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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0
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0answers
17 views

Limit Plot range to infinitely thin region [duplicate]

I want to plot a function only in a specific infinitely thin region, like e. g. ...
2
votes
0answers
107 views

Intersecting RegionPlots

Does the Mathematica graphics system have any concept of intersecting regionplots? I've found about intersecting graphics but not regionplots so far. For example, if I want to show the intersection of ...
2
votes
0answers
46 views

Is DiscretizeRegion not yet ready ro discretize 3D-solids?

In the DiscretizeRegion documentation: "The region reg can be anything that is ConstantRegionQ and RegionEmbeddingDimension less than or equal to 3." With DiscretizeRegion there could be an easy way ...
4
votes
2answers
102 views

How to plot the ranges of the variables of an iterated integral?

I would like to plot the volume of the following integral: $$\int _{-1}^1\int _0^{\sqrt{1-y^2}}\int _{x^2+y^2}^{\sqrt{x^2+y^2}}\left(xyz\right)dzdxdy$$ Here are the ranges of the variables from this ...
1
vote
2answers
62 views

Condition on Inside of Region

How do I handle boundary conditions present in the region. Mathematica complains about the condition v [1 , t ] == u [1,t]. The condition should be given to this ...
3
votes
3answers
160 views

Plotting the region bounded by parallel lines

I am working on the integral $$\int\int_D (2x+y)^2 e^{x-y}dA,$$ where $D$ is the region bounded by $2x+y=1$, $2x+y=4$, $x-y=-1$, and $x-y=1$. I need to shade the region bounded by these lines, so I ...
5
votes
1answer
147 views

Visualize transformation used in multiple integration

In class, we will sketch the region $D$ in $R^2$ bounded by the curves $xy=1$, $xy=4$, $y=x$, and $y=x+2$. Then we will use the change of variables given by $u=xy$ and $v=y-x$. We need to show that ...
28
votes
4answers
638 views

obtaining random element of a set given by multiple inequalities

I try to obtain random elements from a set given by multiple inequalities. This is of general interest to me, but let me present one example here: I have multiple inequalities specifying half spaces ...
1
vote
1answer
70 views

Create region from set of lines and arcs [duplicate]

I have a shape that is a knuckle plate with two holes cut in it, thus: ...
2
votes
3answers
70 views

Create region from polygons and tangential line segments

I have two circles and tangential line segments that I want to define a region: ...
4
votes
5answers
469 views

How to plot a 2D region when there are 3 free parameters?

How could I obtain the region of payments, with the parameters a,b,c,d between 0 and 1 and the sum of all equals 1? After the comment/recommendation of belisarius... I edit the original question ...
11
votes
2answers
122 views

Integration of a PDE solution over a custom-defined subdomain

Preamble: In my previous question I raised a problem of a custom-chosen integration of the solution of a PDE. In that case it was an integration along a line lying within the PDE domain. The solution ...
5
votes
3answers
102 views

ImplicitRegion gives arbitrary boundaries

This question uses Mathematica 10.2.0.0. equation1 is the major unbounded region I would like to generate: ...
6
votes
1answer
148 views

Easy FindMaximum returns a wrong answer

FindMaximum in region is a new function in mma10,but when I tried the following example: ...
1
vote
0answers
34 views
3
votes
3answers
71 views

List connectivity of points in discretized mesh

I'm trying to automate the extraction of the points and a compatible connectivity list for meshes created using the DiscretizeRegion or similar method. If I create ...
7
votes
1answer
185 views
2
votes
1answer
44 views

Using Compiled Function in Implicit Region

I am looking for a way to speed up code and thus would like to use a compiled function in an ImplicitRegion. Here is an example of a region that can be plotted ...
1
vote
0answers
83 views

Change in direction when a line hits an ellipse? [duplicate]

I'm trying to simulate reflecting light off an elliptical mirror. I currently store the ellipse in the form {center,{radii},rotationAngle} and the ray of light is ...
14
votes
2answers
1k views

Neumann boundary conditions in NDSolve over nontrivial region

The problem I would like to solve involves diffusion in the following region ...
10
votes
2answers
130 views

Possible Bug in Computing Surface Area of Certain Geometric Regions

Mathematica 10.2 introduced some new geometric regions. Two of the new regions include SphericalShell and CapsuleShape. ...
5
votes
0answers
107 views

RegionPlot, RegionPlot3D and differing embedding dimensions

RegionPlot seems to be for plotting regions with an embedding dimensions of 2 only, and RegionPlot3D for regions with an ...
4
votes
2answers
129 views

Why do I need to apply DiscretizeRegion to a derived region to visualize it?

What are the design principles, or other explanations, as to why one needs to apply DiscretizeRegion to obtain a graphical representation of a derived region, ...
3
votes
1answer
118 views

Surface Area of a Region inside a Region

I need to find the surface area of a region which is within another region. The regions I'm working with are fairly complex and so I'm looking for a general solution, but I'll use a cylinder and ...
4
votes
2answers
104 views

BoundaryDiscretizeRegion given an ImplicitRegion never returns

I am trying to generate random points on a "simple" 3D surface for testing purposes. The surface is a plane with etched or embossed rectangular structures. I am using ...
0
votes
1answer
59 views

Boundary discretize region of ellipsoid returns a three dimensional region

I need to integrate a rather complicated function on an ellipsoidal surface, specifically a prolate spheroid surface. Im using the mathematica 10 feature of discretize the regions in mesh and pass ...
12
votes
2answers
534 views

Controlling quality of discretized region meshes

EDIT: Impact of this problem has been considerably lessened in v10.2. Although new version is still not performing analytical discretization at sharp corners (there are jaggies), evenness of sampling ...
2
votes
1answer
126 views

DiscretizeRegion on Raspberry Pi 2

Running DiscretizeRegion@Cuboid[] from the documentation under Raspbian on the Raspberry Pi 2, Mathematica version 10.0.0.0, gives the following response: ...
2
votes
1answer
149 views

Evaluating a surface integral

I'm trying to compute the integral $$\int_S x^2+z^2\,{\rm d}S,$$where $S$ is the surface $$S\colon~ \frac{x^2}{2} + \frac{y^2}{3} + \frac{z^2}{2} = 1, \quad y \geq 0.$$ One possible parametrization ...
2
votes
1answer
98 views

Minkowski sum and product of 2D-regions

Let $A_j$, $j=1,\dots,n$ be subsets of $\mathbb C$ defined by $$ A_j=\{z\,|\,f_j(z)\geq0\} $$ where $f_j:\mathbb C\to\mathbb R$ are given functions. I am interested in the following subsets of ...
6
votes
1answer
105 views

Why is RegionMeasure so slow when calculating intersection area of a 2D and a 3D object?

If you think this description is too long, you can read the problem directly I know normally when one wants to calculate an region, this guide is useful. However, when it comes to calculating an ...
28
votes
8answers
1k views

How to generate random points in a region?

The Mathematica 10 documentation was updated for FindInstance adding support for regions. In my use case, I'm trying to sample points in a set of disks: ...
16
votes
1answer
259 views

How can I smooth a 3D surface generated by RegionBoundary?

I have a set of points that belong to the surface of an object. I would like to approximate a surface to which I can compute the distance. of other points. With the nice code of this post, I was able ...
2
votes
3answers
108 views

How should I debug a failed Manipulate of RegionPlot?

I am trying to build a package that will display a sector of an ellipse where the angle is taken from a focus of the ellipse rather than from the center. The code seems to work fine when called with ...
3
votes
2answers
116 views

DiscretizeRegion of ImplicitRegion too small

I have a 2D function that has some sharp peeks within the my domain. I need to find a tight region that contains these sharp peeks. The following is an example of what I would like to do. An example ...
1
vote
1answer
95 views

Calculate area from `RegionPlot` directly

I have a region plot, and I would like to calculate the area: ...
3
votes
0answers
61 views

Simple ways to implement vector dilation

Suppose we have a singly connected but not necessarily convex polygon. Something like shape = CountryData["Chad", "Coordinates"]. Is there a simple way to ...
8
votes
1answer
111 views

Region computations on FilledCurve (with hole)

How can I obtain a precompiled RegionMemberFunction for this geometry? It contains a hole, and the hole's boundary intersects the outer boundary at one point. ...
3
votes
1answer
146 views

Transforming a region obtained with RegionPlot

I have a region r0, obtained from an interpolated function, with the use of RegionPlot. Let's call this function under the ...
2
votes
0answers
77 views

Defining a region from combination of data and geometric region

I would like to define a region in (x,y) by combining the region RegionPlot[ ImplicitRegion[ Sqrt[x^2 + y^2] <= 0.99, {{x, 0.01, 0.99}, {y, 0.01, 0.99}}]] ...
5
votes
1answer
124 views

What are some useful (or hidden) properties of MeshRegion?

There is quite a bit of powerful functionality built in to MeshRegion, but it seems to be lacking in some areas. For example: extracting a list of edges that live ...
3
votes
0answers
104 views

Region Intersection for MeshRegion objects embedded in 3D

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will ...
1
vote
1answer
78 views

RegionPlot3D Empty

I am attempting to cut out holes in a sphere, circumscribed around a regular tetrahedron. To do so I define some points (p1 through p4 are the vertices of a tetrahedron) ...
4
votes
2answers
357 views

Tube vs. Cylinder

What is the practical difference between plotting Tubes and Cylinders? The documentation for each describe a 3D tube/cylinder around the line between 2 points....they seem identical. However, there ...
0
votes
2answers
60 views

How can I plot the following set?

I have a question: How can I plot the following set $$G:=\{(x,y,z)\in\mathbb{R}^3|x^2+y^2\in[0,4],z\in[0,3]\}?$$ Thank you for your help!
9
votes
1answer
356 views

Plotting a region with polar axes

I want to plot the region of points who satisfy the following equation: 2 < r <= 5 && 3/4 π < θ <= 5/4 π I have been able to plot region in ...
10
votes
2answers
539 views

Generating uniform random points over a binary image

So I recently read this excellent post about generating random points over arbitrary regions. I hope Wolfram eventually builds that functionality into Mathematica's Random functions. I want to do this ...
2
votes
2answers
302 views

Count the number of regions made by Lissajous curve

How many disconnected regions does Lissajous curve divide the plane into? For example: Let g=ParametricPlot[{Sin[2 t], Sin[t]}, {t, 0, 2 \[Pi]}] The number ...
4
votes
3answers
171 views

How do I draw random points from a region [duplicate]

as the title,this problem have confused me a whole day.If I have a region,how can I yield a random member in this region.The region such as ...
4
votes
1answer
77 views

Why does EvaluationMonitor in FindMaximum only work for some regions?

This has come about after trying to understand what was going on with this question about FindMaximum and regions. My first thought in that scenario was to set-up ...