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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73 views

Can one employ Disk with symbolic arguments in equations--and, if not, how might the equations in question be formulated?

Opening note: MarcoB edited the initial question--modifying the title and J. M.'s technical difficulties appropriately indicated that the Disk command should be the one under examination and not ...
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1answer
32 views

Obtaining the boundary line of a RegionPlot

I have the following code ...
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69 views

Can this 2D-Venn diagram code--involving Disk--be “upgraded” to a 3D one, involving Sphere?

At https://wolfram.com/language/12/improved-visualization-labeling/venn-diagram.html?product=mathematica one finds the code ...
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2answers
36 views

DensityPlot3D produces complex numbers

This invocation of DensityPlot3D[] is unhappy: ...
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2answers
46 views

RegionBounds wrong with small change

For the following: RegionBounds[ImplicitRegion[0 <= y <= Sqrt[1 - x^2], {x, y}]] I get the correct value of ...
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1answer
55 views

Create a Venn and/or related diagrams given the eight atoms of a three-set (A,B,C) 256-dimensional Boolean algebra

In my recent answer to How can one expand an arbitrary boolean combination into the $2^n$ atoms of the associated boolean algebra of size $2^{2^n}$?, for the eight atoms {G[0],G[1],G[2],G[3],G[4],G[...
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2answers
47 views

Finding the `RegionMemberFunction[]` of the boundary of a `RegionDifference[]`

RegionMember[RegionBoundary[Cuboid[]]] Works, but RegionMember[RegionBoundary[RegionDifference[Cuboid[], Ball[]]]] Returns ...
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1answer
31 views

Question with Integrate and Region

Let's say I've got a 2D region r=Region[Polygon[{{0,0},{1,0},{1,1}}]]. I can do integrals like Integrate[1,{x,y}\[Element]r], or ...
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1answer
53 views

Plot the image of a function $\mathbb{R}^4\to \mathbb{R}^2$

Given a function $f\colon \mathbb{R}^4 \to \mathbb{R}^2$, I would like to plot the set $\mathrm{Im}(f)\cap R\subset \mathbb{R}^2$ where $R$ is a rectangular set in $\mathbb{R}^2$ (ie. the plot range ...
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1answer
36 views

Unable to correctly Region Plot 3D

I have to plot the region shown in the image below. Although it's very simple, Mathematica is not able to plot it when I put the code ...
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2answers
69 views

How to speed up finding region centroid and plot3d

I have the following code to make 3D of 9 regions. ...
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1answer
82 views

How to define a region given boundary? [closed]

If I want the area between, say, E^x and x+3, I can define: ...
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0answers
27 views

RegionDistance and SignedRegionDistance do not work with Polyhedron objects

I have reported this behaviour to WRI. A support case was created with the ID [CASE:4544288] Consider this simple example (tested in Mathematica 12.0 and 12.1): ...
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1answer
44 views

How to compare two RegionPlots?

I want to compare the regions bounded by the two RegionPlot3D. Following are the two equations of my plots along with their graphical representation: ...
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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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1answer
40 views

RegionPlot3D is giving wrong plot

I am seeing discrepancies between plots obtained for same region using Region and RegionPlot3D, When I use ...
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1answer
65 views

TransformedRegion with piecewise function

Is it possible to use TransformedRegion with a Piecewise defined function? I tried the following, but it doesn't work and I don'...
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20 views

RegionPlot[ParametricRegion[···]] failing to generate output with simple rescaling of axes: ParametricRegion[···] cannot be automatically discretized

I'm trying to plot the image of a subset $U\subset \mathbb R^n$ under a map $F\colon \mathbb R^n\to \mathbb R^2$. Here is a piece of code which does the job in a simple case where $F$ is the identity ...
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1answer
23 views

Region difference not centered

I'm subtracting a disk from a rectangle: rec = Rectangle[{-5, -5}, {5, 5}]; dsk = Disk[{0, 0}, 1]; recB = RegionDifference[rec, dsk]; RegionPlot[recB] Why is the ...
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34 views

Finding the volume by rotating the region bounded by the curves $y=\sin(x)$, $y=0$, $x=0$, $x= \pi$ about $y=-1$

I would like to find the volume of the region obtained by rotating the region bounded by the curves $y=\sin(x)$, $y=0$, $x=0$, $x=\pi$ about $y=-1$. Calc 2 wasn't a strong suit of mine, so this ...
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16 views

How to generate a 4D region from a function

I have a 4D potential in phase space meanField[x,vx,y,vy] and I would like to generate the 3D seperatrix from this distribution. I am currently doing it for the $x-...
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33 views

Opening a region plot on wolfram player

I have the following 3d plot ...
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2answers
79 views

Add Text to Diagrams

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1answer
58 views

Annular segment in 3D

I would like to plot a segment of a circular annulus in three dimensions with constant thickness (like a thick washer, but through some limited ranges of angle). This shows the shape: ...
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24 views

Discretize a 1D Region (Boundary) into exactly N Points

I would like to obtain exactly N points of the boundary of a given (randomized) region, or at the very least, always the same number of boundary points for similar regions. Here is an example what I ...
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1answer
249 views

Plot of gradient over a surface

I have the following region: ...
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2answers
79 views

Region function of rotated Polyhedron

Is it possible to find the equation of the internal region of a rotated polyhedron? For example, the analytic region for a Dodecahedron is found by: ...
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3answers
110 views

RegionUnion Fails for Overlapping 3D Regions

Bug introduced in 12.0 or earlier and persisting through 12.1.0 Warning: The below code may crash your kernel! I am trying to make a (simple) 3D mesh of a box for a FEM solution (I am using MMA 12.1 ...
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1answer
68 views

Colour Change of a Convex Hull

I have the following code to draw a convex hull. ...
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1answer
48 views

scale the size of analytic region obtained form PolyhedronData

I would like to know if it is possible to find the equation of the internal region of a polygon, whose size has been rescaled. For example: The analytic region for a Dodecahedron is founded of: <...
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4answers
6k views

Why is raytracing so slow?

I'm trying to get some rays to bounce in a circle. But I want to be able to control the reflections, i.e. the direction the rays bounce in the circle. I have a MWE below, and it is severely limited by ...
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1answer
58 views

RegionPlot with four parameters

I will try to illustrate my question with an example: Let us define the RegionPlot for b and ...
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1answer
99 views

Get Perimeter Region from Object

I can get the region of a disk $\{x,y\}\in\{x^2+y^2 \leq 1\}$ as follows: Region[Disk[]] Now my question is: Is there also an automated way to get the perimeter ...
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1answer
89 views

Define a region of revolution

My goal is to use "RegionCentroid" on a solid of revolution. This works great for 2d regions: ...
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2answers
195 views

Define region between two curves

I'm trying to define the region between two curves, f[x] and g[x], I can easily find where they intersect: ...
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36 views

RegionPlot (or otherwise) with exclusions

I would like to plot something like (just a little toy example, I have many of these): RegionPlot[x != 1 \[And] -5 < y < 9, {x, -10, 10}, {y, -10, 10}] I ...
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4answers
150 views

How do I list start and endpoints of CantorMesh?

How do I extract start and endpoints of each defined interval of iteration n of CantorMesh[n]? The furthest I can go is ...
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1answer
71 views

Convert 3D graph to region

I have a Graphics3D element and want to calculate its RegionCentroid. However, a graph is not considered a proper region by Mathematica. How can I convert my graph (which has tubes or cylinders as ...
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1answer
41 views

AxesLabel -> Automatic behave strange

MMA version 11.3 & 12.1 ...
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2answers
80 views

Analytical Solution for Scattering Cross-Section of Randomly Oriented Cylinder (or Improved Brute Force)

I'm trying to calculate the sum of the shadows that a cylinder can make when rotated through both theta and phi. I have the following code: ...
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38 views

Styling a Region

How do you style a Region, eg with different colours? In all the examples in the help files, they are always blue. It is also very confusing - are they a Graphics3D object, or what exactly are they? <...
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1answer
98 views

Blue background in StreamPlot output? [closed]

In 12.1.0 for Microsoft Windows (64-bit) (March 14, 2020) writing: ...
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1answer
33 views

How to Resize/Rescale a Mesh?

Consider, for example, the mesh given by mesh = VoronoiMesh[RandomReal[10, {6, 2}]] Imagine I want to resize it so that it is framed in the $[0,1]\times [0,1]$ ...
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2answers
98 views

How to group points based on mesh primitive membership

As a simple example of what I want to do, let's say I have a Voronoi mesh in a $10\times10$ area with $10$ random "seed points": ...
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1answer
75 views

Minimization problem and Voronoi Mesh

I have a random convex mesh $Q$, made of $n$ polygons, and I want to test how close it is to a Voronoi tessellation. In other words, I'm looking for generators (seeds) $\{(x_i,y_i)\}_{1\leq i\leq n}$. ...
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0answers
36 views

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

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2answers
205 views

Why can't an annulus be mapped as a rectangle

The following code is used to map an annulus to a rectangle: ...
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2answers
38 views

Selecting Shared Edges from a Mesh

Consider the following mesh mesh0 = VoronoiMesh[RandomReal[1, {50, 2}]] I can select interior polygons with ...
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1answer
47 views

Plotting space defined by implicit equations via pure functions (ContourPlot3d, RegionPlot3D, Graphics3D)

Is there a simple elegant way to plot any implicit curve or surface in 2D or 3D, given the input reg (list of intervals, i.e. cube) and ...
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1answer
80 views

Checking if a Graph forms a Mesh

Given a random graph, I want to define a function MeshGraphQ that tests if the graph is a lattice (or mesh) graph. Here, I don't need the tiling to be regular. ...

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