Questions tagged [computational-geometry]

Questions on constructing graphical objects using relatively complex computations relating to the mathematical structures defining those objects. Examples include convex hulls, Voronoi diagrams, Delaunay triangulations, mathematical constructions, symmetries, genuses of curves and graphs and programmatic constructions of polyhedra.

Filter by
Sorted by
Tagged with
-1
votes
0answers
58 views

How can we divide an N-dimensional space? [closed]

I am new with geometry and mathematics problems so maybe I'm saying some wrong things. I have an $N$-dimensional space where there is a set of points ($2^N$ points) and each point has a coordinate ...
8
votes
2answers
165 views

MorphologicalEulerNumber misbehaving in 3D?

Context I would like to compute the MorphologicalEulerNumber of 3D GaussianRandomField as a function of height above a given threshold. Attempt I proceed as follows:...
2
votes
1answer
69 views

Table of surface Parametric draw

I'm trying to reproduce this kind of graph for a spherical cap, with different span ratios. I tried with this: ...
1
vote
1answer
128 views

How to use VectorAngle[] in AnglePath3D[]?

Suppose I have a specific angle that I calculate from two vectors, in 3D: ...
5
votes
1answer
111 views

Problem with RegionMember

I think there is potentially a bug in RegionMember function, particularly in the RegionMember[reg] form. Can you evaluate the ...
0
votes
2answers
92 views

How to align two ellipsoids along center and long axes?

I'm struggling to understand rotation/translation transforms as applied to things like spheres and ellipsoids. Take the following silly example. Given this pair of random ellipsoids, how do I find a ...
1
vote
1answer
69 views

Transfer distribution of points on a sphere to an Ellipsoid[]?

I've seen this cool function, which generates a given distribution of points on the unit sphere, known as Dimroth-Watson distribution: ...
0
votes
0answers
69 views

Computations on differential geometry

I have to do some really long computations of basic riemannian geometry. I am trying to use Mathematica to check them. This is the kind of computations I want to do. Let $M$ be a riemannian manifold ...
1
vote
0answers
50 views

Grouping vectors into groups of 3 by attribute

Three groups are given, each with eight $3 \times3$-vectors: ...
3
votes
1answer
107 views

Analogue of SpherePoints in higher dimensions?

I'm looking for an analogue of SpherePoints that works in dimensions higher than 3, has this been created already? A random sample from unit ball will be ...
5
votes
1answer
85 views

How to generate an heterogeneous mesh

I'd like to generate a mesh with a big variance in cell size. Something like I'd prefer not to rely on a vertex model and perhaps use something simpler, like ...
2
votes
1answer
94 views

Efficient way to pick up pairwise vertices of certain Euclidean distance in arbitrarily dimensional coordinates? [closed]

I have a grid graph with x and y vertices in each direction. The 2-dimensional coordinates of the graph ...
2
votes
0answers
69 views

Inner polygon approximation

Suppose you want to perform an inner approximation of a planar semialgebraic set by a finite set of polygons. The following is a quick way to yield an approximation but I am not convinced that it is ...
3
votes
1answer
74 views

Does DelaunayMesh use exact computations? What is the treatment of non-generic cases?

Computing Delaunay complexes can be sensitive to numerical instabilities, especially in higher dimensions. I would like to know how much I can rely on Mathematica's answers when using ...
4
votes
2answers
289 views

Generate Aztec triangle of size n automatically?

In the paper titled "Perfect Matchings of Cellular Graphs" by Mihai Ciucu, the Aztec triangle of size n (n= 1, 2, 3, 4, 5, ...) is equivalent to a ...
6
votes
2answers
150 views

Automatically get points in a given triangular lattice and vice versa?

Given a triangular lattice which grows with number n, as follows I want to list all the connected points in the lattice to form the ...
0
votes
1answer
151 views

How do you calculate the area of a surface with edges in mathematica

Like the title indicates, how could I achieve this. Normally what I did for a closed surface is as follows: ...
0
votes
0answers
52 views

Checking Membership of Conic Hull for Multiple Inputs

Suppose I have a given $10 \times 12$ matrix T, a $12 \times 1$ vector Subscript[\[Xi], 0], a $4 \times 12$ matrix ...
1
vote
0answers
41 views

Determine if intersection of Polygon and HalfLine is non-empty

I have a concrete example: ...
4
votes
1answer
91 views
6
votes
3answers
382 views

Efficiently compute Minkowski sum of a 2D Region and a Disc of radius r?

Given a 2D Mathematica Region, e.g. A = Region[RegionDifference[Disk[{0, 0}, 2], Disk[{2, 0}, 1]]], how can I grow the region by an arbitrary radius r? For example, ...
2
votes
3answers
334 views

Voronoi diagram of two data sets

My primary data is ...
1
vote
0answers
49 views

RandomInstance of GeometricScene producing unexpected result

Consider the following scene as an example: ...
9
votes
1answer
199 views

Digitizing a geometrical sensor

I want to quantify the flow from photos taken from a sensor such as this one: For a limited number of readings, I can use a plot digitization method. However, I need to do this many times for ...
0
votes
0answers
95 views

Why the output is not in numerical form in Mathematica 12.2?

Consider the following code: ...
3
votes
2answers
177 views

How to find the MeshConnectivityGraph[] from a list of independent cell mesh regions?

I'm generating a bunch of points inside a BoundaryMeshRegion. Then I generate the Voronoi mesh of the points, and take the intersection of the Voronoi cells into ...
2
votes
0answers
47 views

Maximizing the interior angles of a triangle on the Earth [closed]

Gauss once surveyed a triangle in the Harz mountains formed by Inselberg, Brocken, and Hoher Hagen to check if the sum of the interior angles really added up to $\pi$ radians. With the precision ...
4
votes
2answers
121 views

Determine and plot major and minor axes of ellipse

I have an element (El) constructed from a list of nodal coordinates (Nodes). Note: The list of nodes can be arbitrarily long. I then create a minimal area ellipse that encloses all of the node using a ...
7
votes
1answer
127 views

problem with DelaunayMesh 3D coordinates

I found DelaunayMesh works fine for 2D. For example, ...
0
votes
0answers
190 views

colouring Voronoi cells by their properties

I put a couple of previous posts together How can find the 2D Voronoi cell area distribution? Color code Voronoi cell areas depending on number of vertices color voronoi cell based on area to make the ...
0
votes
0answers
48 views

Fortune's Algorithm (Conditional Step Size in `Manipulate`)

I am trying to implement Fortune's Algorithm. Here is my code so far. ...
17
votes
3answers
570 views

Faster "Closest Pair of Points Problem" implementation?

The closest pair of points problem is a common computational geometry problem: given n points, find a pair of points with the smallest distance between them. A naive algorithm of finding distances ...
5
votes
1answer
144 views

Property "Centroid" of result from ConvexHullMesh[] can not be extracted

As the title describes, specifically, simple code below ConvexHullMesh[RandomReal[1, {10, 2}]]["Centroid"] returns an error in V. 12.2, but it worked in ...
8
votes
2answers
243 views

Generate random lines that don't be too crowded between the intersections

It's easy to generate random lines, such as this ...
5
votes
0answers
158 views

How to obtain the adjacency matrix of morphological components?

I am wondering if there's a simple way to obtain the adjacency matrix of the morphological components of a segmented image. Consider the following example (originally, from this question): ...
1
vote
1answer
67 views

Get coordinates of Translated Polygon

I have many polygons of the following form that I wish to do more complicated processing and analysis based on it's updated location (such as relationships between geometries). ...
4
votes
1answer
129 views

How to unite polygons of the same color into a single polygon?

Let a partition of a planar polygon into colored polygons be given, i.e. something similar to We know the coordinates of the vertices and the color of each part, e. g. in such a way ...
2
votes
2answers
73 views

How to create an ImplicitRegion from a list of 2D coordinates [closed]

I have a set of (x,y) coordinates. How can I link them together to form an ImplicitRegion?
0
votes
1answer
123 views

Adopt Mathematica codes for circumscribed and inscribed ellipsoids to related sets

Users Daniel Huber and Dominic have provided an interesting answer each to the question JohnEllipsoids of constructing circumscribing and inscribing ellipsoids for a certain three-dimensional convex ...
3
votes
2answers
119 views

Estimation of the expected Euclidean distance between two random points on a unit $n$-hemisphere

What is the best approach to estimate, with Wolfram Mathematica, the expected Euclidean distance (in a $(n+1)$-dimensional space) between two points selected uniformly at random on a unit $n$-...
2
votes
3answers
159 views

Estimate the expected distance between two random points on the unit $n$-sphere [duplicate]

What is the best approach to estimate, with Wolfram Mathematica, the expected Euclidean distance in a $(n+1)$-dimensional space between two points selected uniformly at random on the unit $n$-sphere? ...
0
votes
2answers
127 views
2
votes
6answers
322 views

Graph/Construct (John) ellipsoids circumscribing and inscribing a certain 3D convex set

A famous theorem JohnEllipsoids of Fritz John informs us that associated with a convex body are circumscribed and inscribed ellipsoids of minimal and maximal volumes. Now, a body--argued to be convex ...
1
vote
1answer
106 views

Maximum area of projection of cuboid onto plane

For didactic purposes I solve with Mathematica the following problem (see Vasilyev's box on p. 17): when the area of the projection of a rotating cuboid in the three-dimensional space with coordinates ...
2
votes
2answers
145 views

Get 3D surface grown by constant distance

There is a nice example of how to generate an isometric visualisation of surfaces which are at a constant distance from a given region. All these examples are just working on one single region. If one ...
2
votes
2answers
183 views

Exporting a FEM mesh from a parametric surface

How is it possible to export a mesh for suitable finite element analysis (such as Abaqus) from a parametric surface expressions? I'm working on this kind of surface: ...
0
votes
0answers
60 views

Intersection Region of two Conic Hull

I have the following semi-infinite conic hull, r1=ConicHullRegion[{{0,0,0}},{{-1,0,0},{0,-1,0},{1,0,1}}]; r2=ConicHullRegion[{{0,0,0}},{{-1,0,0},{0,-1,0},{0,1,1}}]; ...
2
votes
1answer
116 views

Create concentric circles with numbers inside

Hello there if you can give me a hand I want to create and export to pdf the following figure, which if you realize forms the multiplication table. The idea is to be able to control the central number ...
3
votes
2answers
326 views

Cube cutting problem

Show[Graphics3D[{Cuboid[]}], ContourPlot3D[{x==1/3,y==1/4,z==1/5},{x,-0.2,1.2},{y,-0.2,1.2},{z,-0.2,1.2}]] Three planes divide the unit cube into 8 small cubes, ...

1
2 3 4 5
13