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.

107 questions with no upvoted or accepted answers
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30
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0answers
424 views

Bug in RegionMember?

Bug introduced in 10.0 and persisting through 12.1 RegionMember is new in 10.0 A commenter notes that the issue is with ...
9
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90 views

How can I plot a region parametrized by another region?

I am trying to learn how to describe and plot a 2D-region for $x_1$ and $x_2$ based on / parametrized by another 2D-region for $v_1$ and $v_2$. In the following example, the region ...
9
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121 views

RandomPoint works with a 2D ImplicitRegion but fails for any higher dimension

This is inspired by this answer which features code that I cannot get to work at all, and I tried to figure out why. It boils down to using the function RandomPoint...
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71 views

What may the arguments be to Region (11.1)?

In Mathematica version 11.1, there is a new function Region. While the Documentation Center page ref/Region has a number of ...
6
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112 views

Smoothing out DensityPlot3D over a region quickly

Is there a way to smooth out DensityPlot3D over a region quickly in an aesthetic way? I can set PlotPoints to 100 or even 200, ...
6
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0answers
500 views

RegionPlot, RegionPlot3D and differing embedding dimensions

RegionPlot seems to be for plotting regions with an embedding dimensions of 2 only, and RegionPlot3D for regions with an ...
5
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50 views

What's wrong with definition/visualization of a rectangular region (ImplicitRegion)

In a very simple example I try to define a rectangular region ...
5
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97 views

Is BooleanRegion limited to only the most trivial cases?

Consider these four regions: regions = Disk[#, 1] & /@ Tuples[{0, 4/5}, {2}] Graphics[{FaceForm[Opacity[0.2]], EdgeForm[Black], regions}] I was looking to ...
5
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85 views

Need help understanding weird RegionUnion behavior

I'm trying to understand some weird behaviors of RegionUnion in a small piece of code. In particular, RegionUnion is not ...
5
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74 views

Quality of RegionIntersection[]: How to control?

This code produces a crude intersection. a = {-1/2, -1/2, -1/2}; b = {1/2, 1/2, 1/2}; R = RegionIntersection[Ball[a, 1], Ball[b, 1]]; Region[R] How can I control ...
5
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652 views

Region Intersection for MeshRegion objects embedded in 3D

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will ...
5
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0answers
195 views

Why is this ImplicitRegion empty?

I'm having trouble understanding why the following RegionPlot code produces results: ...
5
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0answers
546 views

Use of RegionFunction with Graphics3D?

I'd like to plot in 3D a long list of polygons created with TetGenConvexHull, but only in regions specified by a function. Is that possible? As I have it my ...
4
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0answers
104 views

Text flow into user-defined outline

I'd like to flow text into a region defined by a curve, such as: ...
4
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0answers
60 views

Regions and their combinations

I met stupid problems playing with combinations of simple 3D regions. Can anyboby explain what is wrong in my code? I need to make a model for 3D-printing. ...
4
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45 views

Wrong output of RegionPlot

I think Mathematica goes wrong if asked to plot this very simple region: Region2 = ImplicitRegion[x < -1 && y < -1/x, {{x, -3, 0}, {y, 0, 1}}] by ...
4
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136 views

Generating random interlocking regions (i.e. countries)

I am trying to subdivide a finite portion of the plane into a set of at least 20 or so random interlocking shapes, with the shape boundaries having a fractal dimension around that of borders between ...
4
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59 views

Error doing region computations on Hexahedrons

I have the following set of points which I use to define a Hexahedron and compute the RegionCentroid ...
4
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65 views

Cannot avoid redundant function evaluations in RegionPlot

I am trying to use RegionPlot to visualize the regions where a function has different integer values. For example ...
4
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336 views

MeshRegion and BoundaryMeshRegion differences between 10.0.1 and 10.0.2

Original text My need is simple: I have many non-overlapping regions that I will need to use as plotting domains and integration domains. The new region type operations in Mathematica 10 has made my ...
4
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258 views

Unnecessary and slow conversion between simple polygons and geometric regions

To my knowledge some (but not all) of the new geometric region functions in Mathematica version 10 require an additional step to convert from geometric shapes into regions. However this step Does not ...
4
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97 views

NIntegrate::ncvbr: How should we interpret and handle this error not mentioned in any documentation?

I have some user-defined module describing my integrand which has to be computed numerically (it's much more complicated than this but bear with me): ...
4
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0answers
169 views

Precision problem while evaluating RegionMember or Element in V10

I'll try to give you a background on where the problem occured. The problem itself is defined near the end of the post. I'm running a sort of a simulation of a particle in a box. I finally got my ...
3
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0answers
59 views

Surface area of a cube

When I try to compute the surface area of a simple cube it appears to give me the surface area of one of its faces, not the whole cube: ...
3
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113 views

Finding the shortest distance of two points and an area

So I have a region defined by something like MeshRegion[{{0, 0}, {1, 1}, {2, 1/2}, {2, -1/2}}, {Line[{1, 2}], Line[{2, 3}], Line[{3, 4}], Line[{4, 1}]}], and two ...
3
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0answers
94 views

Solving PDEs over a region in different co-ordinate system?

Since Mathematica 10 there's been an option to solve PDEs over a region which I'm currently playing around with to solve Poisson-like PDEs in cartesian coordinates. By changing the region from a disk ...
3
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0answers
82 views

Extract explicit region (integration bounds) from ImplicitRegion

Using an ImplicitRegion in NIntegrate by far best performance is obtained by using ...
3
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0answers
40 views

Compute properties of a transformed region?

I want to find the centroid of a transformed region (which will be a symbolic expression): ...
3
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0answers
185 views

Venn Diagrams: Disc size proportional to cardinality of the set

Background Before beginning of my specific question I am stating that I have read the plotting - How to plot Venn diagrams with Mathematica, post. In short what I want to achieve is a generalized ...
3
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0answers
147 views

RegionIntersection and area on GeoPosition polygons

I am trying to write a simple procedure to find the percentage of a large property falls in each surrounding ZIP code. A problem that I am encountering is the fact that RegionIntegration[] and Area[] ...
3
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109 views

TransformedRegion and RegionPlot

I encountered an issue using RegionPlot together with rotated regions. Notice how as long as one drags a slider in this simple ...
3
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0answers
127 views

Why is MeshRegion atomic?

I wanted to make some changes inside a MeshRegion today and found that unlike Graphics objects, it can't be done directly ...
3
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0answers
193 views

Simple ways to implement vector dilation

Suppose we have a singly connected but not necessarily convex polygon. Something like shape = CountryData["Chad", "Coordinates"]. Is there a simple way to ...
3
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0answers
107 views

Bug when using Plot3D over an ImplicitRegion?

Evaluating this expression seems to cause Mathematica to beep and quit the kernel: ...
2
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1answer
41 views

AxesLabel -> Automatic behave strange

MMA version 11.3 & 12.1 ...
2
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0answers
46 views

Encoding spatial data in Mathematica

I am doing some experimentation with machine learning and robotics, and want Mathematica to be my primary platform. For it, I need to represent a room with some obstacles (circles) and a goal (square)....
2
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0answers
74 views

How to use DirichletCondition with DSolve and not just NDSolveValue?

I know one can use Region and DirichletCondition with NDSolveValue. But I do not know why it ...
2
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0answers
81 views

Unexpected behaviour of RegionFunction in 3D plot

I am trying to plot a function defined in a specific parameter space using the RegionFunction option in Plot3D. So, this is how ...
2
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0answers
95 views

DiscretizeGraphics on a RegionDifference not returning a MeshRegion

I want to take region difference of a sub-mesh of a Delaunay Mesh and a discretized ImplicitRegion. However, Mathematica does not recognize the return as a MeshRegion. Moreover, Discretizing the ...
2
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0answers
73 views

Converting character into region and extracting the boundary

I am using Mathematica to draw regions and export them to use in Clewin, a layout program used in lithographic processes for microfabrication. Clewin is rather simple and basically uses polygons to ...
2
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0answers
175 views

Extracting boundary surface of a RegionPlot3D

Is there a way to extract boundary surface from a 3d region plot? I've plotted my equations using: ...
2
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0answers
80 views

How to make BoundaryDiscretizeRegion work for a RegionUnion of polygons?

This question is related to this one. I want to display the RegionUnion of a large set of smaller polygons. If simply use Region ...
2
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0answers
108 views

Resolve implicit region into explicit one

Does Mathematica provide a way to take, for instance: ImplicitRegion[x^2 + y^2 <= 1, {x,y}] and convert it into a region defined explicitly in terms of x and ...
2
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0answers
127 views

projecting a RegionProduct into 3D space

Apparently, RegionProduct should allow you to generate convolution-generated shapes. For instance, take a 1D curve and a sphere, and the region product I would ...
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0answers
16 views

RegionFunction to clip ContourPlot3D results in unexpected shading

I am attempting to use RegionFunction to trim an implicit surface drawn with ContourPlot3D to only show the portion inside of a sphere (instead of the bounding box from PlotRange). However, when I ...
1
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0answers
26 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. <...
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0answers
36 views

Why can't the output of the `DiscretizeRegion` function display completely?

...
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0answers
32 views

Nearest Region of a Point-cloud

For a given examplary set of points p(2D) with known NearestFunction nf ...
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0answers
41 views

NIntegrate 3D Interpolation function in a region extracted from ListContourPlot3D

I have a list of 3D volumetric data points, e.g. for every position in 3D space there is a value. What I want to do is to firstly use "Interpolation" to get a function form of the data f[x,y,z] and do ...
1
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1answer
56 views

How to feed a list of disks to RegionUnion

I have a bit of code which creates a list of disks (I'm exploring Gershgorin circles) based on a matrix tm. ...