# 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 use Mathematica to plot following helix solid geometry?

So, can you provide a method to plot this geometry in mathematica? It is soild instead of a surface. I need it to be printed out from mathematica as stl. document. I have tried with Code "...
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### High-precision solution for the area of a region

I want to solve the area of the region ImplicitRegion[Exp[-(y + x^3)^2] > 1/32 y^2 + Exp[Sin[y]], {x, y}] with high precision (like 100 digits). The region looks ...
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### Problem with RegionIntersection and Polygons with more than 4 points

I have a polygon with 6 points and an InfinteLine and want to find the intersecting line between both using RegionIntersection. Assume this: ...
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### Techniques for NIntegrate on a 3D surface region

I'm looking for ways to speed up NIntegrate[] on a region. My application involves a humongous expression obtained from diagonalizing a 3x3 matrix (see Lattice ...
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### Minimize the number of components in the output of Reduce

Reduce typically tries to minimize the number of components used in describing a region, but it sometimes fails, as in the following example: ...
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### Extending DiscretizeRegion from 2D to 3D [duplicate]

I am trying to construct some 3D printable parts using discretized regions, and am curious if there is a good means to transform a well-designed 2D region into a corresponding 3D region extended ...
• 1,187
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### Checking the formula for solving the Poisson equation with an integral over all of space

EDIT: According to 2.2.3 Rigorous derivation, if we find the integral $u(x,y) = \int \int G(x,y,m,n)f(m,n) dm dn$ then we obtain a function that satisfies the Poisson equation $\nabla^2u(x,y)=f(x,y)$. ...
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### How to make Region from Spline curve

Let bsf = BSplineFunction[{{1, 1}, {-0.5, -0.7}, {-0.4, -1}, {1, 0}}, SplineClosed -> True, SplineDegree -> 3] Than ...
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### RegionMeasure gives finite answer for infinite measure?

I give Mathematica the following command: ...
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### How to find the nearest point using RegionNearest for this case?

Consider the following region: ...
• 5,887
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### How to plot mutiple spiric sections of a torus in a single plot?

Spiric Sections are the cross-sections of a circular torus (radius $a$) cut by a plane parallel to its axis. It has been extensively discussed in the wikipedia page. I want to show the cross-...
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### How to draw the boundary line of intersecting region of a ContourPlot3D and a Graphics3D?

I have mathematical expressions of a cylinder (oriented along the x-axis) and a parabola. And I can easily plot both the surfaces using ContourPlot3D as shown below. ...
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### Strange behavior of VoronoiMesh

In this very simple example the helpful function VoronoiMeshworks as expected. Every point pts is shown with a polygonal ...
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1 vote
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### Why does DiscretizeRegion show the error?

Sometimes (not always) the function DiscretizeRegion cannot work as needed. E.g. let us define 3 simple 3D regions: ...
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1 vote
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### Why does the form of the region affect the integration results?

I try to integrate $e^{\sqrt{x^2+y^2}}$ on the region $x\ge y\ge 0 \&\& x^2+y^2\le4$. Obviously it can be solved by changing the variable. Then I want to verify my result using the Mathematica ...
• 1,144
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Imagine I want the 3D plot of a solid object that has height $H$ and a circular base of radius $R$. The radius of the horizontal cross-section of the object at height $z$ above the base reduces with $... • 4,933 4 votes 1 answer 118 views ### Strategy to speed up two polygons (or region) intersection Basically, I want to compare the overlap between two polygons (or regions). First, I have a reference particle ring that can form a simple polygon, but this type of ring is very thin and long, and its ... • 71 1 vote 0 answers 89 views ### Enclosing ParametricPlot3D to create a solid volume I'm creating a 3D parametric hourglass shape that I hope to fill, making the center solid to use as a 3D volume, because I can't set parameters to it in COMSOL for simulations right now. I know that a ... • 539 5 votes 3 answers 354 views ### How to obtain the list of outermost graph nodes For the following image: The attached code produces a graph. ... • 4,705 4 votes 3 answers 161 views ### Plotting the image of a function of 3 variables in$R^3$Reading the question plotting the image of a function under constraints I see that the TransformedRegion command allows one to plot the image of functions whose domain is in$R^2$and the image is in ... 0 votes 0 answers 42 views ### Parametric Region with Interpolating Function How can I create a ParametricRegion from InterpolatingFunctions? Let's say we have: ... • 1,734 5 votes 1 answer 90 views ### How can I find volume of polyhedron so that Abs[x] + Abs[y] + Abs[z] <= 6$ && Abs[x] + Abs[y] + Abs[z - 2] <= 6?

I am trying find volume of the polyhedron so that $|x| + |y| + |z| \leqslant 6$ and $|x| + |y| + |z-2| \leqslant 6$. ...
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1 vote
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### Shading region under (or over) a curve in horizontal bands

It seems like this should be simple, but I have spent most of the day trying to find a similar example on the web and there appears to be nothing remotely similar. Since I cannot find a way to make ...
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### Rotation of area

I'm trying to illustrate the rotation of the area 0≤y≤1-x^2, 0≤x≤1, when y=1-x^2 is rotated around y=1, and calculate the volume. I read Volume of a region of revolution but could not find a way to ...
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### Calculating vertical displacement to intercept the perimeter of the circle after a horizontal shift

I can't come upon a solution for the question below. The background of the actual work is not interesting for the question, so l won't explain why I need the solution. I would be very thankful if ...
63 views

### DiscretizeRegion fails on a simple implicit region

No matter what option I set to DiscretizeRegion it fails on the region (missing second line). What else can be done? ...
• 20.3k
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### Conic sections: intersection of a plane and a cone. How can I change the equation of the plane to get conic sections automatically?

I tried to draw intersection of a plane and a cone. Hyperbola ...
• 4,013
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### How can I make an animation when using RevolutionPlot3D?

Let ABCD be a square with AB=2. Rotate the filled ABD (see picture) about ...
• 4,013
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### How can I determine coordinates of vertex of parabola as intersection of a plane and a cone?

I want to determine the point I as vertex of the parabola that is the intersection of the plane plane = InfinitePlane[{{0, myy, 0}, {0, myy, -1}, {1, myy, -3}}]; ...
• 4,013
1 vote
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### How can I draw the intersection of a cone and a plane?

I have a cone and a plane myQ = x - 4 y + z + 4 == 0;. How can I draw the intersection of the cone and the plane myQ? ...
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### How to find the region in angles that match the following conditions?

Consider the following function: ...
• 5,887
1 vote
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### Combining surfaces in 3D when using ClipPlanes

Background: I work in the upper half-space interpreted as the model of the hyperbolic space. I want to draw a number of hyperbolic polygons (for simplicity, triangles) having vertices on the boundary. ...
1 vote
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### How can I find distance from a point to a straight line by using projection of the point to the line?

I have a point A(1,2,3) and a line having parametric equation x = 1 + 2t, y = 3t, z = -4+6t. I want to find distance from ...
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### What is simpler way to find projection of a point on a plane?

This is my code to find the coordinate of projection of the point pA = {2, 3, 5} on the plane -284 + 14 x + 2 y + 5 z == 0. <...
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### How to make a specific region in density plot [closed]

There is a variable A(q,a). The plot shows the density plot of "A" with variable q and a. I have a certain range of "A" from (45,50) that i have to mark in the plot, which is in ...
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### How to visualise truncated trapezohedra in Mathematica?

This wikipedia page has some interesting polyhedra: https://en.wikipedia.org/wiki/Truncated_trapezohedron. I have not been able to find them in the PolyhedronData list of mathematica or on Dmccooey. ...
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### How can I draw a random thickness curve?

As we know that add weight factors to Tube, we can get variety thickness tube. I want to know how to do the same thing directly in 2D graph instead of only a 3D ...
• 1,232
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### Borromean rings [closed]

how can I plot the Borromean rings in Mathematica? I am interested in the configuration showcased in figure.
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### Vera Molnár's interruptions - erasing graphic elements

Vera Molnár Vera Molnár (1924 - 2023) was a Hungarian artist who, like Victor Vasarely, lived and worked in France. She was one of the pioneers of computer graphics. Trained as a traditional artist, ...
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### Combining 3D-text (extruded 2D-font) and a simple solid: RegionProduct produces invalid BoundaryMeshRegion

Below is a code fragment demonstrating a problem that has been vexing me for days. The history is in my question #298513 (thanks again to @cvgmt and @user21), but knowledge of that question or its ...
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### Placing a disk of maximum size in a region surrounded by random points

I start with an array of points (cba) and add randomness to generate (cbar). Four point are deleted from it to generate ...
• 56.1k
143 views

### Extrude font into a prism: BoundaryDiscretizeGraphics and Line fail to produce a RegionProduct

I am attempting to use a text character as the base of a three-dimensional prism: ...
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