• Watchers: 3
• Forks: 11
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Vertex Enumeration 3D

__VertexEnumeration3D__ is an efficient tool to enumerate all vertices of a 3D polytope.

# Feature

1. Only [3 header files](https://github.com/ZJU-FAST-Lab/VertexEnumeration3D/tree/master/include/geo_utils) are all you needed.

2. This tool is more efficient and robust than [__cddlib__](https://github.com/cddlib/cddlib) for 3D polytopes.

3. Any __nonzero-volume__ polytope is acceptable even with __degenrate vertices__(one shared by more than 3 facets).

4. An order of magnitude faster than cddlib by leveraging __polar duality__ and mature convex hull algorithms.

# Interface

Only one function is needed.

     bool geo_utils::enumerateVs(const Eigen::MatrixX4d &hPoly, 

                                Eigen::MatrixXd &vPoly);

Inputs:

    hPoly: 

        An Eigen matrix with size N*4. N is the number of halfspaces. The i-th row 

        is (h0, h1, h2, h3) defining a halfspace as h0*x + h1*y + h2*z + h3 <= 0.

        A 3D polytope is defined by the halfspace intersection, thus an arbitrary 

        number of redundant halfspaces is acceptable.

Outputs:

    vPoly:

        An Eigen matrix with size 3*M. M is the number of vertices.

Example: [src/polyve.cpp](https://github.com/ZJU-FAST-Lab/VertexEnumeration3D/blob/master/src/polyve.cpp).

If an interior point of the polytope is already known, the following function can be used instead.

    void enumerateVs(const Eigen::MatrixX4d &hPoly, 

                     const Eigen::Vector3d &inner, 

                     Eigen::MatrixXd &vPoly)

# Results



  



The ground-truth polytope is visualized by blue facets with green edges. The white sphere is an interior point automatically found by the tool. The red spheres are enumerated vertices, which are consistent with the ground truth.