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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17 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. ...
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1answer
68 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 ...
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0answers
51 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: ...
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1answer
69 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 ...
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0answers
46 views

Area of ImplicitRegion is slow or doesn't compute under certain circumstances

I'm trying to find the area of a region defined by ImplicitRegion using the Area function. I have the following: ...
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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 ...
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1answer
45 views

Wrong boundary in RegionPlot after RegionUnion

I have defined three regions, Slice1, Slice2 and Slice3. ...
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1answer
52 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
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1answer
58 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
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1answer
43 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. ...
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0answers
49 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 ...
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4answers
73 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. ...
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0answers
42 views

Bug of the function ConvexHullRegion [closed]

The function ConvexHullRegion give the following bug (Mathematica 12.2) ...
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1answer
77 views

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

Consider some rectangle called ExperimentLocation, and a circle ParticleAzimuthalCoverage: ...
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1answer
124 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): ...
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0answers
90 views

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

Consider the following code: ...
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1answer
70 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
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2answers
306 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) ...
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1answer
97 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. ...
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2answers
161 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 ...
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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} \...
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1answer
48 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 ...
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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: ...
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4answers
375 views

RegionPlot3D KnotData

Is it possible to find or construct a RegionPlot out of KnotData? My motivation is to Texture...
1
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1answer
60 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
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1answer
120 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: ...
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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. ...
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0answers
43 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 ...
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0answers
52 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\...
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2answers
72 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
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2answers
117 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
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1answer
85 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
196 views

How to refine a boundary mesh with MeshRefinementFunction?

MeshRefinementFunction works well to refine elements in a defined spatial domain (here x>0): ...
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0answers
50 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
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3answers
109 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
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2answers
179 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
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1answer
70 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
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1answer
149 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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1answer
103 views

Possible bug in RegionDistance with RegionBoundary?

Code as simple as it is: ...
3
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1answer
162 views

Moment Of Inertia of half cylinder

With cylinder I have: ...
3
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2answers
141 views

Approximate the piecewise constant with a smooth function

Let us first define a two regions as follow : inner=1;outer=2; reg1 = Disk[{0, 0}, inner]; reg2 = Annulus[{0, 0}, {inner, outer}]; glass=1.5;air=1; Now let's say I ...
1
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2answers
54 views

RegionPlot3D ColorFunction Not Centered [closed]

RegionPlot (and RegionPlot3D) appears to use the lower right corner of the plot as the origin for the coordinates fed to ...
1
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1answer
29 views

Computing a Transformation then visualizing with TransformedRegion Function

I have some function $\psi$, I compute the transformation $T = \vec{x} - \nabla \psi$. I'd like to visualize the action of $T$ on a square centered at the origin. The mathematica website shows some ...
6
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3answers
241 views

Exclude a region in 3D plot

I need to exclude a region of $\pi/3\leq x \leq 2 \pi/3 $ and $\pi/3\leq y \leq 2\pi/3$ of this 3D plot: Plot3D[Sin[x*y], {x, -Pi, Pi}, {y, -Pi, Pi}] How to do it?
1
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1answer
43 views

Failed to compute the area of a polygon or to use a polygon as a region of NMaximize function

I have a polygon generated by some data. Sometimes, I cannot compute the area of some of the generated polygons and I cannot correctly apply function NMaxmize on ...
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2answers
52 views

Exact symbolic area of an intersection of two regular pentagons with parameters

The question of finding the area of intwrsection of two regions with parameters has been answered here using and RegionIntersection with delimeter ...
5
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1answer
179 views

Exact symbolic area of an intersection of two polygons with parameters

On the one hand, can handle expressions which include parameters, including polygons, for example: Area[Polygon[{{1, 2}, {-1, 1}, {2, 5}, {1, a}}]] returns ...
4
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2answers
79 views

Move axis and tick labels in RegionPlot to the top, change border color

I use this code RegionPlot[ Sin[t^(1/3)*y] > 0, {y, 0, 5}, {t, 0, 8}, FrameLabel -> {"y", Rotate["t", 270 Degree]}] and the result is ...
4
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0answers
90 views

Is this a bug of BoundingRegion of MinBall

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