Questions tagged [intersection]

Questions on finding intersections of geometric objects: lines, planes, regions etc. with possible aid of ContourPlot, Interval, InfinitePlane and others.

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27
votes
6answers
7k views

How to get intersection values from a parametric graph?

I have this graphed: ParametricPlot[{2.4*Cos[t] + 1.6*Cos[3 t/2], 2.4*Sin[t] - 1.6 Sin[3 t/2]}, {t, 0, 4*Pi}] It is a star, and the lines cross each other twice ...
24
votes
7answers
4k views

Find intersection of pairs of straight lines

I have a list of 24 points, in which two consecutive points (1st and 2nd, 3rd and 4th, …) are supposed to form a line: ...
25
votes
2answers
2k views

Implementation of Balaban's Line intersection algorithm in Mathematica

I'm trying to implement a Brillouin Zone algorithm within Mathematica, including the generation of Brillouin zones of higher order in 2D and 3D. There is a nice implementation of generating these ...
26
votes
2answers
746 views

Graphics`Mesh`FindIntersections[ ] fails to detect intersections

Graphics`Mesh`FindIntersections[ ] is an undocumented function for, well, detecting intersections very efficiently. Take a look: ...
38
votes
6answers
2k views

Finding length of intersection of two surfaces

I would like to know how we find the length of the intersection of two surfaces. For instance, in the following example,a surface intersects with a plane: How do we find the length of intersection ...
21
votes
2answers
2k views

Difference (or intersection) of two convex polyhedra

I have two convex polyhedra stored in the following form: a set of vertices vertices = {{x1,y1,z1},...}, a set of faces, where each face is a convex polygon ...
18
votes
3answers
3k views

Checking if a point is in a convex 3D polyhedron

Extending from these questions How to check if a 3D point is in a planar polygon? and How to check if a 2D point is in a polygon?. I'm trying to do this to render specific shapes made up of spheres. ...
23
votes
6answers
1k views

How to split list into disjoint lists?

I wonder if there is any simple way to split a list into its disjoint sublists, e.g. from list={{a,b},{e,f},{b,c},{c,d},{f,g,h}} get a result ...
10
votes
1answer
595 views

How to solve for the intersection points of two ellipses?

I have a parametric equation of two ellipses as follow $\begin{cases} x=a_1 \text{sin$\theta $}+b_1 \text{cos$\theta $}+c_1 \\ y=d_1 \text{sin$\theta $}+e_1 \text{cos$\theta $}+f_1 \\ \end{cases}...
8
votes
4answers
2k views

How do you find the self-intersection points of a single parametric trigonometric function? [duplicate]

How do you use Solve or FindRoot or other Mathematica functions to find the points at which the graph of ${\bf a}(t) = 3 \cos (3....
2
votes
5answers
3k views

Equation for the line of intersection between two planes

I have two equations: {2 x + y + z == 1, 3 x - 2 y - z == 5} And I have calculated the answers on paper, which gave me $x = 1 + t$, $y = -1 + 5t$ and $z = -7t$. ...
7
votes
4answers
1k views

Finding intersection points of two graphics [duplicate]

I am drawing a curve from a list using: ...
14
votes
3answers
856 views

Rounding an Irregular Polygon

Consider a random irregular convex polygon, for example, the 6-side polygon I want to define a function that, given a certain parameter r (roundness), rounds each ...
5
votes
3answers
1k views

Finding intersection points of two surfaces (lists)

I would like to find the intersection points of two surfaces which are constructed with ListPlot3D. The first list is ...
5
votes
1answer
571 views

Intersection of a MeshRegion and InfinitePlane

The documentation says that RegionIntersection is not implemented for MeshRegion objects embedded in 3D. But I have one such region and would like to slice it with ...
10
votes
2answers
396 views

Finding self-intersections of a closed curve represented by an interpolation function

I've been trying to find particular simple closed curves on a plane. ...
8
votes
2answers
552 views

Finding all sets of elements with two common elements in a large dataset

I have a very large network of atoms ($\approx 10^6$ atoms) with fixed positions that resemble a cellular structure: I have two files including: fixed locations of each atom set of points which ...
4
votes
5answers
1k views

Intersection coordinates of two spheres

I am trying to obtain a list of coordinates at which two spheres intersect. Take for example the spheres: sp1=Sphere[{0, 0, 0}, 1] and ...
3
votes
1answer
126 views

How to find the cells of a region that intersect a line?

I'm looking for the fastest way to access the mesh cell (i.e. polygon) in a Region that intersects a Line in 3D. For example, <...
1
vote
1answer
161 views

The intersection of two “mesh surfaces from points”

I am a fresh user of mathematica, soo thank you in advance for your help. I would like to get a list of points (x,y,z) at any interval (eg every 0.05 by x and y coordinate) which are created by ...
5
votes
2answers
119 views

Plot and find intersection points of multiple curves

I tried to plot and find the coordinates of the intersectrions of more than two curves in a the plot. Is there a special way to do this? Here's my code so yu can visualize the whole thing. ...
4
votes
1answer
683 views

Finding area of intersection regions

I want to be able to find the area of the intersection between a hexagon and a slice. I have tried RegionMeasure or Area but I ...
2
votes
2answers
985 views

intersection between function and plane

I try to solve a ODE system of equations and i want to plot the intersection of the 3D solutions with a costant plane. To do this i use the follow code: ...
1
vote
1answer
553 views

Finding equilibria to a system of 3 ODEs with 11 unknown parameters. Looking for the intersection of 3 surfaces

I have the following system of 3 ODEs of 3 variables $(\ell,M,h)$ and 11 parameters $(\sigma_{\ell},\mu_{\ell},d_{\ell},\sigma_M,\alpha_1,\beta,\alpha_2,\nu_M,\sigma_h,\nu_h,d_h)$: $\frac{d\ell}{...
5
votes
3answers
356 views

Draw line and point into a BodePlot

From the BodePlot function, I would like to plot the vertical line at horizontal axis equal to 10 as in the magnitude plot below and indicate the coordinate of the intersection point. Could anyone ...
3
votes
1answer
323 views

Projecting a Graphics3D object onto a plane

I would like to project a 3-dimensional cone onto a plane and mark the intersection (which is an ellipse) with a line. I find cone2 by performing a transformation ...
2
votes
3answers
89 views

How to get accurate intersection point value of Parametric equation?

I have parametric equation and normal equation,I don't know how to get accurate intersection point value of them. I can only use a imprecise method as below: ...
2
votes
1answer
366 views

Drawing the intersection point of two dynamic lines

I want to find the intersection point of two line segments determined by the position of four locators. ...
2
votes
1answer
211 views

how to find intersection between a parametric trajectoy and a point

I'have a 2d-system of differential equations, analitycally solved, depending on a parameter. I know that, by continuity, there exist a minimum value of the parameter such that trajectory passes ...
2
votes
1answer
193 views

Finding Intersections Between Arbitrary Surface and A Line

I have a self-intersecting surface H defined as follows: ...
1
vote
2answers
216 views

Finding intersection and graphing [duplicate]

1) How do I find the intersection of f[c_] := y^2 - 2 x^2 (x + 3) == c ((y + 1)^2 (y + 9) - x^2) between the plots of f[0] and f[2] I tried plugging-in numbers. ...
1
vote
2answers
975 views

Problems finding intersection points between line and generic function

I'm trying to find Intersection points between a line, which is given by 2 points, and a generic function (I want it to be able to handle polynomial functions, circles/ovals, lines and all ...
0
votes
2answers
239 views

Projection on the xy–plane of the curve of intersection of both surfaces [duplicate]

I am trying to make a projection on the xy-plane of the intersection of the surfaces from the functions: 1 + x^2 - y^2, ...