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Questions tagged [intersection-theory]

In mathematics, intersection theory is a branch of algebraic geometry, where subvarieties are intersected on an algebraic variety, and of algebraic topology, where intersections are computed within the cohomology ring. (Ref: http://en.m.wikipedia.org/wiki/Intersection_theory). Do not use this tag for elementary problems in linear algebra or geometry. (e.g. determining whether two lines intersect)

In mathematics, intersection theory is a branch of algebraic geometry, where subvarieties are intersected on an algebraic variety, and of algebraic topology, where intersections are computed within the cohomology ring. Reference: Wikipedia

Do not use this tag for elementary problems in or . (e.g. determining whether two lines intersect)

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Intersection Between a Cylinder and a Given Line

I have a given point in space (Point C in Figure) and a cylinder, defined by its start/end center points and radius. I have a point on the axis (Point D), and I need to find the intersection between the cylinder and the line for CD. I also know…
ronwelty
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Continuous Deformation of Hypersurfaces

I'm reading Katz "Enumerative Geometry and String Theory". He shows that a degree $d$ hypersurface has cohomology class $dH $(where $H$ is the class of a hyperplane) by the following argument (p.80, I'm paraphrasing a bit): ...we can continuously…
Adam
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How to find intersections of a curve and tetrahedra?

I have a curve going through tetrahedron elements. How to find the intersections of this curve with the tetrahedrons? The curve is constructed by a few points and represents the axis of the artery going through tissue and I have tissue elements…
Elias
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Minimum intersection of n lines

I saw many questions about intersections on here but didn't find an answer to my question. My question: Imagine you have n points which are randomly spread over a table or a sheet of paper or something else. It can be a circle formation or a…
Masirius
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How can I find the volume of intersection between two cubes?

How can I find the volume of the intersection of two cubes aligned to the axis? The cubes can have different sizes and positions. (I add a picture to show a simple example case of two cubes) After deep research, I am quite sure that does not exist a…
Enrico Gliaschera
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Can a curve intersect 0 to inf without crossing inself?

Can you draw a curve such that it intersects every x at y=0 without ever crossing over itself (that is to say, without hitting the same value twice)? Wouldn't accomplishing this feat mean infinitely approaching every point on the numberline? Can…
MetaStack
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the intersection area of several hyperbolas

I have several hyperbolas, whose standard form is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ or visa, rotated, etc. However, I only focus on one curve of each hyperbola (although there are two curves for each hyperbola), say $curve_1$, and define only one…
WYC
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Computing degree of canonical sheaf of a projective bundle

Let $C$ be a projective smooth curve of genus $g$. Let $\Omega_C$ be the sheaf of differentials of $C$ and consider the exact sequence of vector bundles: $$ 0\rightarrow \mathcal{O}_C\rightarrow E \rightarrow \Omega_C \rightarrow 0.$$ If $P(E)$ is…
user315016
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Intercept moving target

Here's a problem that has bugging me for a while: Say I have a friend that is passing my house. My friend is moving at a constant speed in a perfectly straight line. If she already hasn't done so, she will pass my house at a closest approach and…
RagnarDa
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2D line intersection given 2 points (line) and a point with angle

Given $2$ points (limited length), and a point with angle(unlimited). How do I check if they will intersect or not? I've only been able to find line-line or $4$ points intersections. Current progress : line-angle: $y-x = \cot(d) *…
Cookie
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Finding the first line segment intersected by a particular ray

Consider N disjoint line segments and a ray. Let's say the line segments are stored as a list of $N$ 4-tuples, each tuple storing the coordinates of the endpoints of the line segment $(x_0, y_0, x_1, y_1)$. Let's say the ray is stored as a 4-tuple,…
Venu Nathan
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How this inequality works to know a point cross a line or not?

First of all, sorry for my bad english.. but i really want to know how this works. as you see in the picture, there are 3 points and if leftside is greater than rightside, It means the point p0 is not cross the line(p1 - p2). I can't understand…
Hree
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Need help in understanding the meaning of an statement

I getting problem in understanding the sentence Alpha indicates the IoU (Intersection over Union) for neighbouring candidate boxes; step sizes of the sliding windows are determined such that one step results in an IoU of Alpha. What I understand…
Aadnan Farooq A
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Intersection of a set with a powerset

I am now struggling with the basics of Formal Semantics, which is hard to understand without knowing something about the Naive Set Theory. Please help me out. The task is to explicitly write down the set by enumerating its members: {a} ∩ P({a}) I…
Zimbardo
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4 Sets of Co-Ordinates, Calculate the points of intersection

I have 4 sets of co-ordinates that need to be plotted and then I need to find a point of intersection. However, I do not know exactly where the points need to intersect. What I do know is that the co-ordinates would more than likely be pairs. as…
Leon Claassen
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