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3
votes
4answers
74 views

Find the volume of the region defined by $|x|+|y|+|z|<4$

I want to find the volume of the region defined by the following inequality: $\quad \quad |x|+|y|+|z|<4$ In addition to calculating the volume of this region, I would also like to be able to ...
2
votes
2answers
64 views

Creating a bump function on a spline region [on hold]

For a presentation, I'd like to include a 3D plot of a function of two variables x,y with the properties that (a) it looks "smooth" i.e. without jagged edges and (b) has support equal to a given ...
1
vote
0answers
28 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 ...
3
votes
0answers
73 views

Easy FindMaximum returns a wrong answer

FindMaximum in region is a new function in mma10,but when I tried the following example: ...
0
votes
0answers
23 views

Region Plot - Non Intersecting Regions

Is there anyway to plot non intersecting regions with RegionPlot? I was thinking someting in the spirit of: ...
2
votes
4answers
120 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
2answers
97 views
1
vote
0answers
34 views

Find region given by Exists statement

I want to find, calculate its volume and visualize the following region most efficiently: $\Gamma^\delta$ = { $\sigma$: $\exists \sigma' \in \Gamma$ with $F(\sigma,\sigma')\leq 1-\delta^2$}, where ...
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. ...
8
votes
2answers
125 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: ...
1
vote
1answer
68 views

Combine 3D plots into one with Manipulate and different region plots

The following script generates two plots in a row, both of them controlled by Manipulate. I would like to combine them together in one. The problem I don't know how to solve is that the plotting ...
0
votes
1answer
57 views

Draw filled regions in DateListPlot

How do I draw specifiq filled regions in DateListPlot? I trying to plot something like this: Thanks
1
vote
0answers
49 views

ParametricNDSolveValue over a region

I'm getting the following behavior I don't understand when using ParametricNDSolveValue over a region. You can reproduce the behavior considering Poisson's equation ...
1
vote
1answer
44 views

Problem with NIntegrate over a user-defined region

I define a region as follows: ...
4
votes
2answers
78 views

Join Two Element Meshes

Let's say I have two element meshes defined as the following: ...
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 ...
4
votes
0answers
66 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 ...
6
votes
0answers
146 views

Problem with DiscretizeRegion

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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.: ...
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. ...
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: ...
6
votes
1answer
90 views

TransformedRegion, RegionPlot broken in 10.0.2.0?

After having had trouble applying TranslationTransform to a simple region like so ...
2
votes
0answers
80 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 ...
4
votes
2answers
189 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} \\ ...
9
votes
4answers
336 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 ...
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
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. ...
1
vote
0answers
33 views

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 ...
1
vote
2answers
113 views

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 ...
7
votes
3answers
216 views

Unable to compute the area of region

For a set of data: ...
4
votes
0answers
63 views

Why is this ImplicitRegion empty?

I'm having trouble understanding why the following RegionPlot code produces results: ...
0
votes
1answer
125 views

Why this region is bad?

I want to draw a region but the result of Mathematica is not good. Why? ...
0
votes
1answer
81 views

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 ...
2
votes
3answers
153 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 ...
1
vote
2answers
114 views
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 ...
0
votes
1answer
64 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 ...
10
votes
3answers
443 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 ...
0
votes
0answers
49 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 ...
1
vote
0answers
66 views

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 ...
3
votes
2answers
203 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 ...
8
votes
1answer
312 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 ...
3
votes
3answers
162 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 ...
10
votes
2answers
385 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 ...
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 ...
2
votes
1answer
71 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 ...
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: ...
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): ...
1
vote
1answer
150 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 ...
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 ...