Algorithms that answer questions about the relationships among points, segments and polygons. The Bentley-Ottmann algorithm finds the crossings among line segments, the closest pair algorithm finds the two nearest points, the Gilbert-Johnson-Keerthi algorithm measures the distance between convex shapes, Welzl's algorithm finds a smallest enclosing circle, and the point-in-polygon test and the shoelace formula decide whether a point is inside a shape and compute its area.
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Geometric Intersection, Proximity and Measurement Algorithms
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Wikipedia: Snap rounding
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Snap rounding is a method of approximating line segment locations by creating a grid
Wikipedia: Bentley-Ottmann algorithm
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In computational geometry, the Bentley-Ottmann algorithm is a sweep line algorithm for listing all crossings in a set of line segments, i.e. it finds the intersection points (or, simply, intersections) of line segments.
Gilbert-Johnson-Keerthi distance algorithm (Wikipedia)
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The Gilbert-Johnson-Keerthi distance algorithm is a method of determining the minimum distance between two convex sets, first published by Elmer G. Gilbert, Daniel W. Johnson, and S. Sathiya Keerthi in 1988.
Shoelace Formula (Wikipedia)
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The shoelace formula, also known as Gauss's area formula and the surveyor's formula, is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane.
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