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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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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: ...
Konstantin's user avatar
1 vote
0 answers
58 views

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 ...
houzw's user avatar
  • 348
7 votes
2 answers
201 views

3D plotting of parametric curved surface

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 $...
sam wolfe's user avatar
  • 4,863
4 votes
1 answer
106 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 ...
J. W's user avatar
  • 71
1 vote
0 answers
85 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 ...
Char's user avatar
  • 539
5 votes
3 answers
337 views

How to obtain the list of outermost graph nodes

For the following image: The attached code produces a graph. ...
csn899's user avatar
  • 4,315
4 votes
3 answers
147 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 ...
Sergio Parreiras's user avatar
0 votes
0 answers
37 views

Parametric Region with Interpolating Function

How can I create a ParametricRegion from InterpolatingFunctions? Let's say we have: ...
MathX's user avatar
  • 1,709
5 votes
1 answer
81 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 $|x| + |y| + |z-2| \leqslant 6$. ...
minhthien_2016's user avatar
1 vote
2 answers
80 views

How can I get a simpler way to draw a solid?

Let two circles center $O_1$, radius $10$ and center $O_2$, radius $6$ so that $AB$ is a diameter of the circle center $O_2$. I am trying to draw solid when rotate the filled region around line $...
minhthien_2016's user avatar
8 votes
3 answers
547 views

Fitting a disk in a non-polygonal region

...
Syed's user avatar
  • 55.4k
2 votes
1 answer
82 views

The intersection of the same overlapping rectangles

A math challenge had the following statement: [[OVERLAP -Three identical rectangular frames are placed one on top of the other, as Shown (A frame on the left tilted over the center frame and ...
Rubens Vilhena Fonseca's user avatar
6 votes
2 answers
271 views

How can I draw solid when rotate this rigion around Ox axis?

I have this picture, knowing that $AC=2$. The point $B$ is midpoint of $AC$, $D$ is intersection point of the semicirle and arc center at $B$ and radius 1. I want to rotate the region with gray fill ...
Thuy Nguyen's user avatar
  • 1,097
6 votes
3 answers
1k views

How to rotate a triangle to get this picture?

Based on this answer, I am trying to draw the picture b). I tried ...
minhthien_2016's user avatar
4 votes
1 answer
92 views

How can I get a 3D form when rotate the polygon $ABCD$ around the line $AB$

I have polygon $ABCD$ here $A(1,0)$, $B\left (\dfrac{1}{2},\dfrac{\sqrt{3}}{2}\right)$, $C\left (-\dfrac{1}{2},\dfrac{\sqrt{3}}{2}\right)$, $D(-1,0)$. How can I get a 3D form when rotate the polygon $...
Thuy Nguyen's user avatar
  • 1,097
8 votes
4 answers
261 views

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 ...
Mike Pugh's user avatar
2 votes
2 answers
187 views

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 ...
mf67's user avatar
  • 1,293
3 votes
2 answers
108 views

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 ...
Darius E.'s user avatar
2 votes
2 answers
59 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? ...
azerbajdzan's user avatar
  • 18.7k
2 votes
2 answers
131 views

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 ...
minhthien_2016's user avatar
6 votes
2 answers
252 views

How can I make an animation when using RevolutionPlot3D?

Let ABCD be a square with AB=2. Rotate the filled ABD (see picture) about ...
minhthien_2016's user avatar
2 votes
2 answers
150 views

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}}]; ...
minhthien_2016's user avatar
0 votes
1 answer
92 views

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? ...
John Paul Peter's user avatar
0 votes
0 answers
33 views

How to find the region in angles that match the following conditions?

Consider the following function: ...
John Taylor's user avatar
  • 5,827
1 vote
1 answer
45 views

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. ...
colt_browning's user avatar
1 vote
1 answer
95 views

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 ...
minhthien_2016's user avatar
6 votes
2 answers
397 views

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. <...
minhthien_2016's user avatar
-2 votes
2 answers
63 views

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 ...
Amnish's user avatar
  • 47
4 votes
2 answers
158 views

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. ...
P Teeuwen's user avatar
  • 357
8 votes
3 answers
368 views

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 ...
herbertfederer's user avatar
8 votes
1 answer
495 views

Borromean rings [closed]

how can I plot the Borromean rings in Mathematica? I am interested in the configuration showcased in figure.
Yasha Gindikin's user avatar
19 votes
3 answers
1k views

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, ...
eldo's user avatar
  • 74.4k
5 votes
1 answer
221 views

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 ...
Felix Kasza's user avatar
4 votes
1 answer
269 views

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 ...
Syed's user avatar
  • 55.4k
4 votes
1 answer
141 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: ...
Felix Kasza's user avatar
0 votes
0 answers
48 views

Solving a differential equation involving terms depending on integral over an ImplicitRegion, which depends on the solution of the equation

I have a somewhat convoluted problem and am not a Mathematica expert. I am trying to solve (numerically) the Euler-Lagrange equations for a complex Lagrangian. The difficulty lies in the fact that L(x(...
Luke's user avatar
  • 1
2 votes
1 answer
55 views

Issues finding the minimum of a function over an implicit domain

i am new to mathematica and am really having some problems when finding the minimum of a function over a implicitly defined domain. This is my code: ...
Charlie Mahon's user avatar
8 votes
3 answers
427 views

How can I build a cycled curve from three orientable Bezier curves and fill the curved region?

The desired result is ...
herbertfederer's user avatar
3 votes
1 answer
80 views

Trying to surround the area produced by intersecting surfaces with a boundary line

With MMA 12, I have a cone & sphere in 3D, that intersect. The area where they intersect I've managed to color (yellow), but I would like to surround that area with a more prominent line of a ...
fiz's user avatar
  • 734
4 votes
1 answer
117 views

How to get finer discretization of 3D polytope?

For some purposes I need detailed mesh models of 2D and 3D shapes. No problem with 2D, so for Rectangle[] we get for example ...
lesobrod's user avatar
  • 1,699
4 votes
3 answers
485 views

Efficiently fill an ellipse with a k-many random ellipses

So, I can create a circle filled with circles of the same radius that gives this example picture: with this code: ...
Teg Louis's user avatar
4 votes
3 answers
269 views

Setting up a double integral over a polar region

Clear["Global`*"]; f[x_, y_] := 9 - x^2 - y^2; Integrate[f[x, y], {x, -1, 1}, {y, -Sqrt[1 - x^2], Sqrt[1 - x^2]}] Integrate[f[x, y], {x, y} ∈ Disk[]] ...
Syed's user avatar
  • 55.4k
2 votes
2 answers
110 views

Interpreting the output of double integral over a Circle

Clear["Global`*"]; f[x_, y_] := 9 - x^2 - y^2; Integrate[f[x, y], {x, -1, 1}, {y, -Sqrt[1 - x^2], Sqrt[1 - x^2]}] Integrate[f[x, y], {x, y} ∈ Disk[]] ...
Syed's user avatar
  • 55.4k
2 votes
2 answers
120 views

Change opacity of region defined by ParametricRegion

I can not find in the documentation how to set Opacity of region defined by ParametricRegion. ...
azerbajdzan's user avatar
  • 18.7k
15 votes
2 answers
572 views

How can we dice a parametric surface?

A few days ago I asked how to slice three-dimensional surfaces: How can we produce sliceforms? The three outstanding answers make me believe that dicing parametric surfaces should also be possible. ...
eldo's user avatar
  • 74.4k
1 vote
1 answer
116 views

Converting implicit region to line

How to convert ImplicitRegion to Line, InfiniteLine or ...
azerbajdzan's user avatar
  • 18.7k
1 vote
1 answer
84 views

Is this a bug in RegionEqual or something else?

Is this a bug or I am missing something again? I ran the following code on a fresh kernel and each time it outputs randomly different result consisting of all combination ...
azerbajdzan's user avatar
  • 18.7k
1 vote
1 answer
59 views

Is this a bug in RegionEqual?

$Version "13.0.1 for Microsoft Windows (64-bit) (January 28, 2022)" Is this a bug or I am missing something? ...
azerbajdzan's user avatar
  • 18.7k
5 votes
1 answer
158 views

RegionIntersection between a Hyperplane and a 3D solid

...
Syed's user avatar
  • 55.4k
0 votes
1 answer
59 views

Which of the given codes $p1,p2,p3,p4$ is the correct one for imposing assumption in ContourPlot3D using RegionFunction?

I am using ContourPlot3D for the condition f[x_, y_, z_] ==0 assuming that the assumption ...
PhysFan's user avatar
  • 63

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