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24
votes
7answers
949 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: ...
10
votes
3answers
517 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 ...
9
votes
4answers
826 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 ...
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 ...
6
votes
2answers
219 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: ...
7
votes
1answer
102 views

TransformedRegion, RegionPlot broken in 10.0.2.0?

After having had trouble applying TranslationTransform to a simple region like so ...
11
votes
2answers
439 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
4answers
377 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 ...
7
votes
0answers
160 views

Problem with DiscretizeRegion

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1
vote
2answers
352 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: ...
7
votes
1answer
197 views

Can't plot rotated region

I was experimenting with the code from this question when I ran into another problem with regions. ...
5
votes
1answer
118 views

Easy FindMaximum returns a wrong answer

FindMaximum in region is a new function in mma10,but when I tried the following example: ...
7
votes
1answer
204 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
102 views

Join Two Element Meshes

Let's say I have two element meshes defined as the following: ...
4
votes
2answers
84 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
218 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 ...
2
votes
2answers
291 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 ...
0
votes
1answer
199 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 ...