Questions tagged [regions]

Questions about functionality that defines or operates on regions (i.e., an open, connected set), including geometric, mesh-based, or data and formula-defined regions.

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0
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1answer
60 views

When should one use RegionFunction with ParametricPlot3D?

According to the documentation, "RegionFunction is an option for plotting functions that specifies the region to include in the plot drawn", and it can be ...
3
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2answers
131 views

Find intersection points between ParametricRegion and other curves

How do you instruct Mathematica to return intersection points between curves as numerical values, when using ParametricRegion to represent at least one of the ...
1
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2answers
87 views

How can I change the default color of the basic geometric regions in 2D?

I like to use the basic geometric regions in Mathematica, like Parallelogram[...], Rectangle[...], ...
4
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3answers
140 views

Select list points at region [closed]

If I have a list Table[{dj, di}, {dj, 0, 1, 0.2}, {di, 0, 1, 0.2}], how can I select only the points that satisfies $\left(2-\delta_{j}\right)-\sqrt{2\left(2-\...
0
votes
1answer
57 views

ParametricPlot3D with variable plot limits

I would like to use ParametricPlot3D in the following general way: ParametricPlot3D[\[Sigma][u,v],{u,0,2Pi},{v,-f[u],f[u]}]. ...
9
votes
1answer
200 views

DirichletCondition doesn't always work with RegionBoundary

I am trying to solve the heat equation on a circle with a square shaped hole in it. It works: ...
2
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2answers
150 views

Plot the intersection of random half-spaces

The code ...
1
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0answers
73 views

Creating a map of earth from an unknown region of the sphere

Lately I've been trying to use Mathematica to plot a map of earth. I have an analytic function from a known triangle to some part of a unit sphere, described by unknown parametrization. This function $...
2
votes
1answer
70 views

Problems plotting ImplicitRegion

I have run into some rather strange behavior regarding plotting over regions defined by ImplicitRegion. I have a condition given by ...
1
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0answers
59 views

List of conditions Plot [closed]

I made a table of conditions, namely conditions that define spheres. But I can't plot those in "RegionPlot3D", I would really like to know what I can do to surpass this problem. When I get ...
6
votes
2answers
326 views

Maximal circle packing inside a given square

How to pack n equal disks(radius a/2) with maximal area inside a given rectangle ? I'm trying to solve this problem using Mathematicas Region functions. Here my approach: Maximize the area of the ...
0
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0answers
42 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
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0answers
20 views

How can I ask mathematica to fill in small marginal area in regionplot3d? [duplicate]

I am stuck at how to fill in some marginal area in my regionplot3d. Here is my code. ...
0
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2answers
111 views

Drawing the filled Julia set of a polynomial

Suppose I use JuliaSetPlot to draw the Julia set of a polynomial. Is there a way, assuming the set is connected, to fill in the region? My idea was to use ...
0
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0answers
88 views

Slice cylinder as region

I am trying to slice a cylinder, and plot as a region, so I can apply a colour funtion like so: ...
4
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1answer
83 views

Imaginary variables in ImplicitRegion

I am using the function ImplicitRegion[]. RegionPlot[ImplicitRegion[x^2 + y^2 == -1, {x, y}]] which gives me a circle, though in the documentation variables are ...
1
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0answers
28 views
1
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0answers
37 views

How to speedup RegionIntersection?

Consider a circle circle located at the origin of a coordinate frame and with a radius ROffAxisArb (it is parametrized by two ...
0
votes
1answer
47 views

Wrong boundary in RegionPlot after RegionUnion

I have defined three regions, Slice1, Slice2 and Slice3. ...
1
vote
1answer
55 views

How to define a polygonal region in 2D to subsequently integrate over it?

I want to integrate a function f[x,y] over a region like this. Is there any way to define the region using the vertices of the purple polygon? Then I can ...
2
votes
1answer
62 views

RegionPlot3D over non-rectangular range

I want to make a RegionPlot3D only in the range x + y + z < 1. The following works, but is slow and poor quality. ...
2
votes
1answer
45 views

Plotting fundamental domains of $\mathbb{Z}^{2}$ with additional features [closed]

I'm trying to figure out how to plot a region that looks like this: The squares don't have to be painted like that, if I could have just light green, gray, light blue and light red it would be great. ...
2
votes
0answers
53 views

RegionDifference - the command does not work as shown in the help - example

Colleagues, good morning. Unfortunately, while solving my problem, I ran into a problem that stopped my project completely. RegionDifference command does not work as shown in the help topic. All ...
4
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4answers
76 views

Create region/limits for NMinimize from list

NMinimize can accept a region to optimize over. I'm looking to create an expression that represents a region from a list of limits e.g. ...
2
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0answers
45 views

Bug of the function ConvexHullRegion [closed]

The function ConvexHullRegion give the following bug (Mathematica 12.2) ...
0
votes
1answer
78 views

How to generate randomly points that belong to the given range?

Consider some rectangle called ExperimentLocation, and a circle ParticleAzimuthalCoverage: ...
3
votes
1answer
126 views

Optimal triangle (minimal area) surrounding a disk

Using RegionWithin it's quite easy to evaluate a parametric triangle with maximal area inside the disk(constant): ...
0
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0answers
91 views

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

Consider the following code: ...
2
votes
1answer
74 views

How can I create a graphic array of wedges of cylinders (slice of pie)?

I'm trying to create an array of wedges of cylinders. So far I have been able to create an array of a full cylinder as shown in the next figure: Using the next code: ...
2
votes
2answers
308 views

center of mass of a 2D square

Using Mathematica, find the center of mass of a 2D square not centered at the origin. center: (x0, y0) ...
3
votes
1answer
107 views

RegionMember Bug in 12.2?

There appears to be an issue with RegionMember in Mathematica 12.2 when it comes to simple polygons and points. ...
3
votes
2answers
166 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
40 views

Finding region, between four hyperplanes, useful for integration

Consider the function $$ f(x,y,u,v) = \exp\bigl( -x^2 -y^2 -u^2 -v^2 \bigr), $$ and the region $\mathcal{R} = \cap_{i=1}^4 \mathcal{R}_i$ defined by four hyperplanes as follows $$ \begin{align} \...
0
votes
1answer
49 views

plotting an inequality [closed]

Can anyone help in plot an inequallity Abs[[x/[1 + x]] - [y/[1 + y]]] <= Abs[x - y]/[1 + 0.01 Abs[x - y]] where 0 < x< 1 and 0 < y< 1 When I tried with Plot command as well as Plot3D ...
1
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0answers
38 views

RegionPlot3D incorrectly plots regions defined by memoized functions

RegionPlot3D incorrectly plots regions defined by memoized functions. A memoizer: ...
7
votes
4answers
391 views

RegionPlot3D KnotData

Is it possible to find or construct a RegionPlot out of KnotData? My motivation is to Texture...
1
vote
1answer
76 views

Fix (decompose) Degenerate Polygon (vertex coincides with edge)

The code Polygon[{{0,0},{3,0},{3,3},{1,3},{1,1},{2,2},{2,1},{0,1}}] produces, according to Mathematica, a disconnected polygon with 0 area. The vertex ...
2
votes
1answer
124 views

How can I make Mathematica calculate a volume given a set of inequalities on the the three dimensions?

How can I make Mathematica calculate a volume given a set of inequalities over three dimensional space? I know how to plot the 3D region of the volume that I need to calculate, like this: ...
2
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0answers
57 views

Can you calculate the area of region that is plotted with NSolve or FindRoot?

I plotted a pretty complex region in the xy plane (code given below). Basically, one of the inequalities is really complex and needs to be numerically approximated. In my code I do this with FindRoot. ...
0
votes
0answers
44 views

RegionPlot Not Plotting Correctly

Im plotting a region in RegionPlot and it gives me an output but it does not look like it is plotting correctly. This may be an issue with my syntax but I'm not seeing where the error could be. For ...
1
vote
0answers
53 views

Plotting Complicated Region in Mathematica

I'm trying to plot the region corresponding to the following code. The f[0,0,5] lines were just me testing the functions. When its plotted, the region only shows the first part of my region plot ($y\...
1
vote
2answers
76 views

Finding the arc length of a region defined implicitly with an interpolated function

I begin by defining an interpolation of some data I have stored at this link for brevity. The interpolating function is a function of two variables, x and ...
2
votes
2answers
127 views

Get Graphics3D object for only part of a cone

I have the necessary information to define a cone and plot it in Mathematica: ...
2
votes
1answer
89 views

Is there a way to SurfaceArea of each face of 3D shape separately?

Consider the following 3D shape as an example: ClearAll[cylinder]; cylinder[r_,z_]:=Cylinder[{{r,r,0},{r,r,z}},r]; It is a cylinder whose entire ...
8
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2answers
209 views

How to refine a boundary mesh with MeshRefinementFunction?

MeshRefinementFunction works well to refine elements in a defined spatial domain (here x>0): ...
0
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0answers
51 views

3D plot with Region seems inaccurate

Region[ImplicitRegion[x/Max[y,z] == Max[y,z]/Abs[y-z] && x+y+z == 1,{x,y,z}], PlotRange -> {{0.001, 0.999}, {0.001, 0.999}, {0.001, 0.999}}] produces ...
3
votes
3answers
110 views

How can I find polygons in convex hull?

From some geometric computations I get a lot of 3 dimensional points. From theory I know two facts: The points define a convex polyhedron, and this polyhedron has non-regular 3-, 4- and 5-gons as ...
5
votes
2answers
183 views

How to get a clean RegionDifference product

I want to get the difference between the following two regions, an annulus and a crown: Here's the code: ...
5
votes
1answer
73 views

Region for polygonal frustum?

An example of a frustum of a hexagonal pyramid (a.k.a. hexagonal frustum) from Wikipedia: Is there a quick way to build one, given the Region of two $n$-sided ...
7
votes
1answer
158 views

MeshRefinementFunction on 2D surfaces embedded in 3D

DiscretizeRegion doesn't seem to run the supplied MeshRefinementFunction when meshing a 2D surface in 3D. For example: ...

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