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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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!
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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 ...
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2answers
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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 ...
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87 views

Surface area of an Island [closed]

How can I calculate the surface area of an island? Do you know some method to do this? I can't find anything in the Internet. I have a 3D model, but I don't know if it will help. Thank you.
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1answer
41 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. ...
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1answer
104 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. ...
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1answer
64 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) $\{(x_i,y_i)\}_{1\leq i\leq n}$. ...
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2answers
196 views

Why can't an annulus be mapped as a rectangle

The following code is used to map an annulus to a rectangle: ...
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1answer
76 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. ...
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2answers
561 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 ...
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1answer
99 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 ...
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1answer
32 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 ...
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1answer
100 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 ...
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1answer
547 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 ...
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1answer
214 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
107 views

Algorithms used for DelaunayMesh

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

VoronoiMesh as a Graph

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

Updating a graph under ODE dynamics (vertex model)

Consider the following graph, which is obtained from a VoronoiMesh ...
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1answer
39 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 ...
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1answer
178 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 ...
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2answers
110 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. ...
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1answer
87 views

Is this a bug of BoundingRegion?

...
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0answers
119 views

How to get 3D building data in map functions?

Most modern mapping APIs have 3D model data for city buildings built-in. For example: Is there some way to get this functionality in the Geography related functions? I believe ...
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1answer
50 views

How to get the overlap's percentage that occurs between 2 circles or among more than 2 circles?

The following code draws the following circles; ...
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1answer
79 views

Computing cross section area between cylinder and disk

I am creating a cylinder, whose center disk is placed at position vector v1 and whose orientation is given by the disk's normal vector ...
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5answers
482 views

Computing the intersection area of two disks in 3D

Closely related to this question about highlighting intersection of two disks, I am trying to figure out if one can do so similarly for disks embedded in $3D$ (e.g. in a bounding box). The difference ...
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0answers
74 views

Hafnian of a matrix

Is there a Mathematica built-in function for the calculation of the Hafnian of a matrix? I am interested in the function as it appears naturally in the calculation of moments of a multivariate ...
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1answer
100 views

RegionDifference not working properly for a region from a printable STL file

Some time ago I created a printable STL-file with a certain software of my own and now I want to modify it with Mathematica programmatically, mainly by subtracting certain geometric objects (e.g. ...
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0answers
31 views

Constrain values to numeric during Minimize

I understand, that similar questions have been asked before, but I am absolutely new to Mathematica and can not solve it myself: In nuce it is the following: I want to calculate ...
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1answer
127 views

Visualising and detecting stacked oblate particles

Context: I am trying to learn how to visualize a box filled with oblate-shaped particles. These are in contrast to prolates which can be drawn using for example ...
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1answer
84 views

Find the points closest to and farthest from the origin for a region in $\mathbb{R}^6$

Given $A$ being the intersection set between $x + y + z + u + v + w = 1$ and $x^2 + y^2 + z^2 + u^2 + v^2 = 1$, find the closest and farthest points to the origin that belong to $A$ in the space $\...
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1answer
59 views

Making cuts in a paraboloid of revolution modified [closed]

I need my to have like parabolic holes where the bumps or fins are ubicated, like in this image, so that they match with the same fins or bumps: The graphic I have was done with a paraboloid and the ...
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1answer
47 views

Plotting a disk with a z-value different to zero

I'm plotting a disk with ParametricPlot3d, but I need it to be drawn at z = 0.4, in order to join it with another plot. ...
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2answers
135 views

Is there any command similar to Delaunay of matlab?

After finding this webpage where they mention the generation of land using matlab, In its section how it works, explain its operation in detail, I started trying to do it in MMA but I am doubtful of ...
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3answers
97 views

How to rotate a lattice points about an arbitrary axis

I have hexpoints = Table[{Cos[n Pi/3] + 1, Sin[n Pi/3] + \[Sqrt]3/2}, {n, 6}]; Which gives the fundamental cell to be applied in ...
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1answer
59 views

How to obtain the positions of the points in a lattice

I want to know the positions of each point in a hexagon lattice, like I saw some posts where they obtain this lattice using a function ...
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3answers
321 views

Computing the surface area and volume of molecules

Here is a somewhat difficult problem I've had for a long while. Space-filling models of molecules can be easily generated by ChemicalData[], ...
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1answer
65 views

BoundaryDiscretizeRegion Plots does not work with ParametricPlot3D

I am trying wit this data ...
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0answers
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How to find coordinates of the points A, B of a sphere with screen coordinates?

I put my question at here https://tex.stackexchange.com/questions/503745/how-can-i-get-correct-the-point-a-and-b-automatically-in-this-picture/503838?noredirect=1#comment1272706_503838 to find the way ...
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0answers
108 views

Calculate the intersection points of a line and a parametrically defined 3D surface

Thanks to Henrik Schumacher for advice to simplify the sample code: I would be grateful for any pointers on the following issue. A line from an external point intersects the surface at 2 points (...
2
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1answer
75 views

Getting a list of cities that are located in more than one county (within a state; in this case Florida, USA)

To get the list of counties in the State of Florida, I first evaluate: EntityClass["AdministrativeDivision", "USCountiesFlorida"] which gives me a pill-shaped ...
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2answers
172 views

Automatic solution to label boundary elements with BoundaryMarkerFunction

Preparations Mathematica 11.3, Windows. Let us say I have a rectangular region with 10 little holes inside. Their coordinates are given by positionList. The ...
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0answers
53 views

Non-convex hull mesh from 3d points [duplicate]

I am trying to create a 3d mesh object from list of points, but the only options I see in Mathematica are ConvexHullMesh and ...
3
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1answer
69 views

Signed cell adjacency matrices (boundary operators)

In How to obtain the cell-adjacency graph of a mesh? there are some great answers that show how to obtain the cell adjacency matrix of a mesh. How would one generalize these to incorporate the ...
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3answers
125 views

RegionMember does not work with RandomPolyhedron or Polyhedron object

According to the documentation RegionMember should work with regions that are true for ConstantRegionQ. However, the function ...
8
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1answer
380 views

How can I select a specific triangle in my Delaunay mesh?

Here is the code I am working with. I create a list of random coordinates, then I create a triangular mesh with the code: ...
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0answers
91 views

How to make a function for image recognition

For example given a big set of random points, and I extract a small section of the random set of points, how can I find the small set on the big set? As a first approach I tried to do a Delaunay ...
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0answers
61 views

How can I create a Delaunay mesh in set of points inside an image?

Is there a possible way to create a Delaunay mesh inside an image given a set of points inside the image? for instance use the pixel coordinates to create the Delaunay mesh.
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0answers
39 views

Regions detecting/counting

Recently, I solved an analytical problem on the number of possible regions in a similar figure: I conducted numerical experiments on Mathematica to verify the results. Intersection points are easy to ...
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0answers
40 views

Possible bug with InnerPolygon and RegionUnion in version 12

case1 case2 case3 ...

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