Convex Polyhedron: half-planes to triangular mesh

  • Context: Graduate 
  • Thread starter Thread starter nusuto
  • Start date Start date
  • Tags Tags
    Convex Mesh
Click For Summary
SUMMARY

The discussion focuses on obtaining a triangular mesh from a convex polyhedron defined by the intersection of several half-planes. The user seeks efficient methods for triangularization, specifically mentioning the use of Voronoi diagrams and Delaunay triangulation. They have plane equations and can find intersection points to create vertices, but are looking for simpler solutions to construct triangular faces in 3D. The conversation emphasizes the need for effective algorithms in computational geometry.

PREREQUISITES
  • Understanding of convex polyhedra and their properties
  • Familiarity with half-plane intersection techniques
  • Knowledge of Delaunay triangulation and Voronoi diagrams
  • Basic skills in computational geometry algorithms
NEXT STEPS
  • Research algorithms for Delaunay triangulation in 3D
  • Explore methods for constructing Voronoi diagrams from point sets
  • Learn about computational geometry libraries such as CGAL (Computational Geometry Algorithms Library)
  • Investigate efficient techniques for convex hull generation in 3D
USEFUL FOR

This discussion is beneficial for computational geometry researchers, 3D graphics developers, and anyone involved in mesh generation and surface triangulation in computer graphics or CAD applications.

nusuto
Messages
2
Reaction score
0
Hello!

I'm trying to find some information about my problem but it doesn't seem very easy.
1 - I have a convex polyhedron defined as the intersection of several half-planes.
2- Now I would like to obtain a triangularization of the polyhedron surface in the best way.
Can anyone indicate me where to find any documentation about it?
Thank you very much for your help.
 
Mathematics news on Phys.org
Have you got the information about any points? What about the voronoi diagram or delaunay triangulation?
 
I only have the plane equations. Of course, I can find the intersection points to obtain the vertex of the polyhedron. With them, I can construct, for example, a convex hull with trangular faces (I'm always talking in 3D). However, I was looking for a cheaper and easy way to do it.
 

Similar threads

Undergrad The number of intersection graphs of ##n## convex sets in the plane
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Half-face traversal on general polyhedra
  • · Replies 9 ·
Replies
9
Views
3K
Automotive Topology optimization of an engine's cylinder block
  • · Replies 14 ·
Replies
14
Views
1K
Graduate Does multiplication by an invertible matrix preserve convexity?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Estimating the FOV of a thin sliced plano-convex cylindrical lens
  • · Replies 3 ·
Replies
3
Views
2K
Analysis Study plan for Functional Analysis - Recommendations and critique
  • · Replies 13 ·
Replies
13
Views
5K
Graduate Numerical Integration over 3D mesh
  • · Replies 17 ·
Replies
17
Views
6K
Graduate Does the invariable plane of the Solar system have axial precession?
  • · Replies 15 ·
Replies
15
Views
3K
Lin. Alg. - Half Planes (convex)
  • · Replies 4 ·
Replies
4
Views
4K
Graduate The abc conjecture and Virasoro algebra
  • · Replies 1 ·
Replies
1
Views
2K