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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Good examples of “two is easy, three is hard” in computational sciences

I recently encountered a formulation of the meta-phenomenon: "two is easy, three is hard" (phrased this way by Federico Poloni), which can be described, as follows: When a certain problem is ...
5answers
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Fastest Delaunay triangulation libraries for sets of 3D points

Which is the fastest library for performing delaunay triangulation of sets with millions if 3D points? Are there also GPU versions available? From the other side, having the voronoi tessellation of ...
2answers
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Unstructured quad mesh-generation?

What is the best (scalability and efficiency) algorithms for generating unstructured quad meshes in 2D? Where can I find a good unstructured quad mesh-generator? (open-source preferred)
3answers
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Finding which triangles points are in

Suppose I have a 2D mesh consisting of nonoverlapping triangles $\{T_k\}_{k=1}^N$, and a set of points $\{p_i\}_{i=1}^M \subset \cup_{k=1}^N T_K$. What is the best way to determine which triangle each ...
4answers
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Selecting most scattered points from a set of points

Is there any (efficient) algorithm to select subset of $M$ points from a set of $N$ points ($M < N$) such that they "cover" most area (over all possible subsets of size $M$)? I assume the points ...
3answers
812 views

Fitting Implicit Surfaces to Oriented Point Sets

I have a question regarding quadric fit to a set of points and corresponding normals (or equivalently, tangents). Fitting quadric surfaces to point data is well explored. Some works are as follows: ...
4answers
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How to create a random 3D domain representing a plant's root structure?

I would like to model laminar flow of water from roots to the stem of a plant. At the very end of the roots, the tubes vary from millimeter to centimeter scale in diameter and length. As we get closer ...
3answers
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Volume of 3D convex hull of small point sets all on the hull

I have a question that is similar to this one asked before except in 3D, and I only need the volume, not the actual shape of the hull. More precisely, I'm given a small set of points (say, 10-15) in ...
1answer
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Sort a cloud of points with respect to an unstructured mesh of hexahedral cells

Question How would you sort a cloud of points with respect to an unstructured mesh of hexahedral cells? Each cell has a centre and a unique label to represent it. There are two cloud points ...
3answers
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N-dimensional Delaunay Tesselation Software Libraries

I have a set of known points/nodes irregularly spaced in N-Dimensional space (N>=2), and I would like a way to generate the Delaunay triangulation of these points, and return the corresponding ...
3answers
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How to sample points in hyperbolic space?

Hyperbolic space in the Poincaré upper half space model looks like ordinary $\Bbb R^n$ but with the notion of angle and distance distorted in a relatively simple way. In Euclidean space I can sample a ...
5answers
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How are the Voronoi Tesselation and Delaunay triangulation problems duals of each other?

I have always been told that the Voronoi diagram is the dual of the Delaunay triangulation problem. In what sense can they be duals of each other? I thought that dual problems (i.e. in linear ...
2answers
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Is there an algorithm to find an almost-convex hull given a tolerance angle?

I'd like to know if there is an algorithm that given a set o points and an angle computes the convex-hull if the angle is $\alpha = 0$ and given an $\alpha > 0$ computes an envelope that follows ...
1answer
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Given values on a mesh, what algorithm can I use to construct efficiently level set contours?

I have a mesh, faces $F$, edges $E$, and vertices $V$, and I have a list of predefined level set contours. What algorithm can I use to construct contours in the most efficient manner? A plot of the ...
5answers
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Some good reading on polygon algorithms

What are some good resources (books, articles, sites) about polygon intersection and union algorithms?
2answers
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How to get all intersections between two simple polygons in O(n+k)

Basically the formulation of the problem I'd like to solve is very simple. Given 2 simple polygons (without self-intersections) report all intersecting edge pairs in O(n+k) time, where n - is a total ...
1answer
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How to calculate the area of intersection between a 3D volume and a 2D plane

Hello if anyone can offer insight on how to solve my problem that would be great! I am looking to calculate the area of intersection between a 3D volume and a 2D plane. 3D volume: defined by 6 points ...
1answer
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How to efficiently determine the intersection of a vertical cutting plane with a mesh

I have a list of vertical cut planes, and I have a polygonal mesh ( it's a 2D+0.5D mesh, something like a 2D mesh with an extra dimension, $z$ attached to each point). One can assume that the mesh ...
4answers
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1answer
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Maximum and Minimum distance from query point within bounding box

I'm reading an article regarding approximating sums using KD-trees (similar to FMM). As part of the effort I'm trying to make sense of this article , which is cited. I'm having trouble understanding ...