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In geometry, an intersection is a point, line, or curve common to two or more objects. The simplest case in Euclidean geometry is the intersection of two distinct lines, which either is one point or does not exist if the lines are parallel.
Determination of the intersection of flats – linear geometric objects embedded in a higher-dimensional space – is a simple task of linear algebra, namely the solution of a system of linear equations. In general the determination of an intersection leads to non-linear equations, which can be solved numerically, for example using Newton iteration. Intersection problems between a line and a conic section or a quadric lead to quadratic equations that can be easily solved. Intersections between quadrics lead to quartic equations that can be solved algebraically.
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