The intersection of two or more sets, written $A\cap B$ or $\bigcap_{i\in I} A_i$, is the set of all elements contained in *all* given sets.

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1answer
4k views

Intersection between a rectangle and a circle?

I have a poor working knowledge of math. I would like to calculate collision detection between a 2D circle and a 2D rectangle for a simple game of Pong. I thought of splitting the 2D rectangle into 4 ...
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3answers
438 views

Equation to determine radius for a circle that should intersect a given point?

Simple question. I tried Google but I don't know what search keywords to use. I have two points on a 2d plane. Point 1 = x1 and y1, and Point 2 = x2 and y2. I'd like to draw a circle around Point ...
0
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0answers
407 views

regular expression and intersection

I have this language L that contains only one string: $a_{1}a_{1}a_{2}a_{1}a_{1}a_{2}a_{3}a_{1}a_{1}a_{2}a_{1}a_{1}a_{2}a_{3} ....a_{n}...a_{n}$ written more concisely ...
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4answers
16k views

How can I find the points at which two circles intersect?

Given the radius and $x,y$ coordinates of the center point of two circles how can I calculate their points of intersection if they have any?
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1answer
259 views

Intersection of a line segment and a paraboloid in 3D

Suppose I have a line segment $L$ in 3D: $$x=a_1(1-t)+b_1t$$ $$y=a_2(1-t)+b_2t$$ $$z=(a_1^2+a_2^2-k_1^2)(1-t)+(b_1^2+b_2^2-k_2^2)t$$ Because $L$ is line segment then $0\leq t\leq 1$. And defining ...
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1answer
453 views

Automatic calculation of the intersection of discrete curves

first of all, let me apologize for a poor math-english translation, I'll try my very best. I have the following situation: I have over 16.000 data files which I generated from a biometric ...
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1answer
596 views

Ray VS Line intersection

Continue vector vs plane intersection Image How to determine Ray (one point R(rx;ry) and alpha with OX) with line (two points A(ax;ay) and B(bx;by)) intersection?
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1answer
85 views

Vector VS Plane intersection

Could You help me with task: From point $M(3,5)$ that belongs to plane: $A(0,0), B(0,10), C(20,10), D(20,0)$, comes out vector $V$ at an angle a(with $OX$). Need to find point $X(x,y)$ at which he ...
3
votes
2answers
149 views

“Good” closure conditions

[Attention! This question requires some reading and it's answer probably is in form of a "soft-answer", i.e. it can't be translated into a hard mathematical proposition. (I hope I haven't scared away ...
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3answers
17k views

How do I calculate the intersection(s) of a straight line and a circle?

The basic equation for a straight line is $y = mx + b$, where $b$ is the height of the line at $x = 0$ and $m$ is the gradient. The basic equation for a circle is $(x - c)^2 + (y - d)^2 = r^2$, where ...
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2answers
110 views

Angular radius of a sphere

Given a sphere with radius $r$ about a point $c$, what's the apparent angular radius $\alpha$ of that sphere from point $P$? In other words, if $\vec{o} = c - P$, what's the maximum angle another ...
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1answer
213 views

Volume of parallelepiped intersection with oblique plane

Is there an algorithm or program capable to find the volume resulting when a parallelepiped is intersected by an oblique plane? What is most important, although, it's not specified in title is: given ...
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3answers
700 views

Give an example of open, nested sets such that the intersection is closed nonempty.

Give an example of open, nested sets such that the intersection is closed nonempty. I will ask questions if I am in doubt of the example provided. Thank you!
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1answer
186 views

Union, intersection and complement of a set

Is this equation true? $$\mathcal C \bigcap_{M\in A}M=\bigcup_{M\in A}\mathcal CM$$ where C is the complement, M is a set, A is a set of sets. I don't know how to start proving or disproving it ...
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2answers
2k views

Divide circle into 9 pieces of equal area

I'd like to divide a unit circle disk into nine parts of equal area, using circle arcs as delimiting lines. The whole setup should be symmetric under the symmetry group of the square, i.e. 4 mirror ...
0
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1answer
995 views

Find the intersection points of the line L with the three coordinate planes Oxy, Oyz, and Ozx

Let L be the line given by the parametric equations x = 1 + 2t, y = −1 − t, z = 3t Find the intersection points of the line L with the three coordinate planes Oxy, Oyz, and Ozx
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1answer
582 views

Intersection of Two Circles

I have two circles as: $C_1: (x-x_1)^2+(y-y_1)^2=r_1^2$ and $C_2: (x-x_2)^2+(y-y_2)^2 =r_2^2$ and these circles have non-empty intersection. In other words $\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\leq ...
0
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1answer
133 views

Build equation of a curve with set of coordinates

I need to calculate the intersection of two curves. I do not have the equation of the curves, but I will have a finite set of coordinates. Is there a way to build the equation for this curve based ...
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2answers
187 views

Bilinear Interp Surface Intersection

Edit: I rephrased the question to make it clearer, sorry! I'm trying to solve for the intersection of two surfaces in three spatial dimensions and time. Consider each of these surfaces as some ...
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0answers
126 views

Intersection of a hyperplane and a quadric surface.

I have $r, d \in \mathbb{R}^n$. I want to find all $y \in \mathbb{R}^n$ such that $r \cdot y = 0$ and $d \cdot \langle y_1^2, \dots, y_n^2 \rangle = 0$. The trivial $y = 0$ solution is not terribly ...
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0answers
66 views

Intersection between 2 functions describeing falling objects with air drag?

So I got 2 functions, both describing the y position of an object moving with a certain acceleration and air drag(tough a very simplified one) as a function of the time t. ...
2
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1answer
190 views

Angle of first circle where it intersects second circle

First, some background. I'm writing an application which a bit more mathematically challenging than what I'm used to. I have two circles that overlap (not just touch, I mean there are two intersect ...
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1answer
172 views

Intersection of 3D curves parameterised by piecewise defined functions

I need to calculate the intersection of two 3D parametric curves $\vec{C_1}$ and $\vec{C_2}$. link to image Those curves are parameterised by piecewise functions. $\vec{C_1}= ...
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1answer
97 views

Find the intersection between point and circle

given a line segment with endpoints P1 and P2 and a Circle with Center C and Radius R where it is known that P1 lies outside the circle and P2 lies inside the circle, what is an efficient way to find ...
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2answers
278 views

Intersection surface area of 3 circles with 3 different radius

I am trying to find the equations to calculate: The intersection surface area generated by the intersection of 3 circles (3 circles like a Venn Diagram). The 3 circle's radius could be be different ...
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1answer
3k views

Finding the line of intersection of 2 planes by row reducing the linear system matrix

Problem Statement: Find the plane that passes through the point (-1, 2, 1) and contains the line of intersection of the planes: $$x+y-z = 2$$ $$2x - y + 3z = 1$$ I understand there is a means of ...
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2answers
2k views

Calculate intersection of vector subspace by using gauss-algorithm

There are two vector subspaces in $R^4$. $U1 := [(3, 2, 2, 1), (3, 3, 2, 1), (2, 1, 2 ,1)]$, $U2 := [(1, 0, 4, 0), (2, 3, 2, 3), (1, 2, 0, 2)]$ My idea was to calculate the Intersection of those two ...
3
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1answer
170 views

Poincaré duality

Let $X$ be a a compact oriented manifold of dimension $n$. Assume that its (co)homologies have no torsion. Then Poincaré duality says that $$ H^{k}(X,\mathbb{Z})\cong H_{n-k}(X,\mathbb{Z}) $$ holds ...
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0answers
210 views

Algorithm for intersection between polyline and rectangle?

My problem is simple, and probably obvious from the title itself, but I'll still clarify it a bit: I have a rectangle and a polyline (array of N connected points). I need an optimal algorithm that ...
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1answer
117 views

Union of system of inequalities

I have a system of inequalities $$|z-a_k|\le R_k$$ where $z=x+iy$ (complex number) and $a_k$ and $R_k$ are real numbers for $k=1, \dots, n$. Basically the inequality above shows circle with center ...
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1answer
321 views

How to find the intersection of union of two circle groups

I have two groups of circles. S1 is the union of the first group and S2 is the union of the second group of circles. I know center and radius of all circles. I have to find the equation for the ...
0
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1answer
409 views

Circular Sector to Circle Intersection

Is there a formula for determining if a sector intersects a circle (as well as determining if the circle/sector are inside each other)? Sector definition: A center point $P(x,y)$, a starting angle in ...
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0answers
559 views

Submatrix Notation

I'm looking through some computer science papers and I see some notation that I'm just not familiar with. Consider an 5 x 6 matrix $$G = \begin{pmatrix} a_{0,0} & a_{0,1} & ...
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0answers
429 views

Solve for the intersection point, given two sets of data

I need to (numerically, specifically in C++) solve for the intersection point of two curves, f(x) and g(x). I am given two sets of data, one for each curve (eg. ...
3
votes
1answer
789 views

Intersection between a cylinder and an axis-aligned bounding box

Given a 3D axis-aligned bounding box (represented as its minimum point and maximum point) and a 3D cylinder of infinite length, what's the best way to test for intersection?
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2answers
288 views

I want to find 3 planes that each contain one and only one line from a set

The three lines intersect in the point $(1, 1, 1)$: $(1 - t, 1 + 2t, 1 + t)$, $(u, 2u - 1, 3u - 2)$, and $(v - 1, 2v - 3, 3 - v)$. How can I find three planes which also intersect in the point $(1, 1, ...
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4answers
181 views

How many times do these curves intersect?

When the curves $y=\log_{10}x$ and $y=x-1$ are drawn in the $xy$ plane, how many times do they intersect? To find intersection points eq.1 = eq. 2 $$\begin{align*} \log_{10}x &= x-1\\ 10^{x - 1} ...
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1answer
71 views

Finding POI's for the follow two curves

So I need to find the POI (point of intersection) of the following two curves: \begin{align*} r & = 1 + \cos \theta, \\ r & = 2 - 2\cos \theta. \end{align*} What I did was I just set both the ...
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1answer
537 views

3D intersection point between circle and triangle

Given a 3D triangle with vertices $(v0, v1, v2)$ and a 3D circle of radius $r$, centered at $c$, and lying in the plane perpendicular to $axis$, how can I test for intersection points between them? ...
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1answer
463 views

Finding the distance between the centre of an arbitrarily rotated cylinder and a point on that cylinder

this is a bit more complicated than the post title suggests because I was running out of words. I suppose the full title would be: "Finding the distance between the centre of an arbitrarily rotated ...
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2answers
213 views

ray - parallelogram intersection in 2d

i'm looking for a fast method to get the intersecting points between a ray and a parallelgram defined by the 4 vertices! till now i've thought to test the intersection point between ray and the 4 ...
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1answer
1k views

Find the intersection of a line (segment) and an ellipse (from the center of ellipse)

Here is what I know: The location of the center of the ellipse C (20,10). The Major axis (2a) or 400 (a being 200) - this is on the X axis. The Minor axis (2b) or 200 (b being 100) - on the y axis. ...
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1answer
213 views

Intersection between 3D closed contour and 3D plane

I have a set of N 3D points (x,y,z cartesian coordinates) defining a closed contour and a 3D plane defined by a point and a normal. What I want to determine is the point(s) where the closed contour ...
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3answers
383 views

Why doesn't this conditional probability equation hold

This is probably a very stupid question but I can't wrap my head around it. $$ P(B \cap A) = P(A \cap B) = P(B \mid A)\cdot P(A) + P(A \mid B)\cdot P(B) $$ Can someone explain intuitively why the ...
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0answers
42 views

elipsoid surface intersection in $\mathbb{R}^3$

Is there an explicit parametric solution describing the curve result of the intersection of two elipsoid surfaces with abitrary position and orientation in $\mathbb{R}^3$?
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0answers
127 views

Intersection of a cone $x^2+y^2-z^2$ and a generic plane in $\mathbb{RP}^3$

If we take the zero locus of $x^2+y^2-z^2$ to be our cone, I'd like to know how to go about finding the intersection of the cone and a generic plane $Ax+By+Cz+Dw=0$. The result will be a conic, but ...
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2answers
556 views

21 sided regular polygon and its diagonals

In a $21$ sides regular polygon, how many points inside it are intersection of its diagonal? I found that a polygon with $n$ sides has $\dfrac{n(n - 3)}{2}$ diagonals, but I feel this is not so ...
3
votes
1answer
158 views

proving that four axis-parallel rectangles whose intersection graph is a cycle delimit another rectangle

Working on the 2D plane, I'm looking for an elegant proof of the fact that if four regions $A$, $B$, $C$, $D$ delimited by axis-parallel rectangles are such that: $A$ intersects $B$, $B$ intersects ...
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2answers
112 views

Is every invertible rational function of order 0 on a codim 1 subvariety in the local ring of the subvariety?

I have been trying to read Fulton's Intersection Theory, and the following puzzles me. All schemes below are algebraic over some field $k$ in the sense that they come together with a morphism of ...
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1answer
3k views

determine if 2 line segments are intersecting

currently I write a program where finding out whether 2 line segments intersect is an essential part of the algorithm. Could anyone tell me if there's a way to determine if two segments are ...