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Each step removes all points whose closest neighbor is at distance or greater, at least half of the points in expectation, from which it follows that the total expected time for filtering is linear. Once an approximate value of d {\displaystyle d} is known, it can be used for the final steps of Rabin's algorithm; in these steps each grid point ...
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 ...
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.
No two line segment endpoints or crossings have the same x-coordinate; No line segment endpoint lies upon another line segment; No three line segments intersect at a single point. In such a case, L will always intersect the input line segments in a set of points whose vertical ordering changes only at a finite set of discrete events ...
In this algorithm, one recursively draws a line to split the vertices into two sets. The Delaunay triangulation is computed for each set, and then the two sets are merged along the splitting line. Using some clever tricks, the merge operation can be done in time O( n ) , so the total running time is O( n log n ) .
At each step, the algorithm follows a path along the polygon from the stack top to the next vertex that is not in one of the two pockets adjacent to the stack top. Then, while the top two vertices on the stack together with this new vertex are not in convex position, it pops the stack, before finally pushing the new vertex onto the stack.
Coordinate descent is an optimization algorithm that successively minimizes along coordinate directions to find the minimum of a function.At each iteration, the algorithm determines a coordinate or coordinate block via a coordinate selection rule, then exactly or inexactly minimizes over the corresponding coordinate hyperplane while fixing all other coordinates or coordinate blocks.
Each possible contiguous sub-array is represented by a point on a colored line. That point's y-coordinate represents the sum of the sample. Its x-coordinate represents the end of the sample, and the leftmost point on that colored line represents the start of the sample. In this case, the array from which samples are taken is [2, 3, -1, -20, 5, 10].