Questions tagged [intersection]
Questions on finding intersections of geometric objects: lines, planes, regions etc. with possible aid of ContourPlot, Interval, InfinitePlane and others.
184
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Parametrization of intersections
How may we find (at least one real) intersection parametrizations $ x(t),y(t),z(t)$ between two implicit surfaces?
p=9;
ContourPlot3D[{x^2-y-(z-1)^2==1,(x+1)^2+2Sin[3y]-3z==4},{x,-p,p},{y,-p,p},{z,-p,...
- 2,992
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82
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Speeding up RegionIntersection of multiple sets of rectangles
There is a set of disjoint rectangles shadow that change position over time.
I want to find their intersection with another set of small rectangles ...
1
vote
0
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62
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Weird slowdown on data returned by compiled function (bug?)
Mathematica 13.1 - I was cleaning up some computations and I got a x3 time increase when I reduced things to loop over.
Full context is a bit convoluted, I stripped the most I could but the problem ...
- 489
1
vote
1
answer
52
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Intersection of region with triangular lattice in 2D
Is there a function that finds all points that lie in specified region and also are part of triangular lattice defined by {Sqrt[3] i, 3 (2 j + Mod[i, 2])} for ...
- 9,923
5
votes
1
answer
133
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Graphics`Mesh`FindIntersections not working in Mathematica 13.3
I just updated my Mathematica for Windows to 13.3 and when I tried to use the "Graphics MeshFindIntersections" command it doesn't seem to work. Have they replaced it with some other command ...
- 899
4
votes
1
answer
85
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Understanding the MeshShading options
The following code draws the intersection of a surface N: eqNcar=0 with three other surfaces defined by eq1=0, ...
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2
votes
1
answer
65
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3
votes
2
answers
183
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Representation of the intersection between a sphere and a plane
Consider the plane $N: x+y+z-3 q=0$ where $q$ is fixed and the sphere $S: (x-q)^2+(y-q)^2+(z-q)^2=r$ where $r$ is fixed.
I would like to make a 3D plot of $N$ and of $S\cap N$.
Here is my command ...
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1
vote
0
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69
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faster way to find intersections?
I'm writing a g-code generator for a CNC hot wire foam cutter. I have a block of foam (blue cuboid), and two airfoils that define the root and tip of a wing (shown as black curves on the ends of the ...
- 834
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41
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Finding the first and last intersection points from a lists of plots
I am trying to reproduce Figure 4 from this paper (page 7), for which I need to use the line $\tilde{T_p}$ from this figure:
in the output of this figure:
Now by varying the value of $\tilde{Q}$, I ...
- 899
3
votes
2
answers
167
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Intersection point of two lines given starting points and ending points of both lines
I'm creating a program which requires me to get intersection point of two lines. I have tried using different formulas but none of them works perfectly for me. Following is one example which I found ...
- 31
3
votes
3
answers
281
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Intersection points of two-variable polynomials
Let $h$ and $g$ designate two multivariable polynomials:
$$\!\!h(x,y)=-96\! \left(32 x^2\!+\!8 x (3\!-\!8 y)\!+\!40 y^2-28 y+5\right) \left(10 x^2+x (4 y-2)+\quad\quad\quad\\ \quad\quad+(1-2 y)^2\...
- 179
4
votes
2
answers
293
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Identifying lattice squares that are intersected by a closed curve
Given a lattice of unit squares I would like to find the number of squares that a curve (in the example below the curve is a circle) passes through and the number of squares that totally reside inside ...
- 747
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1
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125
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How to generate a random point inside this region/discretize it?
Consider the following region:
...
- 4,731
3
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1
answer
85
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How to include sparse points in a ContourPlot if any?
I'm working with the following expressions:
$$\left(\frac{1-\tanh (X)}{\tanh (X)+1}\right)^{-k}=\pm\frac{P_2^{(k,-k)}(\tanh (X))}{P_2^{(-k,k)}(\tanh (X))}$$
where $X\in[0,5]$ and $k\in\left[-\sqrt{\...
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2
votes
1
answer
83
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How to evaluate open intervals in ContourPlot?
I want to ContourPlot an expression over an interval that excludes some points. Since i dont know how to do it I wrote
...
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1
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0
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55
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Show only countourplot lines inside regionplots, without displaying the regionplots [solved]
I have a countorplot (Fun1) which important curves are those inside one of the two regionplots I'm working on (funA1 or funB2).
The minimal example of what I want to do is the following:
...
- 11
2
votes
1
answer
107
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RegionIntersection extremely slow before throwing error
I am dealing with polygons admitted by using other region functions (like RegionDifference), some of which have insidious problems.
Consider those below;
...
- 1,161
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0
answers
50
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Crash when repeatedly calling RegionIntersection (and/or Mesh functions)
My kernel (v13.1.0 Windows 64-bit) crashes when repeatedly (~9 times) calling Region functions like RegionIntersection upon ...
- 1,161
4
votes
2
answers
134
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Kernel quits upon computing RegionIntersection
Using 12.1.1.0 on MacOS BigSur I observe quitting Mathematica kernels when evaluating RegionIntersections on two regions that apparently only touch.
Example for Regions that cause the Kernel to quit ...
2
votes
1
answer
102
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not being able to find the a good picture of the intersection of two surfaces
I'm having trouble finding a good picture around the origin of the intersection curve of the following surfaces
$z - \dfrac{x^2}{2} - \dfrac{x^3}{12 \sqrt3} + \dfrac{y^2}{2} + \dfrac{x y^2}{4 \sqrt 3}=...
- 95
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votes
1
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75
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Identifying the intersection between a ConditionalExpression and a parametric curve
I'm trying to determine the intersection of lines over a surface (if they exist). My problem is that one of the lines is defined as a conditional expression and for the others I only have a parametric ...
- 563
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0
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81
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Calculate the "intersection" for the given case?
Consider the following task:
There are two cross-sections: the first one is located in the $yz$ plane (the case 1), and the second one is in the $xy$ plane (the case 2). In the spherical coordinate ...
- 4,731
1
vote
2
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112
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Intersection of a set of structurally homogeneous inequalities and extracting a combination of numbers to fully satisfy it
There are a number of structurally homogeneous inequalities:
$\begin{array}{l}
\left| s_1\right| \leq \sqrt{4 s_2} \\
\left| s_2\right| \leq \sqrt{4 s_4} \\
\left| s_3\right| \leq \sqrt{4 s_6} \\
\...
- 2,374
4
votes
2
answers
434
views
How to get a manipulated plot of the intersection points of two curves without finding them numerically?
I have four 2-variables functions for $0<x<3$ and $1<y<3$
...
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1
vote
3
answers
187
views
Plotting the solutions of the equation $e^{-z}=z$ in the complex plane
I would like to plot in the complex plane the solutions of the equation
$$e^{-z}=z.$$
I tried this:
I took $z=a+ib$ and took the real and imaginary part of the equation:
...
- 245
1
vote
2
answers
154
views
Plot the intersection of a plane with the volume of a function
I have the following function:
...
- 291
2
votes
2
answers
400
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How to plot a point in the intersection of two functions?
I'm trying to plot the intersection of a Sum function with a horizontal line and automatically highlight the intersection points.
The code below shows my knowledge of Mathematica and for different ...
3
votes
1
answer
86
views
intersection between box and convex set
I have a task to make an intersection between the convex set and the box , the equation describing the convex set is r1r2r3 - r1 -r2 - r3 + 2 cos(phi) > 0, phi = 45 ,and I plot it using
p2 = ...
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0
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60
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Finding the shared edged between two polygons
Imagine I have two convex polygons pol1 and pol2 with a shared edge. Take, as an example,
...
- 4,179
3
votes
2
answers
282
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Find intersection points between ParametricRegion and other curves
How do you instruct Mathematica to return intersection points between curves as numerical values, when using ParametricRegion to represent at least one of the ...
- 217
11
votes
1
answer
190
views
Mysterious Intersection on Association
This bug has been fixed in version 13.0
I have try to do an intersection on list of associations and the result is astonishing. Here an example:
...
- 381
5
votes
2
answers
657
views
Finding all intersection point between two time series
I've the following time series in smoothedData:
...
- 940
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77
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0
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0
answers
97
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Circular graph construction to minimize overlaps
I wish to create a set of circular graphs with 23 vertices. An example is shown below:
This may be constructed by taking, for example, a random sample of the range:
...
- 1,579
2
votes
0
answers
63
views
How to speedup RegionIntersection?
Consider a circle circle located at the origin of a coordinate frame and with a radius ROffAxisArb (it is parametrized by two ...
- 4,731
1
vote
1
answer
214
views
How to Add Vertical Line and Intersection in Manipulate-Plot-Row Diagram
I would like to represent i) the K^s value as a vertical line in the right diagram and ii) identify the intersection of the vertical line with the downward-sloping curve with "E" (as well as ...
- 307
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1
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113
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How to generate randomly points that belong to the given range?
Consider some rectangle called ExperimentLocation, and a circle ParticleAzimuthalCoverage:
...
- 4,731
1
vote
1
answer
629
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How to find the intersection points of two 3D surfaces in Mathematica?
I have two equations consisting of two variables and I'm plotting those two functions in 3D by defining the range of the two variables. I need to find the points of intersection of these two functions....
- 13
3
votes
2
answers
100
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A condition for one domain to be included in another domain?
Consider two domains:
domain1 = Rectangle[{-2.5, -2.5}, {2.5, 2.5}];
domain2[R_] := Disk[{0, 0}, R]
I would like to check whether the second domain is completely ...
- 4,731
2
votes
1
answer
193
views
How to find the area of circle inside the rectangle?
Consider a circle located at the origin
circ[R_] := Circle[{0,0},R]
and an arbitrary rectangle
...
- 4,731
4
votes
2
answers
274
views
How do you turn a normal intersection to a strict one for arbitrary number of sets?
What is the best way to generalize the following interaction of 3 sets to any number of sets:
...
- 9,113
2
votes
2
answers
89
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RegionIntersection: extra intersections
I have got an array of points, which can be represented as a ListLinePlot. Then I am trying to find the number of intersections of this ListLinePlot with a certain line. Obviously, in the demonstrated ...
- 23
1
vote
0
answers
118
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How to determine the domain (intersection and disjoint set) of two functions define on a set? [closed]
Suppose I have two multivariate functions $f(x,y,z)$ and $g(x,y,z)$ such that $0<x<1,0<y<1,0<z<1$. $f(x,y,z)$ is defined on values satisfying $\{0<x<1,0<y<1/2, z>y\}$ ...
- 147
17
votes
4
answers
1k
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Find the equidistance curve between two curves
I have three function $f(x)=x^x$, $g(x)=\ln(x)^{\ln(x)}$, $h(x)=\ln(x)^2$ and I want to find (numerically) $C$ the center of the circle tangent to the three curves.
I think that one way is to find ...
- 489
2
votes
1
answer
44
views
CountourPlot3D problem when intersecting semiplanes
I have the following code:
...
3
votes
1
answer
190
views
Plot ellipses in a exponential curve
I am trying to produce a single plot, where the ellipses fits neatly within the given curve function, and with each intersecting the curve at exactly 4 points.
The ellipses is $x^2/a^2+y^2/b^2=1$, ...
- 89
3
votes
1
answer
230
views
Intersection between a right elliptical cone region and a plane region
I am encountering difficulties in finding the intersection between a region defined as an elliptical cone and another region. For the time being the other region is a simple ...
- 197
2
votes
3
answers
909
views
3D plot of Intersection of sphere with plane (basic)
I should be able to get this from the answer here - but, with apologies, I'm afraid I can't figure it out.
I have a sphere and a plane as follows:
...
- 2,141
1
vote
0
answers
155
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Find the intersection coordinate of a line and a 3D surface defined by a contour plot
I have two points, for instance {1, 1, 1} and {10, 11, 15} that connected to form a line. I also have an enclosed surface region ...
- 437