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.

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1answer
34 views

VoronoiMesh with boundary edges removed

I would like to create a Voronoi diagram without the boundary edges highlighted. This code gVD = VoronoiMesh[X, MeshCellStyle -> {{1, All} -> {Thick, Red}}] ...
4
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1answer
93 views

Drawing a “realistic” VoronoiMesh

Consider a set of points generated via Lloyd's relaxation algorithm ...
1
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0answers
34 views

An apparent bug in Geometry`ConvexHull2

I was replacing some usages of Geometry`ConvexHull2 with ConvexHullMesh and found one of my tests failing. It turned out the ...
1
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1answer
30 views

Generating points inside convexhullmesh

How could I generate these points hexagon={{0, Sqrt[3]/2}, {1/2, Sqrt[3]}, {3/2, Sqrt[3]}, {2, Sqrt[3]/2}, {3/2, 0}, {1/2, 0}} following this rule ...
1
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2answers
63 views

How to Parallel submit nested do loop

This is the first time I'm trying to parallel compute something on Mathematica. So this question might be silly. I have a nested Do loop of the form: ...
3
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1answer
72 views

Hyper Tetrahedron in terms of inequalities

The command Tetrahedron[] seems to work fine for the 3-d case. But how can we get hyper-tetrahedron for 4-d case in terms of inequality? Take for example the points: ...
2
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1answer
60 views

Region bounded by planes in terms of inequalities

Suppose I have 5 planes that intersect to give a bounded region in 4D. For example, the planes are x1==0; x2==0; x3==0; x4==0; x1+x2+x3+x4==1; ...
3
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1answer
38 views

Convert ConvexHull in a array to Inequality

This question is in continuation with the previous post Convert ConvexHull to Inequality There are two problems that I faced. Suppose we have two or more convex hull defined using an array R[i], like ...
7
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1answer
178 views

Convert ConvexHull to Inequality

I have the following convex hull. P0={0,0,0}; P1={1,0,0}; P2={0,1,0}; P3={0,0,1}; ConvexHullMesh[{P0,P1,P2,P3}] Now I want the region algebraically as equality ...
1
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0answers
34 views

Image Size change with changing ViewPoint

I have the following code to show the intersection of two convex hulls. The plot has no problem when ViewPoint->Default. But when I try to change the viewpoint manually by holding and dragging the ...
1
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1answer
34 views

How to label vertex of a 3D convex hull?

I have the following code to plot a 3d convex hull with 4 corners only. ...
3
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3answers
66 views

A DistanceFunction for use with a mouse in a DynamicModule

I need to have a mouse cursor that identifies points that are close to the mouse position on a graphics plot. The difficulty is that the scaling of the plot makes this difficult. I think I am missing ...
6
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1answer
98 views

RandomPoint inside mesh for walk-on-spheres Monte Carlo PDE solver

I'm trying to understand a Monte-Carlo Laplace/Poisson PDE solver: http://www.cs.cmu.edu/~kmcrane/Projects/MonteCarloGeometryProcessing/paper.pdf This method inspired by random-walks and ray-tracing ...
3
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0answers
36 views

DelauneyMesh in 4d and higher

Is there any way to find the DelauneyMesh in 4D (or higher)? Its documentation implies that it should be possible "A Delaunay mesh consists of intervals (in 1D), ...
1
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0answers
76 views

Periodic Voronoi Mesh in a box

Is it possible to generate a periodic Voronoi Mesh inside a rectangular domain? I would also like to obtain the coordinates of each cell separately so that I can perform further operations on each ...
7
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2answers
351 views

How to add 'border' to Voronoi diagram

Suppose I have a set of points pts, from which I generate a Voronoi diagram VD: ...
4
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2answers
298 views

Finding shadow area of a 3D object

Given a 3D object, how could one find the area of the shadow? In effect, this is a measure of optical cross section. The ultimate goal would be a table showing latitude, longitude, and, optical cross ...
2
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2answers
70 views

How to speed up finding region centroid and plot3d

I have the following code to make 3D of 9 regions. ...
1
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0answers
27 views

How to find intersection of higher dimensional convex hull?

I have often used ConvexHullMesh to obtain a convex hull for 2-d and 3-d points. But when I try to find it for 4-D points I encounter error even for simple cases. <...
1
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1answer
56 views

Represent a Concave Mesh Volume

I programmatically generate a shape, where the top surface is defined by a series of polygons. I generate all the points of the polygon. ...
2
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1answer
118 views

Periodic boundaries for a 3D walk in a Bravais lattice?

I'm using a Bravais lattice, 'face-centered', which is implemented in Mathematica in LatticeData[]. I want to simulate a random walk over neighboring points using ...
0
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0answers
12 views

How to concatenate multiple `CapsuleShape[]` while changing their size?

I am trying to create a 'chain' of capsules so that they are concatenated at certain points. Then, I want to change the size (radius, etc) of a given capsule, while preserving the relative orientation ...
0
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0answers
63 views

Projecting a 3D mesh region to 2D

How do I project a 3D MeshRegion to a 2D MeshRegion (or equivalent for a BoundaryMeshRegion). This question is similar to ...
5
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2answers
333 views

Shading Intersection Region

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1answer
23 views
0
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0answers
37 views

Boxed Convex Hull

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0answers
43 views

Convex Hull Mess Axis Label

P0={0,0}; P1={1,0}; P2={-1,0}; R[1]=ConvexHullMesh[{P0,P1,P3},Axes->True ] I use this code to draw the convex hull but I want to also label the ...
2
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1answer
60 views

How can I calculate volume of such a MeshRegion Object

The Data is here: meshData === PolygonData is here ...
1
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0answers
91 views

How to use Mathematica to find the coordinates of 7 points?

Could anyone please help me with using Mathematica to find the coordinates of 7 equally spaced points on the unit sphere $S^3$ in $\mathbb{R}^4$? Thanks a lot!
0
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0answers
31 views

Torus Hex Mesh - Need Unique Hex Dimensions

I'm looking to laser cut a bunch of hexagons and assemble them into a torus (using hot glue or tape). How do I get the dimensions of the individual unique hexagons? I've seen Create a torus with a ...
6
votes
2answers
101 views

Penalty function on discrete mesh using Laplace-Beltrami operator?

Context I am interested in extending to the ill-condionned regime the inversion of linear equations arising from inverting differential equations which have been solved via 0-splines over a mesh ...
0
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1answer
45 views

Finding an instance of a parametric equation that intersects given points

So I have this equation for a circle centered at the origin that has some orientation in 3D space. ...
2
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1answer
107 views

Mathematica Won't Recognize a MeshRegion

I've implemented the code in the top answer of this question on the Plateau problem in differential geometry, and it works with the example shown in Example 1, so there is nothing wrong with the code. ...
5
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1answer
83 views

Minimization problem and Voronoi Mesh

I have a random convex mesh $Q$, made of $n$ polygons, and I want to test how close it is to a Voronoi tessellation. In other words, I'm looking for generators (seeds) $\{(x_i,y_i)\}_{1\leq i\leq n}$. ...
5
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2answers
207 views

Why can't an annulus be mapped as a rectangle

The following code is used to map an annulus to a rectangle: ...
6
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1answer
84 views

Checking if a Graph forms a Mesh

Given a random graph, I want to define a function MeshGraphQ that tests if the graph is a lattice (or mesh) graph. Here, I don't need the tiling to be regular. ...
8
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2answers
586 views

How to visualize a spherical mesh on a squared plane?

I need to visualize the points of a spherical mesh on a squared plane (this question is different than this one, I believe). For instance, let us first generate points ...
3
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1answer
106 views

Efficiently finding spheres furthers apart along and perpendicular to a given direction

Setting I am dealing with a box of spheres, all having the same radius and inserted into a finite box size without any overlaps. Along a given direction $\mathbf v$, I am trying to find: (a) The two ...
2
votes
1answer
35 views

unbounded Voronoi iteration with finite and non-equal point radii

I would like to create a cool differential line growth animation based on this great tutorial. The only missing part is the relax node, but I couldn't find any pointers on the web how to implement ...
9
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1answer
118 views

How to calculate border length between adjacent Voronoi regions?

I have a set of Voronoi cells that I partition into some defined regions. I would like to then calculate the length of the "borders" between these adjacent regions, using the edges of the underlying ...
1
vote
1answer
139 views

Retrieving boundary points of concave hull (or alpha shape) in 3D

I am trying to find the boundary points of some concave 3D region which is described by a list of points. If the region were convex I would take the convex hull and simply extract the coordinates ...
17
votes
1answer
564 views

Making a graph or network interactively over an image

Given an image, is it possible to manually draw a graph over it? For example, taking the following image: I want to manually pick the vertices and draw the edges in a "Paint-like" manner to get, for ...
7
votes
1answer
229 views

Getting cell edges from a picture

I would like to write a program that, given a picture of an epithelium (2D cell array), for example automatically detects the cell edges and returns the corresponding lattice. Illustratively, ...
6
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1answer
109 views

Algorithms used for DelaunayMesh

Is it possible to find what algorithms are used for Delanunay triangulations?
4
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2answers
106 views

VoronoiMesh as a Graph

I want to draw the following graph using VoronoiMesh. For example, since ...
6
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1answer
134 views

Updating a graph under ODE dynamics (vertex model)

Consider the following graph, which is obtained from a VoronoiMesh ...
0
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1answer
42 views

How to plot parametric time dependent plot with different parameters taking average of time?

I am trying to plot the solution given in the code with respect to "delc". Now the problem is that it can be plot for a particular value of "t" like t=10,20,50,60,.. upto 100 but what i need is mean ...
5
votes
1answer
181 views

Where to get the detailed code of MMA for grid mesh

I know DelaunayMesh can triangulate the specified area, but I can't see the code and partition idea of this built-in function. I want to know how to get the source ...
4
votes
2answers
120 views

Rectilinear polygon

It is possible to generate a random Rectilinear Polygon (without holes) in WL? I found this option, but without any possibility to ask for a Rectilinear Polygon. ...
7
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1answer
92 views

Is this a bug of BoundingRegion?

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