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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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: ...
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 ...
16
votes
1answer
252 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 ...
13
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 ...
12
votes
2answers
517 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 ...
11
votes
3answers
726 views

How to remove unwanted regions in a three-dimensional surface

As the title indicates, I want to delete some unwanted regions in a three-dimensional surface created using ContourPlot3D. Here is the corresponding code ...
11
votes
2answers
477 views

How to create subregions for the NDSolve FEM Solver

I am trying to create a 2d region consisting of two subregions. The inner region has several holes, where boundary conditions are applied. The figure shows the idea. I have tried to create this ...
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 ...
10
votes
3answers
556 views

Generating hatched filling using Region functionality

Before v.10 came out there were several Q&A on generating hatched filling for Plot, ListPlot etc. In v.10 we have new ...
10
votes
1answer
2k views

Using RegionFunction on multiple plots

I realize that the Plot function can plot multiple functions of x at the same time, using { }. I also know that the ...
10
votes
2answers
123 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. ...
9
votes
4answers
416 views

How discretize a region placing vertices on a specific non-uniform grid

Given a generic region, for example: Ω = ImplicitRegion[ 2 x^2 + 3 y^2 + 2 x y - 2 <= 0 ∧ x^2 + y^2 > .1, {x, y}]; and a non-uniform grid, for ...
9
votes
4answers
832 views

Showing a rectangular plot on an almost-closed sphere

I am currently teaching some students about the "point at infinity", and how it allows us to treat circles and lines as "the same", etc. I would like to kind of show this happening with a series of ...
9
votes
1answer
346 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 ...
9
votes
2answers
235 views

Solve a PDE over a region defined by a Bezier patch

I am using NDSolve to find the solution to a PDE over an arbitrary domain. The domain is specified by a Bezier patch. ...
8
votes
5answers
427 views

Calendar view outline

How to compute the outline of a calendar month like this D3 example. (D3 is a functional language built on JavaScript developed at Stanford and used by New York Times to deploy interactive ...
8
votes
1answer
346 views

Calculate inertia tensors

Moments of inertia and inertia tensors are well-known characteristics of rigid bodies in physics and applied mathematics. How to calculate them in Mathematica? Is possible to use regions which was ...
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: ...
8
votes
1answer
206 views

How to display MeshRegion without vertices

I'm writing a library for handling very large and complicated (boundary) mesh regions on the order of ~150,000 vertices, ~450,000 edges, and ~300,000 triangles. The regions themselves are the cortical ...
8
votes
1answer
104 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. ...
8
votes
2answers
432 views

Ideas on how to improve the rendering of the letter B in this 3D region plot?

I have been playing with the RegionPlot3D idea from this question and have been trying to approximate the Gödel, Escher, Bach logo, but I am a little bit stuck on how to improve the rendering of the ...
7
votes
3answers
233 views

Unable to compute the area of region

For a set of data: ...
7
votes
1answer
208 views

Strange behavior of `BoundaryMeshRegion`

BoundaryMeshRegion is new function of version 10. I am not familiar with the function. I want to decide whether a point is inside or outside in the Boundary using ...
7
votes
1answer
207 views

Can't plot rotated region

I was experimenting with the code from this question when I ran into another problem with regions. ...
7
votes
2answers
326 views

Union of plotted regions as sum of colors

I wish to plot 2 functions $f$ and $g$ so that the region bounded by $f$ has color $c_f$, the region bounded by $g$ has color $c_g$, and the region bounded by both has color $c_f+c_g$. E.g. $c_f$ is ...
7
votes
1answer
106 views

TransformedRegion, RegionPlot broken in 10.0.2.0?

After having had trouble applying TranslationTransform to a simple region like so ...
7
votes
1answer
185 views

Problem with DiscretizeRegion

Bug fixed in 10.1.0 ...
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 ...
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: ...
6
votes
2answers
224 views

Simplify 2D polyhedral Regions like Interval

I don't think there's a built in "RegionSimplify" for polyhedral Regions and derived akin to how Interval automatically simplifies its argument expression: ...
5
votes
3answers
150 views

Trouble Discretizing a ParametricRegion; Joukowsky Map and Wing Profiles

I'm trying to compue a mesh of full 2D region delimited by the a circle transformed with a Complex map. ...
5
votes
3answers
149 views

Find Unconnected Subregions

If I have a region, how can I identify sub regions that may be disconnected, if any exist? region defines a rectangular region given two diagonally opposed ...
5
votes
1answer
148 views

How can I prevent a Plot expression from evaluating points forbidden by its RegionFunction?

I just ran into this and it had me scratching my head for a good while. Say I have a function which may produce error messages for certain inputs, like e.g. ...
5
votes
1answer
108 views

Integrate over implicit 1D region: works for algebraic but not transcendental equation?

QUESTION How come this works: NIntegrate[1, {x, y} ∈ ImplicitRegion[{x == y^3, x <= 1, x >= 0}, {x, y}]] But this fails: ...
5
votes
0answers
101 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
224 views

Equation of a transformed (roatted) ellipsoid

Given an ellipsoid with semi-axis {a,b,c} and cantered at {a,0,0}, how do I use ...
4
votes
2answers
336 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 ...
4
votes
2answers
100 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 ...
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
2answers
210 views

How to plot this region?

Consider the $2\times 2$ matrices \begin{align} A=\begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix} \end{align} and \begin{align} B=\begin{bmatrix} b_{11} & b_{12} \\ ...
4
votes
3answers
181 views

Regarding how to use Reduce

Say for example I am doing the following in Mathematica ...
4
votes
1answer
112 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 ...
4
votes
1answer
69 views

ImplicitRegion gives arbitrary boundaries

equation1 is the major unbounded region I would like to generate ...
4
votes
1answer
70 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 ...
4
votes
2answers
118 views

Join Two Element Meshes

Let's say I have two element meshes defined as the following: ...
4
votes
2answers
95 views

NMinimize in one-dimensional Interval

An Interval should be a one-dimensional region, so a region. I tried to minimize a function over an interval, e.g.: ...
4
votes
0answers
81 views

MeshRegion and BoundaryMeshRegion differences between 10.0.1 and 10.0.2

Original text My need is simple: I have many non-overlapping regions that I will need to use as plotting domains and integration domains. The new region type operations in Mathematica 10 has made my ...
4
votes
0answers
71 views

Why is this ImplicitRegion empty?

I'm having trouble understanding why the following RegionPlot code produces results: ...
4
votes
0answers
64 views

NIntegrate::ncvbr: How should we interpret and handle this error not mentioned in any documentation?

I have some user-defined module describing my integrand which has to be computed numerically (it's much more complicated than this but bear with me): ...
4
votes
0answers
108 views

Precision problem while evaluating RegionMember or Element in V10

I'll try to give you a background on where the problem occured. The problem itself is defined near the end of the post. I'm running a sort of a simulation of a particle in a box. I finally got my ...