Sub-quadratic algorithm for finding the intersections between two sets of spherical arcs
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Is there an algorithm that can find the intersections between two sets of spherical great-circle arcs (on the same sphere) with an worst-case runtime complexity better than the $O(n ÃÂ m)$ brute-force algorithm? Intersections between arcs in the same set are irrelevant, I only need to find the intersections between two arcs in different sets.
The arcs are defined by two points on the sphere, taking the shorter great-circle path (the one with length < ÃÂ, assume none of the pairs of points are antipodal). The arcs are not necessarily the same length.
algorithms computational-geometry
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up vote
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down vote
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Is there an algorithm that can find the intersections between two sets of spherical great-circle arcs (on the same sphere) with an worst-case runtime complexity better than the $O(n ÃÂ m)$ brute-force algorithm? Intersections between arcs in the same set are irrelevant, I only need to find the intersections between two arcs in different sets.
The arcs are defined by two points on the sphere, taking the shorter great-circle path (the one with length < ÃÂ, assume none of the pairs of points are antipodal). The arcs are not necessarily the same length.
algorithms computational-geometry
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Is there an algorithm that can find the intersections between two sets of spherical great-circle arcs (on the same sphere) with an worst-case runtime complexity better than the $O(n ÃÂ m)$ brute-force algorithm? Intersections between arcs in the same set are irrelevant, I only need to find the intersections between two arcs in different sets.
The arcs are defined by two points on the sphere, taking the shorter great-circle path (the one with length < ÃÂ, assume none of the pairs of points are antipodal). The arcs are not necessarily the same length.
algorithms computational-geometry
Is there an algorithm that can find the intersections between two sets of spherical great-circle arcs (on the same sphere) with an worst-case runtime complexity better than the $O(n ÃÂ m)$ brute-force algorithm? Intersections between arcs in the same set are irrelevant, I only need to find the intersections between two arcs in different sets.
The arcs are defined by two points on the sphere, taking the shorter great-circle path (the one with length < ÃÂ, assume none of the pairs of points are antipodal). The arcs are not necessarily the same length.
algorithms computational-geometry
asked Aug 17 at 7:31
taylor swift
396210
396210
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