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If the point is closer than ε to the line segment, then any points not currently marked to be kept can be discarded without the simplified curve being worse than ε. If the point farthest from the line segment is greater than ε from the approximation then that point must be kept. The algorithm recursively calls itself with the first point and ...
Then A[I] is equivalent to an array of the first 10 elements of A. A practical example of this is a sorting operation such as: I = array_sort(A); % Obtain a list of sort indices B = A[I]; % B is the sorted version of A C = A[array_sort(A)]; % Same as above but more concise.
An algorithm for the dynamic closest-pair problem in dimensional space was developed by Sergey Bespamyatnikh in 1998. [10] Points can be inserted and deleted in O ( log n ) {\displaystyle O(\log n)} time per point (in the worst case).
The Z-ordering can be used to efficiently build a quadtree (2D) or octree (3D) for a set of points. [5] [6] The basic idea is to sort the input set according to Z-order.Once sorted, the points can either be stored in a binary search tree and used directly, which is called a linear quadtree, [7] or they can be used to build a pointer based quadtree.
The Bentley–Ottmann algorithm will insert a new segment s into this data structure when the sweep line L crosses the left endpoint p of this segment (i.e. the endpoint of the segment with the smallest x-coordinate, provided the sweep line L starts from the left, as explained above in this article).
In machine learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector ...
The rotating calipers technique for designing geometric algorithms may also be interpreted as a form of the plane sweep, in the projective dual of the input plane: a form of projective duality transforms the slope of a line in one plane into the x-coordinate of a point in the dual plane, so the progression through lines in sorted order by their ...
An array data structure can be mathematically modeled as an abstract data structure (an abstract array) with two operations get(A, I): the data stored in the element of the array A whose indices are the integer tuple I. set(A, I, V): the array that results by setting the value of that element to V. These operations are required to satisfy the ...