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Analysis of Algorithms Articles
Page 10 of 17
Kinetic Data Structures
Basic conceptA kinetic data structure is defined as a data structure implemented to track an attribute of a geometric system that is moving continuously. For example, a kinetic convex hull data structure tracks the convex hull of a group of n moving points.The development of kinetic data structures was inspired by computational geometry problems involving physical objects in continuous motion, for example collision or visibility detection in robotics, animation or computer graphics.OverviewKinetic data structures are implemented on systems where there is a set of values that are changing as a function of time, in a called fashion. So the system ...
Read MoreHilbert Tree in Data Structure
Hilbert R-tree, an R-tree variant, is defined as an index for multidimensional objects such as lines, regions, 3-D objects, or high-dimensional feature-based parametric objects. It can be imagined as an extension to B+-tree for multidimensional objects.R-trees' performance depends on the quality of the algorithm that clusters the data rectangles on a node. Hilbert R-trees implement space-filling curves, and specifically the Hilbert curve, for imposing a linear ordering on the data rectangles.Hilbert R-trees are of two types: one for static databases, and one for dynamic databases. In both cases Hilbert space-filling curves are implemented to achieve better ordering of multidimensional objects ...
Read MoreR* Tree in Data Structure
Basic conceptIn case of data processing, R*-trees are defined as a variant of R-trees implemented for indexing spatial information.R*-trees have slightly larger construction cost than standard R-trees, as the data may require to be reinserted; but the resulting tree will generally have a better query performance. Same as the standard R-tree, it can store both point and spatial data. Concept of R*-tree was proposed by Norbert Beckmann, Hans-Peter Kriegel, Ralf Schneider, and Bernhard Seeger in 1990.Difference between R*-trees and R-treesR*-Tree is constructed by repeated insertion. There is little (i.e. almost no) overlap in this tree, resulting in good query performance. ...
Read MoreConverting B-Reps to Trees in Data Structure
1 B-rep StreamsIt is clearly stated to set up a producer process importing a B-rep, externally defined by some standard polygonal format, e.g. either a wave front or java3D obj file, into an input stream for our geometric pipeline. The boundary representation provided by polygons and normal must be coherently oriented. A filtering of the input file to cope with nonplanar polygons and other geometric inaccuracies may be required for generally archived geometric models implemented primarily in computer graphics. The output stream of coherently-oriented triangles, is then transformed into our twin progressive-BSP (Binary Search Partitioning) trees by the algorithmic steps ...
Read MoreBSP Trees as a Multi-Dimensional Search Structure
Spatial search structures are based on the same ideas that were invented in Computer Science during the 60's and 70's for solving the problem of quickly processing large sets of symbolic data, as opposed to geometric data, for example lists of people's names. It was invented that by first sorting a list of names according to alphabet, and storing the sorted list in an array, one can compute whether some new name is already in the list in log2n operations using a binary search algorithm, rather than n/2 expected operations required with the help of a sequential search. This is ...
Read MoreCompressed Quadtrees and Octrees in Data Structure
Compressed QuadtreesAt the time of storing every node corresponding to a subdivided cell, we may end up storing a lot of empty nodes. Cutting down on the size of such sparse trees is possible by only storing subtrees whose leaves have interesting data (i.e. "important subtrees"). Again we can actually cut down on the size even further. When we only consider important subtrees, the pruning process may avoid long paths in the tree where the intermediate nodes have degree two (a link to one parent and one child). It turns out that we only require to store the node U ...
Read MoreRegion Quadtrees in Data Structure
The region quadtree is useful to represent a partition of space in two dimensions by breaking the region into four equal quadrants, subquadrants, and so on with each leaf node consisting of data corresponding to a specific subregion. Each node in the tree either is associated with exactly four children or no children (a leaf node). The height of quadtrees that follow this decomposition strategy (i.e. subdividing subquadrants until and unless there is interesting data in the subquadrant for which more refinement is required) is sensitive to and dependent on the spatial distribution of interesting areas in the space being ...
Read MoreQuadtrees in Data Structure
Quadtrees are trees implemented to efficiently store data of points on a two-dimensional space. In this tree, each node has maximum four children.We can build a quadtree from a two-dimensional area implementing the following stepsThe current two dimensional space is divided into four boxes.If a box consists of one or more points in it, build a child object, storing in it the two dimensional space of the box.If a box does not contain any points, do not build a child for it.Perform recursion for each of the children.Quadtrees are implemented in image compression, where each node consists of the average ...
Read MoreRange Trees in Data Structure
A range tree is defined as an ordered tree data structure to hold a list of points. It permits all points within a given range to be efficiently retrieved, and is typically implemented in two or higher dimensions. It is same to a kd-tree except with faster query times of O(logd n + k) but worse storage of O(n logd-1 n), with d indicating the dimension of the space, n indicating the number of points in the tree, and k indicating the number of points retrieved for a given query. Range trees may be differentiated with interval trees: instead of ...
Read MoreHalfedge data structure
IntroductionA HDS for template parameters or halfedge data structure (abbreviated as HalfedgeDS) is defined as an edge-centered data structure capable of maintaining incidence information of vertices, edges and faces, such as for planar maps, polyhedra, or other orientable, two-dimensional surfaces embedded in random dimension. Each edge is broken into two halfedges with opposite orientations. Each halfedge stores one incident face and one incident vertex. One incident halfedge is stored for each face and each vertex. Reduced variants of the halfedge data structure can eliminate some of this information, such as the halfedge pointers in faces or the storage of faces ...
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