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1
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0answers
32 views
0
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0answers
27 views

ImplicitRegion gives arbitrary boundaries

equation1 is the major unbounded region I would like to generate ...
3
votes
3answers
68 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
183 views
2
votes
1answer
42 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 ...
13
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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
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2answers
120 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
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0answers
99 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 ...
3
votes
2answers
122 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
113 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
97 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
54 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
515 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
123 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
144 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
95 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
101 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 ...
27
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
250 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
103 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
114 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
89 views

Calculate area from `RegionPlot` directly

I have a region plot, and I would like to calculate the area: ...
3
votes
0answers
58 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
103 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
133 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
74 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}}]] ...
4
votes
1answer
110 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
90 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
76 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
335 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
343 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
529 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
297 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
149 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
68 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 ...
5
votes
1answer
122 views

Easy FindMaximum returns a wrong answer

FindMaximum in region is a new function in mma10,but when I tried the following example: ...
22
votes
3answers
1k views

RegionPlot3D in cylindrical or spherical coordinates?

RegionPlot3D is awesome. Unfortunately, it appears to work only for Cartesian coordinates. While there are ways to draw surfaces in spherical or cylindrical coordinates, I can't find a way to draw ...
3
votes
4answers
107 views

Find the volume of the region defined by $|x|+|y|+|z|<4$

I want to find the volume of the region defined by the following inequality: $\quad \quad |x|+|y|+|z|<4$ In addition to calculating the volume of this region, I would also like to be able to ...
2
votes
2answers
76 views

Creating a bump function on a spline region [closed]

For a presentation, I'd like to include a 3D plot of a function of two variables x,y with the properties that (a) it looks "smooth" i.e. without jagged edges and (b) has support equal to a given ...
0
votes
0answers
32 views

Region Plot - Non Intersecting Regions

Is there anyway to plot non intersecting regions with RegionPlot? I was thinking someting in the spirit of: ...
2
votes
4answers
145 views

Using ArcLength in Mathematica 10 using absolute values

With Mathematica 10, I can nicely plot: y = x^2 - 4 Abs[x] - x But I have not been able to use ArcLength to get the length of ...
1
vote
0answers
38 views

Find region given by Exists statement

I want to find, calculate its volume and visualize the following region most efficiently: $\Gamma^\delta$ = { $\sigma$: $\exists \sigma' \in \Gamma$ with $F(\sigma,\sigma')\leq 1-\delta^2$}, where ...
3
votes
2answers
107 views

Reflecting lines in ellipses: speed up the code?

I have the following code which calculates a list of points that a line would take after bouncing off various ellipses. ...
8
votes
2answers
141 views

Area of Self-Intersecting Polygon with Repeated Vertices

So Mathematica uses an even-odd rule for self-intersecting polygons, both when rendering them and when calculating their area: ...
1
vote
1answer
87 views

Combine 3D plots into one with Manipulate and different region plots

The following script generates two plots in a row, both of them controlled by Manipulate. I would like to combine them together in one. The problem I don't know how to solve is that the plotting ...
0
votes
1answer
74 views

Draw filled regions in DateListPlot

How do I draw specifiq filled regions in DateListPlot? I trying to plot something like this: Thanks
1
vote
0answers
57 views

ParametricNDSolveValue over a region

I'm getting the following behavior I don't understand when using ParametricNDSolveValue over a region. You can reproduce the behavior considering Poisson's equation ...