# Tagged Questions

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169 views

### Unable to compute the area of region

For a set of data: ...
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### How to find the intersection of a Line with the boundary of a Region?

Given a 2-D Region $\Omega$, i.e. RegionQ[\[Omega]] && RegionDimension[\[Omega]] == 2 is ...
505 views

### Neumann boundary conditions in NDSolve over nontrivial region

The problem I would like to solve involves diffusion in the following region ...
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### How to find the direction of the outward normal in a point of the boundary of a 2D region?

Suppose we have a domain $\Omega$ such that RegionQ[\[Omega]] is True and ...
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### Why is this ImplicitRegion empty?

I'm having trouble understanding why the following RegionPlot code produces results: ...
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### Why this region is bad?

I want to draw a region but the result of Mathematica is not good. Why? ...
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### Extract ROI from image by hand into Matrix Form

I have a 3D Image (each pixel contains information for various wavelengths). I draw the image for one wavelength by using ...
65 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 ...
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### How to use ParametricPlot and fill closed areas with blue and red?

The current code is : ...
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### 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 ...
58 views

### RegionPlot Difficulty

This code: Plot3D[ArcTan[Tan[y/x]], {x, -1, 2}, {y, -2, 1}, RegionFunction -> Function[{x, y}, 1 <= x^2 + y^2 <= 4 && y <= x]] Give this ...
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### 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 ...
298 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 ...
212 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 ...
151 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 ...
43 views

### Change in direction when a line hits an ellipse?

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 ...
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### projecting a RegionProduct into 3D space

Apparently, RegionProduct should allow you to generate convolution-generated shapes. For instance, take a 1D curve and a sphere, and the region product I would ...
156 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 ...
483 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: ...
372 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 ...
192 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: ...
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### 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 ...
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): ...
130 views

### 3D Contour Plot - parts with gradients less and more than zero

I'm trying to plot sections of the 3D Contours, with gradient less than zero, and more than zero and equal to zero. It manages to solve for the derivative, but when I apply the conditions ...
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### 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: ...
238 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 ...
54 views

### Bug when using Plot3D over an ImplicitRegion?

Evaluating this expression seems to cause Mathematica to beep and quit the kernel: ...
170 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 ...
145 views

### Regarding how to use Reduce

Say for example I am doing the following in Mathematica ...
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### 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 ...
296 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. ...
150 views

### Can't plot rotated region

I was experimenting with the code from this question when I ran into another problem with regions. ...
84 views

### Excluding region with RegionDifference

I can't make RegionDifference work for two Rectangle: ...
106 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 ...
146 views

### Computing integral over explicit region [closed]

I need to integrate $f(x,y)=y^2-2x^2y+6x^3-3xy+2y-6x$ over $\{y\geq 2x^2-2, y\leq 3x\}$ Im using Boole in the following way; ...
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### 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. ...
78 views

### Unknown limit of an array of area integrals

Could someone explain why Mathematica can't finish computing this limit (this is a limit of an array, when n -> Infinity (n ...
181 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 ...
126 views

### ListDensityPlot: How to only retain regions with data without using interpolation?

I'm working with ListDensityPlot on a set of triples, $\{\{x_1, y_1, z_1\}, \dots\}$. The data is on a semi-regular grid and looks just as it should through most of ...
252 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 ...
706 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 ...
136 views

### Manipulate doesn't work for plotting a region where a matrix is positive semi-definite

I'm facing the following problem and would very much like you help. Thanks is advance! I have defined the following 4x4 matrix: S=\left( \begin{array}{cccc} ...
250 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 ...
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### How to judge if a point is in the interior of a closed curve or not? [duplicate]

For example: pts = {{0, 1}, {-(Sqrt[3]/2), -(1/2)}, {Sqrt[3]/2, -(1/2)}}; trig=JoinedCurve[Line[pts], CurveClosed -> True]; Then ...
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### 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 ...
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 ...
468 views

### Highlight integer points in RegionPlot

Is there any way to mark integer points after plotting region in Mathematica? For example, if I: ...
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 ...
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 ...