# Tagged Questions

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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### Intersection coordinates of two spheres

I am trying to obtain a list of coordinates at which two spheres intersect. Take for example the spheres: sp1=Sphere[{0, 0, 0}, 1] and ...
71 views

### Why does RegionUnion fail for these Regions?

Introduction Lately, I asked for a solution to inflate and unite a List of BoundaryMeshRegions: Inflate and unite a list of 0D to 2D regions JasonB came up with a ...
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### Is there a better way to produce a shape with exclusions in RegionPlot3D? [duplicate]

I'm attempting to create a certain shape. It's essentially a rectangular prism with an array of cylinders cut out of it, and then some half shells of cylinders along the sides. My attempt is basically ...
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### Intersection of volumes defined by inequalities

I have 5 inequalities with some parameters like dh, din and thetawhich I intend to vary. In ...
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### Why are there these jagged “shards” in my RegionPlot3D?

I'm creating a region out of two component regions. Before anyone suggests it (because a lot of similar questions are about it), I don't think the problem is increasing PlotPoints. I've increased it ...
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### Volume of a Region defined by Inequalities [duplicate]

I am trying to compute the volume of a 3-dimensional region defined by 5 inequalities. Mathematica takes too long to compute it. In fact, I haven't ever seen it complete the execution of the below ...
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### How to plot the difference between two regions? [duplicate]

I'm trying to take the difference between two regions. In this case, one region is a cuboid, and the other is a cylinder. Here's what they look like drawn with Graphics3D: ...
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### Issue formulating RegionPlot3D to visualize RegionIntersection

Description I am looking to visualize gas cloud growth within custom modules. For demonstration purpose, it is assumed gas cloud takes a spherical shape whilst module is defined using a ...
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### How to embed a filled Region in a Graphics?

Let for example: regn = RegionDifference[Rectangle[{-2, -2}, {2, 2}], Disk[{0, 0}, 1]]; The only documented way I found to draw a gereric region ...
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### Randomly generate points on a van der Waals surface

I'm looking to randomly place an atom $\mathbf{A}$ onto a van der Waals surface formed by atoms $\mathbf{B}$, such that the distance between the randomly-generated atom $\mathbf{A}$ and the nearest ...
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### Projection of a 4D region defined by function on 3D region

I am trying to project a 4D region defined by a function onto a 3D region so I could visualize it. I am trying to use Resolve to achieve this but it is not working. ...
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### How to Discretize a Tube

In Is there a way to outline text?, I was amazed that BoundaryDiscretizeGraphics can discretize a Text primitive. So in a ...
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### 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 ...
67 views

### Deleting circular regions from a larger Circle

I am trying to determine how the Dirichlet eigenvalues of the Laplacian of a circular region change. I would calculate the principal eigenvaluen of this image, and gradually decrease the radius of the ...
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### RegionPlot with rank constraint

I am trying to plot the feasible region of a rank constrained semidefinite program shown below: The Mathematica code that I am using is the following: ...
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### RegionPlot Failing on my System

I am running Mathematica 10.4.1.0 on a MacBook Pro OSX 10.11.5. I opened the documentation for TransformedRegion, went to this example in Scope, Formula Regions. When I open this particular ...
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### Is it necessary to introduce ImplicitRegion and ParametricRegion in version 10?

In version 10.0, Mathematica introduced a new function about region plotting: ImplicitRegion. But I'm wondered that haven't this function been already existed in the older version? That is, ...
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### 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 ...
37 views

### Inconsistent behavior from RegionMeasure on the RegionIntersection between a Polygon and a Line

Consider a Polygon with lines drawn between two of its vertices, ...
131 views

### Create a filled ListPlot, where the points in the list come from within the regions rather than from the region boundaries

Is it possible to fill, color, under the points in ListPlot where the points define the area and the boundary? Assuming that the number of points are large enough ...
118 views

### Defining a region from combination of data and geometric region

I would like to define a region in (x,y) by combining the region RegionPlot[ ImplicitRegion[ Sqrt[x^2 + y^2] <= 0.99, {{x, 0.01, 0.99}, {y, 0.01, 0.99}}]] ...
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### RegionIntersection puzzle

I am using RegionIntersection[] to intersect two rectangles, phrased as Polygon[]s: ...
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### Selecting and plotting points belonging to a region from a random sample

I'm facing a problem with RandomReal when using ListPlot to plot some constrained points. I found that at every run of MA kernel ...
73 views

### How-to derive conical region in an arbitrary geometry?

Description I have been working with derived geometric regions and ran into a problem when deriving RegionIntersection of a Cone...
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### Disobedient RegionPlot3D

I faced a strange behavior of a RegionPlot3D. I am drawing a piece of a plane bounded by a parabola. This works: ...
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### How to apply DiscretizeGraphics to a tube? [duplicate]

I want to export the numerical solution of the Chan-Lee oscillator as an STL file so that I could print it out. But when I expanded the curve into a tube, ...
120 views

### The unexpected behavior of region calculate

In my this answer,I get some overlapped disk like this placed with red arrow point out But actually that function of diskMake is designed to produce ...
384 views

### Join Two Element Meshes

Let's say I have two element meshes defined as the following: ...
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### RegionPlot error

I'm trying to represent the following table using the command regionplot. The rectangle (0,0), (0.5,0), (0,1),(0.5,1) should be covered, however it is not. Does anyone know what the problem is? Thank ...
114 views

### Find coordinate {x, y, z} where two functions are minimal

I am trying to find a point in a ListPointPlot where the total RegionDistance is minimal AND the total differences of the <...
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### 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 ...
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### Region traced by the endpoints of all vectors given by a parametric expression [closed]

I have the expression of a vector e, with 3 parameters tt1 tt2 and tt3: ...
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### Minimize with Interval restriction

If for instance I have a problem of this sort: ...
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### 1D ImplictRegion can not be plotted with RegionPlot

I am using Mathematica 10.4 In the documantion page of ImplicitRegion, there is an example ...
127 views

### RegionPlot with LogScale

I would like to have my RegionPlot with logarithmic scale in x and y. My code looks like ...
100 views

### How to remove parts of a curve?

I have a curve that have some unwanted parts. How can I remove them ? Or how to constraint the curve to a specific region ? Here's a MWE that shows the problem : ...
148 views

### How to assign Element marker at boundary edges

How to assign marker at the boundary edges as 1, 2, 3, 4 respectively and set all of the inside elements of region as 0? for example: Code: ...
49 views

### Simplify Expressions used to define Region

For example, RegionPlot[{x + y > 1, x - y > 1, y - x > 1, -x - y > 1}, {x, -2, 2}, {y, -2, 2}] can be somehow written as: ...
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### Bug in RegionMember?

Bug persisting through 10.4.1 RegionMember (new in V10) appears to have a bug. For some polygons it finds points that are clearly outside to be "members" of the ...
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### Defining a MeshRegion from a list of points and Polygons with duplicate points does not work in 10.4

Bug introduced in 10.4 and persists through 10.4.1 This code produces a MeshRegion in versions 10.0 through 10.3.1, ...
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### Is this a bug in DiscretizeRegion in 10.4?

Bug introduced in 10.4 and persists through 10.4.1 Consider the following implicit region: ...
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### DiscretizeRegion does not include the boundary specified in ImplicitRegion (10.1)

I am trying to do some 3D PDE solving, and I keep running into problems with boundary conditions because my meshed boundaries are not what I expected. For example, the following code ...
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### DiscretizeRegion fails for a triangular region

I define an implicit region like R = ImplicitRegion[ 0 < Sin[u]/Cos[v] < 1 && 0 < Sin[v]/Cos[u] < 1, {{u, 0, 2}, {v, 0, 2}}] But when I ...