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21
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 ...
18
votes
6answers
697 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: ...
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 ...
11
votes
3answers
665 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 ...
10
votes
3answers
438 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
2answers
383 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 ...
9
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 ...
9
votes
2answers
410 views

Controlling quality of discretized region meshes

I want to discretize 3D constructive solids, supported by Mathematica 10 regions functionality. Quality of resulting meshes must be controllable, and meshes must be useful for further computation. ...
9
votes
2answers
207 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
4answers
797 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 ...
8
votes
4answers
330 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 ...
8
votes
2answers
124 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
309 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 ...
7
votes
3answers
215 views

Unable to compute the area of region

For a set of data: ...
7
votes
5answers
400 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 ...
7
votes
1answer
285 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 ...
7
votes
1answer
165 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 ...
7
votes
1answer
199 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
186 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
287 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
2answers
417 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 ...
6
votes
1answer
89 views

TransformedRegion, RegionPlot broken in 10.0.2.0?

After having had trouble applying TranslationTransform to a simple region like so ...
6
votes
2answers
212 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: ...
6
votes
0answers
146 views

Problem with DiscretizeRegion

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5
votes
3answers
130 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
140 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
95 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: ...
4
votes
2answers
188 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
159 views

Regarding how to use Reduce

Say for example I am doing the following in Mathematica ...
4
votes
1answer
135 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. ...
4
votes
2answers
74 views

Join Two Element Meshes

Let's say I have two element meshes defined as the following: ...
4
votes
2answers
69 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
65 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
63 views

Why is this ImplicitRegion empty?

I'm having trouble understanding why the following RegionPlot code produces results: ...
4
votes
0answers
106 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 ...
3
votes
2answers
202 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 ...
3
votes
2answers
655 views

RegionPlot3D contour problem

I have a little problem and didn't succeed trying to solve it on my own. Situation is, I need a visualization of the function $s - 3\cdot s\cdot q + q$ as a region on p == 0 if function's value is ...
3
votes
3answers
160 views

Trouble plotting an ImplicitRegion

I have an implicit region: R = ImplicitRegion[-Sqrt[-1 + 1/4 (x + 1/(x + I y) + I y)^2] + 1/2 (x + 1/(x + I y) + I y) == x + I y, {x, y}] I tried plotting it ...
3
votes
2answers
93 views

RegionFunction generalized to plot a different colour/style for the largest expression [duplicate]

I have several functions of two variables defined in some region, say functions[x_,y_]:={0,x-y,Sin[x^2-y]} I'd like a plot to show at a glance the regions where ...
3
votes
0answers
57 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): ...
3
votes
0answers
56 views

Bug when using Plot3D over an ImplicitRegion?

Evaluating this expression seems to cause Mathematica to beep and quit the kernel: ...
3
votes
0answers
279 views

Use of RegionFunction with Graphics3D?

I'd like to plot in 3D a long list of polygons created with TetGenConvexHull, but only in regions specified by a function. Is that possible? As I have it my ...
2
votes
4answers
511 views

Highlight integer points in RegionPlot

Is there any way to mark integer points after plotting region in Mathematica? For example, if I: ...
2
votes
3answers
152 views

How to embed a filled Region in a Graphics?

Let for example: regn = RegionDifference[Rectangle[{-2, -2}, {2, 2}], Disk[{0, 0}, 1]]; The only documented way I found to draw a gereric region ...
2
votes
4answers
115 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 ...
2
votes
1answer
257 views

How can I get dotted boundaries on a RegionPlot?

How do I plot something like $$\{(x,y): 1 \leq x^2 + y^2 < 9\}?$$ I want to be able to make the boundary $x^2 + y^2 = 9$ dotted line and the unit circle filled and coloured region in between? I ...
2
votes
2answers
88 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. ...
2
votes
2answers
95 views
2
votes
1answer
70 views

Combine ImplicitRegion

I have a starting and a target set which I would like to represent via ImplicitRegion. I can evolve each point p of the starting ...
2
votes
0answers
79 views

Unnecessary and slow conversion between simple polygons and geometric regions

To my knowledge some (but not all) of the new geometric region functions in Mathematica version 10 require an additional step to convert from geometric shapes into regions. However this step Does ...