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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32
votes
5answers
741 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 ...
32
votes
8answers
2k 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: ...
12
votes
3answers
801 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 ...
15
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 ...
20
votes
2answers
568 views

Convert binary voxel image to geometric region

I have a binary voxel image which described a contiguous region in space. Example: ...
10
votes
1answer
178 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 ...
9
votes
4answers
897 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 ...
13
votes
2answers
692 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
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 ...
6
votes
2answers
239 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: ...
3
votes
1answer
139 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 ...
3
votes
2answers
124 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
1answer
115 views

TransformedRegion, RegionPlot broken in 10.0.2.0?

After having had trouble applying TranslationTransform to a simple region like so ...
2
votes
3answers
104 views

Create region from polygons and tangential line segments

I have two circles and tangential line segments that I want to define a region: ...
-1
votes
1answer
104 views

How to input functions into Mathematica [closed]

I need help with this assignment like asap. I've never been taught how to use this program and our math department expects us to learn how to use it, but it is just so complicated!!! Please help me ...
12
votes
2answers
639 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 ...
22
votes
3answers
2k 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
3answers
438 views

Find the volume of Phobos and Deimos

How can we calculate the volume of a 3D object using the new-in-10 computational geometry functions? For simple objects this works: ...
9
votes
4answers
549 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
1answer
157 views

How to discretize a BezierCurve?

Bug introduced in version 10.0 and persisting through 10.3 DiscretizeGraphics is new in 10.0. I need to create a discretized region from a ...
25
votes
5answers
2k views

Generate two random numbers with constraints

I want to generate two random numbers, $p$ and $q$, between $0.5$ and $1$. They are connected by the constraint $1/(2q) > p$. How do I generate $p$ and $q$?
7
votes
1answer
206 views

Problem with DiscretizeRegion

Bug fixed in 10.1.0 ...
5
votes
3answers
116 views

ImplicitRegion gives arbitrary boundaries

This question uses Mathematica 10.2.0.0. equation1 is the major unbounded region I would like to generate: ...
4
votes
5answers
522 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 ...
1
vote
2answers
474 views

3D Contour Plot parts of sphere with gradient less than 0, equal to 0 and more than 0

I want to plot only parts of the sphere of radius 1 where the gradient $\frac{\partial z}{\partial x}$ is < 0, = 0 and > 0. The full sphere is given by: ...
10
votes
2answers
137 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. ...
7
votes
3answers
896 views

Region bounded by x^2+y^2=1, y=z, x=0, z=0, in first octant

I need to draw (pencil and paper) the region bounded by $x^2+y^2=1$, $y=z$, $x=0$, and $z=0$ in the first octant. So the first assistance I asked of Mathematica is: ...
7
votes
1answer
251 views

Can't plot rotated region

I was experimenting with the code from this question when I ran into another problem with regions. ...
6
votes
1answer
151 views

Easy FindMaximum returns a wrong answer

FindMaximum in region is a new function in mma10,but when I tried the following example: ...
5
votes
2answers
180 views

Separate boundaries of multiply connected region

I have a multiply connection two-dimensional region such as the following: br = BoundaryDiscretizeGraphics@Graphics[Disk[#, 8/9] & /@ CirclePoints[9]] I am ...
5
votes
0answers
141 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 ...
8
votes
1answer
403 views

How to use Undocumented Functions Prism, Tetrahedron and Hexahedron

Taking a look at this question and this one, I checked to see if Mathematica really does not have a Prism primitive. To my surprise the function ...
7
votes
2answers
172 views

A method to discretize a three-dimensional solid

Consider the following region: ...
7
votes
1answer
217 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 ...
4
votes
2answers
211 views

Join Two Element Meshes

Let's say I have two element meshes defined as the following: ...
4
votes
2answers
120 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
2answers
298 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
1answer
63 views
3
votes
2answers
324 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 ...
2
votes
0answers
48 views

DiscretizeRegion fails on two clearly intersecting cylinders

Intersecting cylinders has been on the top here lately, so it got me to thinking of this, ...
0
votes
0answers
37 views

non-intersecting cylinders and DiscretizeRegion, RegionIntersection [duplicate]

This is a sequel to my previous post. ...
0
votes
0answers
67 views

Region from Points

Is there a built-in way to define a 3D region from an arbitrary list of points. The points will represent vertices of the edges of the region and we can assume that 1) they are not all on the same ...
0
votes
1answer
314 views

Integral over geometric region [duplicate]

I'd like to calculate this integral $$ \int_E y\ dydz $$ where $E = \{ (x,y,z) \in R^3 : z^2+6 < y^2 < 5z \}$ By hand i've got $\frac{1}{12}$ but i'm not sure, and i'd like to verify this ...