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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3
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1answer
257 views

$2D$ Line Segment - Triangle Intersection

I've seen similar questions but could not solve my problem with those. My question is how to detect an intersection of a line segment and a triangle on a 2D coordinate system? I don't need the point ...
18
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0answers
441 views

How many points of intersection between an ellipse and an $L_p$-circle?

Consider an ellipse $E$ in the plane, centered at the origin. (In my case, the minor axis points into the nonnegative quadrant.) Let S be an "$L_p$-circle": $S = \{(x,y) : |x|^p + |y|^p = 1\}$, ...
7
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0answers
669 views

How can I tell when two cubic Bézier curves intersect?

I'm working a little program that converges on vector-based approximations of raster images, inspired by Roger Alsing's genetic Mona Lisa. (I started on this after his first blog post two years ago, ...
4
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0answers
27 views

Minimum number of vertex moves to un-intersect a polygon with itself

In my game, I have n points that form a self-intersecting polygon. The points can be moved by dragging them. How can I form a non-intersecting polygon this way, in ...
2
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0answers
30 views

Probability for Subsets

I am examining a set S, which is composed of a finite number known of elements. The size of the set is much larger than the number of possible types of elements, so each repeats many times. I am ...
2
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0answers
91 views

What is the Area formed when a line is traced between two 3D curves?

This question is quite related to intersection of cylinders, Hyperbolic paraboloid and modelling. I am welding a trunnion to a pipe (both are hollow cylinders in different geometry). They intersect ...
2
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0answers
174 views

intersection multiplicity and tangents

I haven't been able to find a proof of the following fact, which I have seen mentioned a few times: two non-singular curves have multiplicity intersection greater than 1 at a point P if and only if ...
2
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0answers
78 views

Intersection of line with discrete hypercubes in n-dimensional space

I am looking for a method to determine the hypercubes that intersect a line between two points in a high dimensional space. I think what I want is the supercover of a line in high dimensional space. ...
2
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0answers
535 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} & ...
2
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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 $\mathbb{R}^3$?
2
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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 ...
2
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0answers
35 views

How do I use k-dimensional planes as bounds for generating k-dimensional vectors?

I am an essentially self-trained programmer with little mathematical background. I do not quite know where to start for this problem, and do not know the terminology to help me get conclusions ...
2
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0answers
741 views

How to find all intersection points of two splines?

2D-Cubic splines are given in parametric form (X(t), Y(t) and X(s), Y(s)). Every segment has it's own X and Y expression. And I want to find all intersection points. Some segments are intersecting ...
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0answers
59 views

Intersection between sphere and ellipsoid

I am failing since two days to compute and to plot the intersection of an ellipsoid in parametric notation ...
1
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0answers
44 views

Is there a relation for when a circle intersects more than half the perimeter/circumference of another circle?

Is there some nice formula or algoritm for determining when a circle "hides"/intersects more than half of the perimeter of another circle, in a circle-circle interaction. Example image: Two example ...
1
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0answers
25 views

Finding intersections points of pairs of polar curves?

Find all intersections of the curves $r=3^{(1/3)}\cos(\theta) , r=\sin(\theta)$ What I have done so far is to just put them equal to each other like this: $3^{(1/3)}\cos(\theta)=\sin(\theta)$, but ...
1
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0answers
95 views

Find the basis for the intersection of two subspaces in infinite-dimensional vector spaces

For an infinite-dimensional vector space U, and two subspaces W and V, we assume at least one of the two subspaces (W and V) is also infinite-dimensional. How can I find the basis for the ...
1
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0answers
25 views

Odly phrased big-oh question, have I done what is required? (because it's not really big-oh, it's more graph sketching)

I've encountered these before, but never phrased or defined as follows, I'd like to know if I've done whatever the question wants to draw attention to (if it didn't want to draw attention to ...
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0answers
46 views

Finding the intersection of two three-dimensional functions

I have two large equations, both of the same form which I am trying to find the intersections of. The equations are: $$ f(x, y) = \frac{\frac{x ^ 2}{r_1} + \frac{y ^ 2}{r_2}} {1 + \sqrt{1 - \frac{p_1 ...
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0answers
35 views

Arc To Plane Intersection

I have a plane and an arc with center, radius, start and end angles. All i need to find if if the arc hits on the chosen plane or not. Line to plane intersection is much easier as the surface is ...
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0answers
42 views

Probability on intersection

If I have two sub-areas confined in a larger area, and I have the intersection of these two sub-areas. If I replace one of the sub-areas with a new sub-area, which is the same size. What is the ...
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0answers
54 views

Probability for intersection of sets

(It is an easier - hopefully - formulation of a question I asked previously). Assume that we are given $J$ sets, each set with $n_j$ elements ($J$ and $n_j$ for each $j \le J$ are known). The ...
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0answers
84 views

Vector Tangent to Curve of Intersection

I am having problems solving this. Find a vector tangent to the curve of intersection of $z = 4x^2 + y^2$ and $z=(27-x^2-y^2)^{1/2}$ at the point $(1,1,5)$. I'm able to do this kind of thing using ...
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0answers
56 views

Finding the equation of a plane

I need to find the equation for the plane which goes through the intersection line of the planes $x-z=1$ and $y+2z=3$, and perpendicular to the plane $x+y-2z=1$. What I got so far - to find the ...
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0answers
61 views

Equation to calculate intersected cells in a grid, given a selection rectangle

I am looking for an equation which will calculate which cells (returned either as a pure index or as a row/col) are intersected by a selection rectangle when provided with the box coordinates of each ...
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65 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. ...
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0answers
420 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. ...
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0answers
72 views

Segre classes of singular projective varieties

Corollary 4.2.4 from Fulton's Intersection Theory gives a method for computing the Segre class of varieties, but in particular it allows computation of the Segre class for singular varieties. Let $X$ ...
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0answers
214 views

Intersection and union of 2 variable intervals with integers and indexes

I have a set of indexes of integer $\mathbb{I} =\{i_0, i_1, ..., i_n\}$, and an environment $f: \mathbb{I} \rightarrow \mathbb{Z} \times \mathbb{Z}$ which assigns a pair of integer to each index. For ...
0
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0answers
19 views

Area covered by multiple (possibly intersecting) circles on surface of sphere

I have a number of circles of same radius on surface of sphere (Google Maps API). I'm trying to calculate the total area covered by these possibly intersecting circles. My current solution is ...
0
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0answers
48 views

Geodesics intersection on a cylinder

My problem is the following: I have a cylinder, and a couple of geodesic segments on its surface. The segments are defined by the coordinates of their start and end points. I have to obtain the ...
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0answers
22 views

Are all subbasis subsets of basis?

In topology, each element of basis $\{B_k\}$ can be expressed as finite intersections of elements of subbasis, i.e. $B_k=S_{n_1}\cap ...\cap S_{n_m}$ Does the meaning of "finite intersections" also ...
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0answers
19 views

Transversal Intersection

If $X, Z$ are manifolds of complentary dimension in $Y$, where $X$ compact, $Z$ is closed. Then show that in $ X \times Z, I_2(X \times \{0\},\{0\} \times Z) = 1$. Is this obvious because they ...
0
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0answers
19 views

Detect Regions Described By Lines in Rectangular Coordinates

Need some help from the superior math minds here. This problem is part of a software project. Essentially, I have a Cartesian grid. The user can create lines by plotting points (every 2 points ...
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0answers
74 views

Conic equation from cone/plane intersection

In an orthonormal cartesian frame $(O; \vec{x}, \vec{y}, \vec{z})$ consider: an infinite plane $P$ defined by: a point $p = (p_x, p_y, pz)$ an normal vector $\vec{n} = (n_x, n_y, n_z)$ a cone $C$ ...
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0answers
24 views

Probability of objects position

So I have an interesting problem. I've got two objects, their area and position for their centre of mass in Cartesian coordinates. Their position is given as a bivariate normal distribution and I've ...
0
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0answers
40 views

Solving quartic equations

I am solving quartic equations by finding the intersections of two quadratics. The given quartic function is of the form $x^4 + px^2 + qx + r = 0$. I know one of the quadratic functions to be $y=x^2$. ...
0
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0answers
103 views

Find points of intersection with cone on a plane at a given angles

The provided variables are the cone angle(cA) of a cone that starts at the origin along the Z axis, the vertical angle (vA) of the direction the cone is facing, and a horizontal angle (hA) along with ...
0
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0answers
38 views

Area of intersection between square and annulus

The annulus' larger radius is $1$, smaller radius is $r>0$, and center is $(0,0)$. The square's sides are parallel with the axes, the lower left corner's coordinates are $(a,b)$, and the upper ...
0
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0answers
114 views

How to determine the point of intersection between two points and a vector as seen from a “plane-line” perspective?

I have two points which I call Point(X,Y,Z) and PlaneCenter(X,Y,Z), and a vector called ...
0
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0answers
83 views

Ray and Elliptic Paraboloid intersection

I have ray: P + V*t*. An elliptic paraboloid: focal point: r0 + f * n (orientation of the paraboloid is n from the point r0 with f distance) I would like to find the intersection(s) of the ...
0
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0answers
27 views

Can interval intersection be reduced to comparing values of a function of the interval ends?

More specifically, is there any function $f : \mathbb{N}\times\mathbb{N} \to \mathbb{R} $ such that $[a, b) \cap [S,E) \equiv f(-\infty, S) \le f(a, b) \lt f(E, \infty)$ I managed to show that any ...
0
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0answers
100 views

Intersection of a hollow cone and a circular disc in 3D

I'm trying to calculate the area of a hollow cone intersecting a circular region on a surface. Basically a hollow cone is defined by its starting apex and its ending apex, the height of the cone from ...
0
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0answers
101 views

Line Triangle Intersection Mathematics

I am following the math in the book Real Time Collision Detection by Christer Ericson. On pages 184 thru 188, he discusses how to test for an intersecting line against a triangle. I replicated the ...
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0answers
136 views

Finding area of intersection of two spherical caps on a sphere

Suppose I have a unit sphere centered at the origin, and within this sphere I inscribe a tetrahedron. At each vertex of the tetrahedron, I draw a cap to the sphere with with area $\pi$ such that the ...
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0answers
56 views

Probability for intersection of size $i$ between $k$ sets of size up to $N$

Assume that the elements in each set are sampled uniformly from $r$ possible elements ($N \le r$). It is also given that an element does not appear twice in a set.
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403 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 ...
0
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0answers
124 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 ...
0
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0answers
207 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 ...
0
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0answers
366 views

How to find intersections of hyperbolas by MATLAB

Let's have two hyperbolas given by equations: $$\mathbf{r}^T\cdot \mathbf A_1\cdot\mathbf r+\mathbf b_1^T\cdot\mathbf r+c_1=0$$ $$\mathbf{r}^T\cdot \mathbf A_2\cdot\mathbf r+\mathbf b_2^T\cdot\mathbf ...