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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3
votes
3answers
90 views

1D ImplictRegion can not be plotted with RegionPlot

I am using Mathematica 10.4 In the documantion page of ImplicitRegion, there is an example ...
3
votes
2answers
88 views

RegionPlot with LogScale

I would like to have my RegionPlot with logarithmic scale in x and y. My code looks like ...
3
votes
2answers
88 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 : ...
-2
votes
0answers
40 views

Several RegionPlots in one big plot [closed]

I have 3 RegionPlots and want to merge them into one plot. To illustrate my point I want to summarize it in the following: I have a piece wise defined function like ...
8
votes
2answers
118 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: ...
0
votes
2answers
47 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: ...
16
votes
0answers
165 views

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 ...
7
votes
0answers
78 views

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, ...
7
votes
0answers
90 views

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: ...
3
votes
2answers
64 views

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 ...
6
votes
1answer
62 views

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 ...
4
votes
2answers
108 views

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 ...
3
votes
1answer
53 views

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}]] ...
8
votes
2answers
131 views

How to improve accuracy of NIntegrate over ImplicitRegion

I'm trying to compute the area of a implicit region given as ...
1
vote
0answers
25 views

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 ...
0
votes
0answers
34 views

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 ...
11
votes
0answers
74 views

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 ...
7
votes
1answer
126 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 ...
3
votes
1answer
70 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 ...
12
votes
1answer
149 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 ...
21
votes
4answers
505 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: ...
23
votes
5answers
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 ...
2
votes
1answer
81 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}] ...
2
votes
1answer
57 views

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.: ...
2
votes
2answers
108 views

Generating periodic structure using RegionPlot3D

I am trying to create a periodic structure from a unit cell figure which I created using RegionPlot3D: ...
1
vote
1answer
116 views

Low resolution with RegionPlot3D [duplicate]

To draw a cuboid with RegionPlot3D I can simply specify a function: ...
7
votes
0answers
79 views

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. ...
17
votes
0answers
292 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: ...
1
vote
0answers
47 views

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 ...
9
votes
3answers
593 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 ...
3
votes
1answer
73 views

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. ...
11
votes
1answer
127 views

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 ...
3
votes
1answer
38 views

Getting a set of disjoint regions from the set of overlapping regions

Suppose I have two overlapping regions $R1$ and $R2$ looking like this: ...
0
votes
1answer
262 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 ...
1
vote
1answer
153 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 ...
5
votes
1answer
98 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 ...
9
votes
1answer
203 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 ...
5
votes
2answers
205 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 ...
2
votes
2answers
139 views

Can't find maximum of a function on a region

for h=0.2 I'm trying to find the maximum value of (-h^2/3)*(-1/x^2) subject to ...
1
vote
1answer
59 views

Exists[ ] statement inside RegionPlot[ ] too hard to resolve?

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 ...
2
votes
1answer
126 views

MeshRegion: How to take out a subregion

I have this application at hand: I need to find the Voronoi Regions of a finite set of point and then i have to find the center of mass of each of these Voronoi regions for a given mass distribution. ...
7
votes
1answer
153 views

Alternative to the `DiscretizeRegion`?

I have a polygon: pgn = Polygon[{{0, 0}, {0, 0.018}, {0.155, 0.018}, {0.155 + 0.015, 0.008}, {0.222, 0.008}, {0.222, 0}, {0, 0}}]; here: ...
0
votes
2answers
139 views

3D-plot region between two surfaces

I'd like to 3d-plot the region between the infinite cone: $z=1-x^2-y^2$ and the plane: $z=1-y, z \ge 0$ in Mathematica 10. Also i'd like to know if there is any way (in Mathematica) to calculate the ...
3
votes
2answers
185 views

How can I get a smooth plot of a bounded region?

From the iterated integrals $\int_{0}^{1}\int_{\sqrt{y}}^{1}\int_{x^{3}}^{1}f(x,y),$ we have the region $$\Omega=\{0\le y\le1,\sqrt{y}\le x \le 1,x^{3}\le z \le 1\}.$$ How can I use Mathematica to ...
3
votes
1answer
98 views

Strange behavior with SliceDensityPlot3D using custom surfaces, Mesh lines have a great influence on the density plot

In this answer I was trying to make a 3D stack of disk-shaped density plots, so I was using ListSliceDensityPlot3D. I resorted to using a set of nonrectangular ...
6
votes
1answer
262 views

How can I subtract one surface from another?

I have one surface for which I have an analytical solution, and another represented by a list of 3D points. My question is: how can I plot the part of one that lies outside the other? The first ...
6
votes
1answer
134 views

Area of a image region

I've applied Mathematica to the problem of estimating the area of an estuary, but when I got the results I wasn't able to understand in which unit of area it was given. My approach is the following: ...