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No three line segments intersect at a single point. In such a case, L will always intersect the input line segments in a set of points whose vertical ordering changes only at a finite set of discrete events. Specifically, a discrete event can either be associated with an endpoint (left or right) of a line-segment or intersection point of two ...
Two intersecting lines. In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line.Distinguishing these cases and finding the intersection have uses, for example, in computer graphics, motion planning, and collision detection.
The Shamos–Hoey algorithm [1] applies this principle to solve the line segment intersection detection problem, as stated above, of determining whether or not a set of line segments has an intersection; the Bentley–Ottmann algorithm works by the same principle to list all intersections in logarithmic time per intersection.
For two non-parallel line segments (,), (,) and (,), (,) there is not necessarily an intersection point (see diagram), because the intersection point (,) of the corresponding lines need not to be contained in the line segments. In order to check the situation one uses parametric representations of the lines:
If s itself contains the origin, NearestSimplex accepts s and the two shapes are determined to intersect. The simplices handled by NearestSimplex may each be any simplex sub-space of R n. For example in 3D, they may be a point, a line segment, a triangle, or a tetrahedron; each defined by 1, 2, 3, or 4 points respectively.
In its most general form, the problem is, given a partition of the space into disjoint regions, to determine the region where a query point lies. For example, the problem of determining which window of a graphical user interface contains a given mouse click can be formulated as an instance of point location, with a subdivision formed by the ...
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Green line has two intersections. Yellow line lies tangent to the cylinder, so has infinitely many points of intersection. Line-cylinder intersection is the calculation of any points of intersection, given an analytic geometry description of a line and a cylinder in 3d space. An arbitrary line and cylinder may have no intersection at all.