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Dynamic convex hull maintenance: The input points may be sequentially inserted or deleted, and the convex hull must be updated after each insert/delete operation. Insertion of a point may increase the number of vertices of a convex hull at most by 1, while deletion may convert an n -vertex convex hull into an n-1 -vertex one.
Convex hull, alpha shape and minimal spanning tree of a bivariate data set. In computational geometry, an alpha shape, or α-shape, is a family of piecewise linear simple curves in the Euclidean plane associated with the shape of a finite set of points.
For the sake of simplicity, the description below assumes that the points are in general position, i.e., no three points are collinear.The algorithm may be easily modified to deal with collinearity, including the choice whether it should report only extreme points (vertices of the convex hull) or all points that lie on the convex hull [citation needed].
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.
In two dimensions, the diameter can be obtained by computing the convex hull and then applying the method of rotating calipers.This involves finding two parallel support lines for the convex hull (for instance vertical lines through the two vertices with minimum and maximum -coordinate) and then rotating the two lines through a sequence of discrete steps that keep them as parallel lines of ...
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.
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.