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3
votes
0answers
53 views

Simple ways to implement vector dilation

Suppose we have a singly connected but not necessarily convex polygon. Something like shape = CountryData["Chad", "Coordinates"]. Is there a simple way to ...
1
vote
1answer
78 views

Calculate area from `RegionPlot` directly

I have a region plot, and I would like to calculate the area: ...
14
votes
0answers
150 views
+50

How can I smooth a 3D surface generated by RegionBoundary?

I have a set of points that belong to the surface of an object. I would like to approximate a surface to which I can compute the distance. of other points. With the nice code of this post, I was able ...
3
votes
2answers
102 views

DiscretizeRegion of ImplicitRegion too small

I have a 2D function that has some sharp peeks within the my domain. I need to find a tight region that contains these sharp peeks. The following is an example of what I would like to do. An example ...
8
votes
1answer
100 views

Region computations on FilledCurve (with hole)

How can I obtain a precompiled RegionMemberFunction for this geometry? It contains a hole, and the hole's boundary intersects the outer boundary at one point. ...
2
votes
2answers
90 views

How should I debug a failed Manipulate of RegionPlot?

I am trying to build a package that will display a sector of an ellipse where the angle is taken from a focus of the ellipse rather than from the center. The code seems to work fine when called with ...
3
votes
1answer
127 views

Transforming a region obtained with RegionPlot

I have a region r0, obtained from an interpolated function, with the use of RegionPlot. Let's call this function under the ...
2
votes
0answers
71 views

Defining a region from combination of data and geometric region

I would like to define a region in (x,y) by combining the region RegionPlot[ ImplicitRegion[ Sqrt[x^2 + y^2] <= 0.99, {{x, 0.01, 0.99}, {y, 0.01, 0.99}}]] ...
4
votes
1answer
97 views

What are some useful (or hidden) properties of MeshRegion?

There is quite a bit of powerful functionality built in to MeshRegion, but it seems to be lacking in some areas. For example: extracting a list of edges that live ...
1
vote
1answer
71 views

RegionPlot3D Empty

I am attempting to cut out holes in a sphere, circumscribed around a regular tetrahedron. To do so I define some points (p1 through p4 are the vertices of a tetrahedron) ...
4
votes
2answers
312 views

Tube vs. Cylinder

What is the practical difference between plotting Tubes and Cylinders? The documentation for each describe a 3D tube/cylinder around the line between 2 points....they seem identical. However, there ...
3
votes
0answers
80 views

Region Intersection for MeshRegion objects embedded in 3D

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will ...
0
votes
2answers
60 views

How can I plot the following set?

I have a question: How can I plot the following set $$G:=\{(x,y,z)\in\mathbb{R}^3|x^2+y^2\in[0,4],z\in[0,3]\}?$$ Thank you for your help!
10
votes
2answers
515 views

Generating uniform random points over a binary image

So I recently read this excellent post about generating random points over arbitrary regions. I hope Wolfram eventually builds that functionality into Mathematica's Random functions. I want to do this ...
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 ...
4
votes
3answers
134 views

How do I draw random points from a region [duplicate]

as the title,this problem have confused me a whole day.If I have a region,how can I yield a random member in this region.The region such as ...
3
votes
4answers
102 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
75 views

Creating a bump function on a spline region [closed]

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 ...
4
votes
1answer
66 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 ...
5
votes
1answer
120 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
30 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
142 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
117 views
1
vote
0answers
38 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
95 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
134 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
80 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
68 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
56 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
59 views

Problem with NIntegrate over a user-defined region

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

Join Two Element Meshes

Let's say I have two element meshes defined as the following: ...
8
votes
1answer
192 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
74 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 ...
7
votes
0answers
161 views

Problem with DiscretizeRegion

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4
votes
2answers
85 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
227 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
104 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: ...
7
votes
1answer
105 views

TransformedRegion, RegionPlot broken in 10.0.2.0?

After having had trouble applying TranslationTransform to a simple region like so ...
2
votes
0answers
98 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
204 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
384 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
148 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
147 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. ...
2
votes
0answers
46 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
126 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
229 views

Unable to compute the area of region

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

Why is this ImplicitRegion empty?

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

Why this region is bad?

I want to draw a region but the result of Mathematica is not good. Why? ...
0
votes
1answer
91 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
165 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 ...