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

Consider a Polygon with lines drawn between two of its vertices, ...
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### 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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### An issue evaluating RegionInteresect

Description: I am trying to find a RegionIntersect between a Disk and a Polygon. I have ...
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### Voronoi diagram using RegionPlot, using the hyperbolic metric

I want to compute the Voronoi diagram on the unit disk, using the hyperbolic metric. So, I want to input a list of points and obtain a plot of the cells associated with each of the points. I defined ...
104 views

### Problems with integrating over a region

Following the example of this answer: Find the volume of the region defined by $|x|+|y|+|z|<4$ I tried to compute the following integral over a region by using ImplicitRegion. However, when I ...
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### How do I Maximize over a Cuboid region?

So, I want to, say, find a maximum value of $|x_1x_3+x_1x_4+x_2x_3-x_2x_4|$ in a unit cube in 4D; how do I do that? I've tried ...
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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

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 ...
103 views

### RegionPlot with LogScale

I would like to have my RegionPlot with logarithmic scale in x and y. My code looks like ...
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### 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 : ...
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### 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: ...
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### 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 ...
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### How to create a surface mesh embedded in 3D?

I am working on a problem where I want to optimize current densities on 2D surfaces embedded in 3D to generate magnetic fields. The current density on a surface can be written as a scalar function ...
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### Confused about the behavior of the properties of Regions

Actually we can get some information in here.But I'm confuse this phenomenon still: test = ConvexHullMesh[RandomReal[1, {7, 2}]] ...
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### How to improve accuracy of NIntegrate over ImplicitRegion

I'm trying to compute the area of a implicit region given as ...
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### Problem with unbounded implicit region over integers

I have a region specified implicitly, and want to find the region bounds, however there are some problems when the region is defined over the integers and it is an unbounded region. This unbounded ...
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### Can I convert a 2D Region embedded in 3D into a 3D region, filling in the shell? [duplicate]

Here's a simple example, where there are built-in functions to describe both objects. {shell, ball} = DiscretizeGraphics /@ {Sphere[], Ball[]} The first of ...
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### What is a robust way to determine if two polygons overlap? Possible bug in RegionIntersection or Area

When trying to determine if two polygon objects overlap, I think the intuitive way to do this would be to use the RegionIntersection function to find the ...
139 views

### How to convert a graph to a mesh region

As we know,the region is very convenient in Mathematica.And we can convert a MeshRegion into graph like this ...
74 views

### How to color the exterior of a region in a RegionPlot?

One can color the interior of a region by ColorFunction. But how to color the exterior of a region of a RegionPlot (I want to ...
158 views

### RegionNearest and neighborhoods

In this previous question we see that RegionNearest isn't quite as 'capable' as Nearest for some things. Similarly, I need to ...
511 views

### Find the volume of Phobos and Deimos

How can we calculate the volume of a 3D object using the new-in-10 computational geometry functions? For simple objects this works: ...
1k views

### Rounding the Corners of a Shape

I was wondering whether there is an option in Mathematica that enables me to smooth the corners of a shape. The example I want to start with is the pentagon. This can be crudely specified as ...
82 views

### How to do a ParametricPlot within a subregion

I currently have the following parametric plot. ParametricPlot[{(b - a) x/b + a x/r, (b - a) y/b + a y/r} /. {a -> 2, b -> 3}, {x, -4, 4}, {y, -4, 4}] ...
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### Partition a line around intersections

I've got a bunch of lines (ideally in a single Region) as well as a single new line, e.g.: ...
109 views

### Generating periodic structure using RegionPlot3D

I am trying to create a periodic structure from a unit cell figure which I created using RegionPlot3D: ...
118 views

### Low resolution with RegionPlot3D [duplicate]

To draw a cuboid with RegionPlot3D I can simply specify a function: ...
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### RegionIntersection: Point or Line?

This may be a minor point, but I'm wondering why RegionIntersectionof the two rectangles below gives 3 Lines rather than 2 Lines and 1 Point. ...
298 views

### RegionPlot returning a number

Bug introduced in 10.0 and persisting through 10.4 or later I had updated my mathematica to version 10 few days ago. And I had been shocked by the following fact: ...
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### Handling Self-Intersecting Regions

I am trying to test various parametric regions of a function for membership of the origin (point {0,0}). I generate the boundary by creating four parametric boundary curves, and then use RegionMember ...
633 views

### Calculate inertia tensors

Moments of inertia and inertia tensors are well-known characteristics of rigid bodies in physics and applied mathematics. How to calculate them in Mathematica? Is possible to use regions which was ...
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### RegionPlot not plotting BoundaryRegion

This question is related to RegionPlot not plotting some regions. I have the following region and want to plot the area and the boundary. In Mathematica 10.3.1 it works fine but not in 10.4. ...
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### How to make a two letter monogram in 3d like the one on www.mymo.is? [duplicate]

I want to achieve the same effect like the project on http://www.mymo.is/. By taking two letters and combine them in 3d, you can get a complex shape that looks like one letter on the one side and the ...
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### Getting a set of disjoint regions from the set of overlapping regions

Suppose I have two overlapping regions $R1$ and $R2$ looking like this: ...
264 views

### Speed up RegionPlot

I want to plot a system of equalities and inequalities. I used a combination of ImplicitRegion and RegionPlot (since RegionPlot cannot plot lines or points). But this method is very slow than using ...
156 views

### Boundary Problems

I am trying to study what happens to a wave as it passes different boundaries. This is the working wave equation defined on a plane ...
102 views

### RegionPlot not plotting some regions

RegionPlot appears to have regressed in version 10.4 In 10.3.1 RegionPlot[ImplicitRegion[x^2 + y^2 == 1, {x, y}]] gives ...
216 views

### How to discretize a BezierCurve?

Bug introduced in version 10.0 and persisting through 10.4 DiscretizeGraphics is new in 10.0. I need to create a discretized region from a ...
214 views

### RegionPlot of ImplicitRegion is incorrect

Bug fixed in 10.4. Why does RegionPlot of the ImplicitRegion give an incorrect plot? Also, will how does this affect ...
I've got a very complicated existential boolean expression, call it $\exists x: condition$, involving variables $p, q,$ and $x$. Is there a way to plot the region in which this statement holds ...