Search results
Results from the WOW.Com Content Network
The convex hull of a simple polygon is divided by the polygon into pieces, one of which is the polygon itself and the rest are pockets bounded by a piece of the polygon boundary and a single hull edge. Although many algorithms have been published for the problem of constructing the convex hull of a simple polygon, nearly half of them are ...
The points lying inside of that triangle cannot be part of the convex hull and can therefore be ignored in the next steps. Recursively repeat the previous two steps on the two lines formed by the two new sides of the triangle. Continue until no more points are left, the recursion has come to an end and the points selected constitute the convex ...
A demo of Graham's scan to find a 2D convex hull. Graham's scan is a method of finding the convex hull of a finite set of points in the plane with time complexity O(n log n). It is named after Ronald Graham, who published the original algorithm in 1972. [1] The algorithm finds all vertices of the convex hull ordered along its boundary.
The problem consists in the maintenance, i.e., keeping track, of the convex hull for input data undergoing a sequence of discrete changes, i.e., when input data elements may be inserted, deleted, or modified. It should be distinguished from the kinetic convex hull, which studies similar problems for continuously moving points. Dynamic convex ...
In geometry, the convex hull, convex envelope or convex closure [1] of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space , or equivalently as the set of all convex combinations of points in the subset.
A 2D demo for Chan's algorithm. Note however that the algorithm divides the points arbitrarily, not by x-coordinate. In computational geometry, Chan's algorithm, [1] named after Timothy M. Chan, is an optimal output-sensitive algorithm to compute the convex hull of a set of points, in 2- or 3-dimensional space.
Thus, using kinetic convex hull to maintain the upper and lower envelopes, a kinetic sorted list on these intervals to maintain the antipodal pairs, and a kinetic tournament to maintain the pair of maximum distance apart, the diameter of a moving point set can be maintained. This data structure is responsive, compact and efficient.
The gift wrapping algorithm begins with i=0 and a point p 0 known to be on the convex hull, e.g., the leftmost point, and selects the point p i+1 such that all points are to the right of the line p i p i+1. This point may be found in O(n) time by comparing polar angles of all points with respect to point p i taken for the center of polar ...