# 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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### How to build the following region?

Consider a 3D figure defined by the dependence $\Delta x(z),\Delta y(z)$. One example is a pyramidal frustum, for which $\Delta x, \Delta y$ are linear functions of $z$, and $z$ lies inside the ...
72 views

### How to transform the regions in which a piecewise function are defined?

I have a function f[x,y,z] that has a piecewise definition, i.e., its values depends on the ranges of the arguments. Now suppose I have a coordinate transformation <...
1 vote
223 views

### Is there a projection to draw north point and south point of a sphere like this and keep form of all circles on sphere?

I see this picture and draw this picture by 3dtools If I tried put two points $N$ and $S$ like the first picture, I get one cicrle Is there a projection to draw north point and south point of ...
1 vote
82 views

### Coarse mesh of a tube (cylinder surface)

Based on this answer Coarse mesh of a sphere DiscretizeRegion[Sphere[], MaxCellMeasure -> #,AccuracyGoal -> 0] & /@ ({.001, .01, .1 } 4 Pi) I would ...
1 vote
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### RegionBoundary of a regular polygon in 3D

For a regular Polygon in 3D I would expect some Line regions for the boundary ...
83 views

### How to achieve local area distortion zoom?

This work was authored by Victor Vasarely. I wanted to reproduce a similar image effect and colour effect. I made a simple attempt to draw out the original background section first. ...
44 views

### How can I make a boundary mesh region where one surface is defined by a 2D array of heights and the other surfaces are determined explicitly?

Suppose I have an array of height values such as: SeedRandom heights = MeanFilter[RandomReal[{0, 9.9} + .1, {50, 50}], 5]; I want to make a 3D surface mesh ...
251 views

### A bug about Region plotting?

I used one of the examples in the documentation, but by trying all three versions, V12.0, V13.2, V13.3.0, they all ran as follows: ...
1 vote
69 views

### Subtract ParametricRegions from each other

I have 2 surfaces defined parametrically that overlap. I want to subtract the helical surface from the cylindrical surface to obtain a mesh of just the blue surface in the image. The parameter bounds ...
180 views

### How to get a RegionIntersection output as a primitive instead of a BooleanRegion?

line = ParametricRegion[{2 + 3 t, -1 + t, 3 - 2 t}, {t}]; plane = ImplicitRegion[2 x + 3 y - z == 9, {x, y, z}]; r3 = RegionIntersection[line, plane] ...
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### Speeding up RegionIntersection of multiple sets of rectangles

There is a set of disjoint rectangles shadow that change position over time. I want to find their intersection with another set of small rectangles ...
194 views

### How to remove this white background for text in RegionPlot？

In regionplot, How to remove this white background for text？ ...
1 vote
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### Area of a Polygon doesn't evaluate?

For an examplary plane polygon in space ...
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### RegionWithin returns incomprehensible result

I try to get the condition "ball inside cube" RegionWithin[Cuboid[{0, 0, 0}, {a, b, c}], Ball[{x, y, z}, r]] but Mathematica v12.2 gives error ...
877 views

### Hat Polykite Shape

How can I create the hat polykite shape, also known as the "einstein" in mathematics?
115 views

### How can I improve the plotting speed of plot3D with region calculations?

I'm looking to achieve the desired result as shown in the attached image. There may be various methods to obtain such a plot, but my current code seems to be running quite slowly. Unfortunately, my ...
515 views

### Tomographic Reconstruction of a Convex Polyhedron from its Silhouettes

So, I can construct a random polyhedron and find its 3 silhouettes onto the 3 standard planes. For example, ...
97 views

### Assign BoundaryStyle to more than one region in Region Plot using a theme

Consider the minimal example RegionPlot[{x^2 < y^3 + 1, y^2 < x^3 + 1}, {x, -2, 5}, {y, -2, 5}] Then I can use ...
199 views

### Computation time unexpectedly long for a Volume

The command is Volume[Region[ImplicitRegion[{Sqrt[x^2+y^2]<=Abs[Sin[z]],0<=z<=2Pi},{x,y,z}]]] The computation time is exceeding my expectation. The ...
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### How to estimate Lake area and volume in Mathematica?

I have a satellite image of the lake and I want to estimate its area and volume. Actual volume:1.49*10e8 m^3 Actual Area:36.9 km^2 I did the following command to find the volume, but it is not very ...
78 views

### Restrict the background colour in a ParametricPlot region

I am trying to plot this diagram, distinguished into three separate regions by the white curve. The code that I used for this purpose is provided below: ...
1 vote
52 views

### Intersection of region with triangular lattice in 2D

Is there a function that finds all points that lie in specified region and also are part of triangular lattice defined by {Sqrt i, 3 (2 j + Mod[i, 2])} for ...
307 views

### Volume of Region Contained by 3D Data Points

I have a dataset consisting of (x,y,z) data that describe a surface, and I need to find the volume of the region bounded by that surface. The data do not follow any mathematical equation, but the ...
160 views

### Graphing the locus of points a unit distance from a rectangular prism

I am a new Mathematica user. For one of my first projects, I am attempting to graph the locus of all points that are a unit distance from a rectangular prism with given dimensions. I have no idea how ...
147 views

### How to show a region defined by an inequality within the specified domain?

Firstly, I wrote the following code to specifiy the domain of the variables a and x: ...
1 vote
45 views

### Why does the MaxCellMeasure option in DiscretizeGraphics not work for cylinders?

There is an example in the doc of DiscretizeGraphics ...
244 views

### Why does RegionDifference crash my PC?

I have a simple polygonal region difference: ...
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### NMaximize with generic domain

I want to have a function that gets generic domain and function and does maximum on this domain. For this I tried the following straight-forward code: ...
252 views

### Drawing angle bisectors in a triangle

In triangle $\triangle ABC$, the angle $\angle BAC$ is equal to $60°$, $|AB|=2$, $|BC|=\sqrt 6$, and $AD$ bisects the angle $\angle BAC$ and $BC$ at point $D$. How can I find the length of the angle ...
162 views

### How to draw axes inside an ellipsoid

I would like to draw the axes showing dimensions a, b and c inside an ellipsoid: ...
300 views

### How to create a random belt polygon or belt polyhedron?

A zonogon is a convex polygon that is made up of parallel sides. Generating a random zonogon in Mathematica can be found here. A natural generalization of zonogons is called belt polygons. A belt ...
895 views

### Find the farthest pairs of two points in 2-dim

I wonder if Mathematica can find the pairs of two points that are the farthest in a given list. Let's say a list, XYlist, of points with (x,y) coordinates. ...
142 views

### Restricting Plot3D to an area inside parametrically defined region

I have a region specified as a simple closed curve, suitable for ParametricPlot (as in this question). What is the easiest way to restrict 3D plot to only plot ...
1 vote
68 views

### A non-degenerate region error in DiscretizeRegion

Consider the following region: ...
964 views

### How to create a random zonogon?

A zonogon is a polygon that is convex and is made only out of pairs of parallel sides with the same length. Any regular polygon with an even number of sides is an example of a zonogon. When I use: <...
360 views

### Visualizing region outlines

I want to generate a picture like this, highlight its outlines, don't show extra edges. The built-in MengerMesh will have extra edges ...
205 views

### Fill data points within the boundary established by the given points

I have the following data points: ...
154 views

### Fill ParametricPlot3D into 3D solid shape

i have data point and transform it with matrix and plot with ParametricPlot3D and look like this my goals is to fill this and get the centroid with ...
1 vote
63 views

### efficient way of generating convex hull of binarized image

I have a binarized image with 4 disk-like dots. I want to find the convex hull of these 4 dots. The conventional method using MorphologicalComponents ...
296 views

### A possible bug about ParametricPlot in version 13.3

example 1 ParametricPlot3D[{x, y, 0}, {x, y} ∈ MengerMesh[2, 2]] // AbsoluteTiming example 2 ...
92 views

### ToElementMesh with OpenCascadeShape returns incomplete region

I am solving a PDE using the NDSolve over a cylinder (length L=0.03 m and radius r=0.0025 m). I define the cylinder using OpeCascadeLink and the mesh as shown below. The problem is, the output of the ...
65 views

### Crossing out region on surface

Consider the following Wolfram Mathematica code ...
124 views

### Eliminate artifacts in a region region defined by RegionDifference

Consider the following region: ...
182 views

### How to get rid of the boundary at the regions merging in the plot?

Consider the following region: ...
145 views

### VectorDisplacementPlot is stuck in certain geometries

I want to plot some deformation fields on some geometries with two holes. I do it using VectorDisplacementPlot. In some of the cases the distance between the holes is very small (for example: ...
96 views

### Plots are "jagged" for a simple function

I have a weird problem with DensityPlot, ContourPlot, and Plot3D. The function I want to ...