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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10 votes
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How can I generate a Swiss-Cheese type region and render it transparent?

I am trying to visualize a percolation model that is equivalent to a swiss-cheese where the holes are conducting. At some point, the size of the holes gets large enough for them to touch and a ...
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  • 101
5 votes
4 answers
306 views

Calculate list of points inside a 3D region with specific spacing

I'm trying to get a list of points inside a 3D region. However, I want these points to have a certain spacing in x-, y- and z-directions. As of now I generate a list of points with the appropriate ...
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  • 345
2 votes
1 answer
113 views

Truncated pyramid in Mathematica

Consider a truncated pyramid bounded by two rectangles: Rectangle[{-100, -125}, {100, 125}] Rectangle[{-200, -250}, {200, 250}] The first rectangle is located at z ...
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  • 3,544
0 votes
0 answers
155 views

Why is regioncentroid not giving correct results?

I am trying to calculate and plot the x-axis of a volume centroid for the region between zx-plane and a function squared $u(t,x,z)$ from time $t=15$ to $25$. The function is a numerical solution to a ...
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  • 43
1 vote
1 answer
103 views

Integrals on symbolic regions

Let's define a region as r=Polygon[{{-a,0},{a,0},{a,h}}]. I want to integrate some function over that area. Say x^2. So, ...
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1 vote
1 answer
159 views

How to plot the "trapping region" in Henon Map?

I am writing a paper that makes use of the Henon map. I have managed to plot the Henon map but now require plotting the "trapping region" shown in the image. Do I require to plot it as a ...
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6 votes
3 answers
331 views

I want to count number of points inside the given shape

...
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4 votes
1 answer
103 views

Why is this region in RegionPlot3D wrong?

I believe this is simple, but I can't wrap my head around forming region for RegionPlot3D. I have been reading and trying to understand how to write the region but ...
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  • 1,750
5 votes
2 answers
139 views

How to measure the volume of a 3D point cloud - not using ConvexHull or RippleyRassonRegion. Rather like "boundary" function in MatLab

RipleyRassonRegion and ConvexHull provide the smallest convex region enclosing all points in the set. For regions with real concavities, the volume of this region overestimates the actual volume. For ...
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4 votes
2 answers
151 views

For "RegionPlot", how to fill lines, points, or grids in different areas?

For "RegionPlot", how to fill lines, points, or grids in different areas? I have tried "Mesh", but it fills all region in same mesh. I want to get the result just like this picture,...
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  • 41
0 votes
2 answers
115 views

How to generate random dots with given distances?

I am interested in the following problem, and am curious if Mathematica could be used to solve it. I start with a radius function $\rho:D\to \mathbf{R}_{\ge 0}$ on a region $D\subseteq \mathbf{R}^n$. ...
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8 votes
2 answers
128 views

How to do boolean operations between a large amount of regions

I want to do boolean operations between a large amount of regions. For convenience, I consider a simplified problem. The problem is as follows, digging out a large number of small hemispheres on the ...
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  • 165
2 votes
1 answer
75 views

Why does this RegionIntersection return EmptyRegion?

Why does the first one return EmptyRegion[2] while the second one works? I expected the result is Line[{{0, 0}, {1, 1}}] as the ...
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  • 1,750
5 votes
3 answers
259 views

How can I fill regions from range of x and y?

I have two lists below and each element in rangeX with the corresponding element in rangeY form a region/regions (or a line/...
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  • 1,750
0 votes
2 answers
51 views

Use Show to Display an Arbitrary Number of Objects

(As always, feel free to inform me on how I can better ask questions if my formatting isn't preferred) Just to use an arbitrary case, say I have a function in Mathematica ...
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  • 1
4 votes
1 answer
120 views

How to find boundary of the intersection of two mesh regions in CW or CCW?

I have two lists of points as follow and they're not fixed. ...
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  • 1,750
1 vote
0 answers
38 views

Expressions using matrix variables in SemidefiniteOptimization

The SemidefiniteOptimization function allows one to specify the region for the optimization variable, such as in ...
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  • 11
5 votes
2 answers
185 views

How to create cylinder pie using `ParametricRegion`?

I'm wondering that this simple definition of a cylinder pie doesn't work ...
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6 votes
2 answers
211 views

RegionPlot is slow to plot a simple region

I start out with 5x5 matrix gCorrMatrix[g] depending on a parameter $g$ and an unknown $W_2$ ...
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4 votes
0 answers
97 views

Possible Mathematica bug

I believe the following two integrals should have the same value, since the Boole[] expression always evaluates to 1 in the ...
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7 votes
1 answer
181 views

How to union 3D region to calculate volume?

I have a Teapot likes: region = RepairMesh[ExampleData[{"Geometry3D", "UtahTeapot"}, "MeshRegion"]] I want to calculate the volume ...
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  • 23.4k
2 votes
0 answers
46 views

Problem with BooleanRegion

Suppose I take the following regions B=Disk[{-0.932439, -0.185209}, 1.04], A=RegionDifference[Disk[{0, 0}, 10], B] When I try to ...
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  • 703
3 votes
2 answers
158 views

Complex Map Using ComplexRegionPlot

I am self-studying complex analysis using Dennis Zill's, A First Course in Complex Analysis. I'm a bit stuck on one of the exercises in Chapter 2.4, which asks us to find the image of the region shown ...
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  • 199
5 votes
1 answer
141 views

How to combine several surfaces into a solid and compute its volume?

plot1 is taken from the BSplineSurface document. I add two Disk ...
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2 votes
2 answers
181 views

How can I express the integral path of a curve integral?

A second sort of curve integral: $\oint_{\Gamma}\left(y^{2}-z^{2}\right) d x+\left(z^{2}-x^{2}\right) d y+\left(x^{2}-y^{2}\right) d z$ The integral path $\Gamma$ is the cut-off line obtained by ...
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  • 1,365
2 votes
2 answers
147 views

How to plot this 3D ParametricRegion?

I want to plot this 3D ParametricRegion by using Region, ...
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  • 1,365
3 votes
2 answers
95 views

Transform a region using the flow of differential equation

I was looking to apply a nonlinear transformation to a geometric region, say a rectangle to obtain a transformed region. According to the documentation for TransformedRegion, one requires a Region and ...
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  • 117
6 votes
2 answers
458 views

How to quickly test if two regions intercept?

If I randomly generated two cylinders, how do I test if they intercept? For example: ...
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  • 123
6 votes
2 answers
223 views

Maximum of a group of overlapping circles

I am studying Huygen's principle, and I would like a way to only highlight the wavefront of an advancing wave. At the moment, I have a group of overlapping circles, but I don't know how to highlight ...
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  • 203
1 vote
2 answers
99 views

MomentOfInertia help

Radius and angle must be assigned in order to get the result. When radius and angle are variables, how to get the result? ...
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  • 1,365
4 votes
2 answers
185 views

Plotting functions defined via NIntegrate. Too slow

I have the following two functions xs[u,v] and ys[u,v] defined through numerical integration of $\alpha$ and $\beta$ and $\theta$...
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0 votes
0 answers
36 views

Axial Convolution of Plane and Spherical DiracDelta?

I'd like to evaluate this convolution to a function of r, z and r0 giving a density for the resulting region: $\boldsymbol{\pi}(z) \ast \delta(r-r0)$ WHERE $\boldsymbol{\pi}(z)$ is an xy planar region ...
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0 votes
1 answer
41 views

Incompatible dimensions when trying to use an array of functions within Region3D function [closed]

When trying to plot an array of functions within the region3D function, I get the error code ...
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  • 3
2 votes
1 answer
100 views

Intersect plot and parametric region

I have a vector plot and a region plot on the same scale and I wish to join them like when using Show[ , ]. Now, the vector plot has part outside the region that I would like to delete. Any idea how ...
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4 votes
2 answers
131 views

ParametricRegion is not showing complete region

I am trying to plot a region using the following code ...
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  • 43
0 votes
0 answers
41 views

RegionMeasure works very slow for BooleanRegion

Consider two regions: ...
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  • 3,544
1 vote
1 answer
51 views

Why does not ContourPlot consider the condition given in RegionFunction in the given code?

I have two functions $f(x,y)$ and $g(x,y)$. I am using RegionFunction in ContourPlot to see those values of $(x,y)$ for which $...
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  • 463
0 votes
1 answer
82 views

RegionMember command alternative that can check members exactly?

My problem is as follows: I have an exact rational polygon created using ConvexHullMesh and given a rational point I need Mathematica to decide exactly if it is ...
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  • 553
4 votes
1 answer
125 views

Why RegionMeasure returns a complex value?

Bug introduced in 12.1 or earlier and persisting through 13.0 Consider the following region: ...
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  • 3,544
2 votes
1 answer
63 views

Minimize relating a geometric test

I want to find a circle with a center and a radius that includes all given points, like a circumscribed circle for the points. points data: https://www.dropbox.com/s/0unlv1vbngopu38/new_ref.txt?dl=0 ...
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3 votes
1 answer
115 views

How to generate a 2D region from a 1D region boundary?

For example: ...
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  • 1,365
1 vote
2 answers
102 views

Intersection of a set of structurally homogeneous inequalities and extracting a combination of numbers to fully satisfy it

There are a number of structurally homogeneous inequalities: $\begin{array}{l} \left| s_1\right| \leq \sqrt{4 s_2} \\ \left| s_2\right| \leq \sqrt{4 s_4} \\ \left| s_3\right| \leq \sqrt{4 s_6} \\ \...
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  • 1,636
3 votes
1 answer
96 views

A question about ParametricRegion/Region

If $\left(x_{0},y_{0}\right)\in\left(0,\infty\right)\times\left(0,\infty\right)$, then it easy to get $\left(u_{0},v_{0}\right)\in\left(0,\infty\right)\times\left(0,1\right)$ though the parametric ...
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5 votes
5 answers
412 views

Normal equation of plane through a point and line

I need to find the normal vector of the form Ax+By+C=0 of the plane that includes the point (6.82,1,5.56) and the line (7.82,6.82,6.56) +t(6,12,-6), with A=1. Of course, this is easy to do by hand, ...
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  • 127
3 votes
1 answer
141 views

RegionIntersection returns unevaluated for 3D regions

I'm trying to find the volume an ellipsoid and a prism share. I tried using RegionIntersection, but it returns unevaluated. Input: ...
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  • 345
0 votes
0 answers
71 views

Error calculating RegionDifference of two disk sectors

I am trying to implement an exercise that should be straightforward. I have two sectors of disks (in blue and orange below) with an overlap. I am trying to calculate their Region Difference, but it ...
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  • 473
3 votes
1 answer
107 views

Problem with RegionDisjoint and 3D-Polygons

Bug introduced in 12.1 or earlier and persisting in 13.0.0 I have a flat 3D-Polygon (all points have the same z-Value) and a 3D-line, which I need to check if they intercept using ...
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2 votes
0 answers
111 views

FindRegionTransform again

Bug introduced in 13.0.0 [CASE:4895492] [CASE:4895697] Studying a new command of version 13.0.0 FindRegionTransform, I execute an example from the documentation: <...
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  • 16.8k
2 votes
1 answer
99 views

RegionIntersection for big mesh, AnatomyData["skin","MeshRegion"]

I want to cut a human in half. Say skin=Entity["AnatomicalStructure","Skin"]. So, ...
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  • 2,648
11 votes
2 answers
255 views

Definition of Tube as a Region

Bug introduced in 13.0.0 and fixed in 13.0.1 [CASE:4894156] In version 13, Tube is a recognized region. E.g., ...
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  • 1,135

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