# Tagged Questions

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.

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. ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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: ...
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: ...
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 ...
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 ...
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: ...
148 views

### Easy FindMaximum returns a wrong answer

FindMaximum in region is a new function in mma10,but when I tried the following example: ...
34 views

### RegionPlot generates unwanted mesh lines [duplicate]

Consider this example: ...
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 ...
185 views

### Problem with DiscretizeRegion

Bug fixed in 10.1.0 ...
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 ...
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 ...
1k views

### Neumann boundary conditions in NDSolve over nontrivial region

The problem I would like to solve involves diffusion in the following region ...
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. ...
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 ...
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, ...
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 ...
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 ...
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 ...
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 ...
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: ...
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 ...
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 ...
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 ...
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: ...
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 ...
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 ...
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 ...
95 views

### Calculate area from RegionPlot directly

I have a region plot, and I would like to calculate the area: ...
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 ...
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. ...
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 ...
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}}]] ...
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 ...
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 ...
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) ...
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 ...
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!
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 ...
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 ...
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 ...