# 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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### ContourPlot3D with variables within a ball

My attempt is (Mathematica 12.0) ...
80 views

Why doesn't this RegionPlot3D not plot anything? ...
170 views

### Strange RegionDifference output on simple example

Why is the output so irregular in the following simple example? ...
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### How to control the spatial discretization of a 3D Region object

I am using constructive geometry to build up a complex 3D shape. I do so by combining Region objects of Graphics3D[] primitives using RegionUnion[] and RegionDifference[]. Here is the code that I use: ...
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### plot and volume of y^2+z^2=1 cut by the plane y=x and x=1 in the first quadrant

I need to plot and find the volume of y^2+z^2=1 cut by the plane y=x and x=1 in the first quadrant So far, ...
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### RegionDifference of a sphere and pyramid - Not correctly specified

I would like to cut out a pyramid from the sphere with the following but somehow I am missing something due to an error "RegionDifference object is not a correctly specified region" ...
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### complex region plot - tweaking

ComplexRegionPlot[Abs[z + 1 - I] <= 1, {z, -2, 1 + 2 I}, AxesOrigin -> {0, 0}, AspectRatio -> 2/3] ComplexRegionPlot[Arg[z - 1] <= 3 Pi/4, {z, -2, 1 + 2 I}, AxesOrigin -> {0, 0}, ...
223 views

### Finding Ellipse Axes

Consider the following ellipse, generated by the bounding region of the following points ...
101 views

### Use a table of data to plot a region instead of RegionPlot

I have an equation that I want to plot as a region plot but it takes a long time to plot and in the future, I will need to replot it multiple times so is it possible to replot a region plot from a ...
125 views

### How to find the image of a region under a matrix?

I want to write code that, given a matrix, finds the image of a unit disk under that matrix. I googled this and I could not find much but this seems like such a simple task. I found the command ...
44 views

### Why RegionPlot plots only the first equation? [closed]

I want to RegionPlot three regions, each of them are $$t_1<t<t_2<0, \quad t<t_1<t_2<0, \quad t_2<t<t_1<0,$$ but it seems that the ...
415 views

### Problem with exporting RegionPlot as PDF

I have the following RegionPlot (which code I don't present since it comes from a long expression): When I right click on it (within the notebook) and try to save ...
460 views

### 3d printing flat pattern

Four copies of a flat region defined below ( length AH = 10 mm and prism Thickness= 2 mm typically) is to be 3d printed so that edges LM,KI coincide. Writing ...
87 views

### NSolve unable to solve system of equations with domain specification

I have a system of two equations in two unknowns that I would like to solve with NSolve within a specified region. However, while Mathematica solves the system if I omit the domain specification, it ...
135 views

### Obtain Data Points (x,y) from a 2D region plot generated from an inequality

I have a code that generates a region plot modeling an aperture. I would like to generate a table of ordered pairs (x,y) for a given u that manipulates my inequality. When I attempt to great a table ...
1k views

### Checking if two line segments intersect

What is the fastest way of checking whether two line segments of the form Line[{p1,p2}] intersect at a point? I don't need to know what the point of intersection is,...
92 views

### How can I solve the 2D diffusion equation over a region that contains mobile sinks?

I am looking for guidance on how to simulate the following system in 2D. I have a region, assumed to be rectangular for simplicity. A substance is diffusing into this region from its boundary. Again ...
107 views

### How plot the domain of multivariable function? [closed]

I want to get and plot the domain of the following function with mathematica : $$Arccos(xy)$$ Any idea ?
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### Define Implicit Region using Interpolating Function

Suppose I have a set of points $\{(x_1,x_2) : g(x_1,x_2) > f(x_1,x_2)\}$, how would I turn this into a mesh that acts as a region for PDE solvers, or even to use as a plotting region? I have tried ...
76 views

### RegionPlot for " < " and " <= " is the same on the boundary? [duplicate]

RegionPlot[{1 <= x < 5 && 2 < y < 5}, {x, 0.8, 5.2}, {y, 1.8, 5.2}, BoundaryStyle -> Dashed] Is there a way to use SOLID line for "less ...
70 views

### What causes RegionResize errors for maps of specific countries?

I want to resize the map of the country as below. ...
60 views

### Mysterious RegionDistanceFunction::regp message

Bug introduced in 12.3.1 or earlier [CASE:4853257] I encountered a strange problem with RegionDistanceFunction. Consider this list of points (I'm forced to use <...
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### NIntegrate over 2D region failed. Simple integrand. Complicated region

The integrand is simply a Gaussian curve over one of the variables PDFTheta[the_] := PDF[ NormalDistribution [0, DeltaTheta/2], the] The region of integration is ...
84 views

### How to make these lines smooth when using ContourPlot inside of a region?

Consider a region in the $(R,T)$ plane defined by the conditions $$0 < R\leq \pi,\quad |T|+R<\pi\tag{1}$$ Define $t(R,T)$ to be t(R,T)=\dfrac{1}{2}\left(\tan\left(\dfrac{T-R}{2}\right)+\tan\...
39 views

### Finding the shared edged between two polygons

Imagine I have two convex polygons pol1 and pol2 with a shared edge. Take, as an example, ...
79 views

### When should one use RegionFunction with ParametricPlot3D?

According to the documentation, "RegionFunction is an option for plotting functions that specifies the region to include in the plot drawn", and it can be ...
160 views

### Find intersection points between ParametricRegion and other curves

How do you instruct Mathematica to return intersection points between curves as numerical values, when using ParametricRegion to represent at least one of the ...
100 views

### How can I change the default color of the basic geometric regions in 2D?

I like to use the basic geometric regions in Mathematica, like Parallelogram[...], Rectangle[...], ...
146 views

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### Problems plotting ImplicitRegion

I have run into some rather strange behavior regarding plotting over regions defined by ImplicitRegion. I have a condition given by ...
63 views

### List of conditions Plot [closed]

I made a table of conditions, namely conditions that define spheres. But I can't plot those in "RegionPlot3D", I would really like to know what I can do to surpass this problem. When I get ...
339 views

### Maximal circle packing inside a given square

How to pack n equal disks(radius a/2) with maximal area inside a given rectangle ? I'm trying to solve this problem using Mathematicas Region functions. Here my approach: Maximize the area of the ...
52 views

### Checking Membership of Conic Hull for Multiple Inputs

Suppose I have a given $10 \times 12$ matrix T, a $12 \times 1$ vector Subscript[\[Xi], 0], a $4 \times 12$ matrix ...
21 views

### How can I ask mathematica to fill in small marginal area in regionplot3d? [duplicate]

I am stuck at how to fill in some marginal area in my regionplot3d. Here is my code. ...
123 views

### Drawing the filled Julia set of a polynomial

Suppose I use JuliaSetPlot to draw the Julia set of a polynomial. Is there a way, assuming the set is connected, to fill in the region? My idea was to use ...
94 views

### Imaginary variables in ImplicitRegion

I am using the function ImplicitRegion[]. RegionPlot[ImplicitRegion[x^2 + y^2 == -1, {x, y}]] which gives me a circle, though in the documentation variables are ...
32 views

This code ...
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### How to speedup RegionIntersection?

Consider a circle circle located at the origin of a coordinate frame and with a radius ROffAxisArb (it is parametrized by two ...
54 views

### Wrong boundary in RegionPlot after RegionUnion

I have defined three regions, Slice1, Slice2 and Slice3. ...