# Questions tagged [computational-geometry]

The study of efficient algorithms and data structures to solve various problems involving point sets, line segments, polygons, polyhedra, simplices, etc.

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### Hi I am trying to model a 2D Lug angle using Gmsh 4.6. How can I combine transfinite quad and regular full quad meshes in the following geo file?

I need transfinite mesh a small section of the bolt hole to insert a crack. However, The transfinite mesh and regular full quad mesh seem being incompatible and throwing errors. How can I combine ...
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### Producing Voronoi diagram in three dimensional

A Voronoi diagram is a kind of tesselation that divided the medium into polygons in 2D and polyhedrons in 3D. Although there are many algorithms to construct a Voronoi diagram, some of them are faster ...
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### Fortune algorithm for voronoi diagram

Although there are many algorithms to construct Voronoi diagram, some of them are faster than others. Based on my knowledge Fortune algorithm is fastest for construct Voronoi diagram either in two ...
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### What are some algorithms to calculate the width of an arbitrary polygon when a bounding box approximation is inaccurate

What are some alternative algorithms to creating a bounding box for finding the max width of a concave, simple winding polygon, like the one in the below image? I prefer solutions that are more ...
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### For traditional FEM and FVM, why can't we use mesh to represent geometry and use the mesh which represent the geometry to do the computation directly?

Isogeometric analysis  has the advantage of integrating geometric and mesh models using NURBS or Spline. At the same time, I would like to ask a question to my friends: for traditional FEM and FVM, ...
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### Can the mesh generation methods in FVM and FEM be totally based on the knowledge of the mesh generation theory in computer graphics?

The main references of mesh generation methods in computer graphics (CG) I found are discrete Differential Geometry  and a famous book "Polygon Mesh Processing" , while the "...
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### How to minimize $(x-a)^2+(y-b)^2$ subject to $\sqrt{a}+\sqrt{b}=\sqrt{2}$?

I am not sure if this is on-topic here, but I am trying. Let $x,y$ be positive real numbers. I am trying to find $$\min_{\sqrt{a}+\sqrt{b}=\sqrt{2}}(x-a)^2+(y-b)^2$$ I tried using Mathematica for ...