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37 Cards in this Set
- Front
- Back
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Define tessellation |
a gorup of regular or irregular portions of space which together fit all of that space. no gaps every point in space assigned to only one cell/pixel also called meshes / tilings |
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Classifications of tessellations |
Regular - square raster Irregular - TIN, voronoi Hierarchical regular - region quadtree Hierarchical irregular - point quadtree Cell centre - Voronoi Node centred - TIN |
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Definition of Geometry 'Shape' |
shape: number of edges at vertex number of vertiecs |
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Definiton of Geomery ' Adjacency' |
adjacency via edges, vertices, or both -eg Hexagon = edges only Adjacency distacne = between centroids |
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Tessellation decomposability? |
the ability to deconstruct a shape into other shapes. eg hexagon = six equilateral trinagles |
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Packing property of a tessellatino? |
The 'stability' of tessellation Hexagon econonomical at packing space |
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Heirarchical tessellations |
can approximate to the shape of a spatial entity. (using diff tessellation sizes) Can be an efficient spatical reference method Suited to a square. because good decomposability, - triangles could also be sued. |
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Qualities of hierarchies |
Aperture - tessellation parameter. Ratio of parent to area of child. Aligned - centre of parent is the centre of child Congruent - edges parent are the edges of child Self similar - parent and child have same shape |
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Central Place Theory |
Central place theory is a geographicaltheory that seeks to explain the number, size and location of human settlements in an urban system |
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What is the best shape for spherical tesselation |
Octahedron |
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Hexagon or Rhombus quadtree |
HoR Uses the uniform adjacency of hexagons the divisibility of rhombi uniform orientation at all levels in the hierarchy |
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Adaptive Recursive Tessellations ART |
ART allows midifiable cell size (enabled by variable decopmosition ratio) and shape. Based on a number of levels - level 0 = smallest cell size. Each level has uniformly oriented cells. |
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BTU |
Basic Tessellation Unit. Uniform and rectangular at each level. Defined by the lengths of their x and y Parent BTU must decompose into a discrete number of child BTU's tessellation parameter = number of child BTUs that can fit into Parent BTU. lower left pixel linked to coord system |
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Whats the approach of a quadtree? |
Area of interest identified first, rigid decomposition into 4 equal parts until some atomic level is reached algorithm led |
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What is the approach of ART. |
Adaptive Recursive Tessellation. Number of levels and sizes of cell specified. checked for size compatibility between levels. Application -led Example is remote sensing data fom diff sources - this structure can integrate different resolutions as is without sampling. |
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Triangulation Types |
Delaunay: Low variance in edge length Triangles closest to equilateral Fewer long thin triangles The dual of Voronoi Constrained Delaunay: Includes predefined lines Greedy Trinagulation Shortest edges possible |
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Criteria for aesthetically pleasing triangulations |
Adjacency (conforming): -each edge shared by no more than two triangles. -Guarnatees a continuous surface Nesting: -children are comletely bounded by the parent -simpler data storage, ease of navigation Streakiness: -too many traingulations at a given vertiex. Sliveriness: -delauany tries to avoid this by definition -equilateral triangles are good |
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Preconditions for spatial indexes |
Traditional indexing not used for spatial data - relies on total order of a key (attribute) Need to base index on object proximity in geometric plane. - implies preservation of locality. -closeness in space means closeness on dis. Scalability -no loss of performance with higher amounts of data |
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Database indexing: Fixed Grid structure? |
Fixed grid - divide a planar region into cells of fixed size Featuers in the same cell (bucket) are stored together in a disk block. (this covers proximity) Number of cells dependent on number of features. -capacity of disk block -average range magnitude of query. |
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Disadvantages of fixed grid database indexing? |
Feautre population within a bucket (cell) varies - especially with nonuniform distribution. Some buckets have no features. Susceptible to overflow. |
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Database indexing: Point quadtree |
similar to region quadtree... partition into quadrants centred on coordinate.s |
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2D tree ( KD-tree) |
Similar to point quadtree Lessens dangling nodes - to two Lessens exponential growth of descendents with increasing dimensions - makes a deeper tree structure One dimension at alternate depths (x at even depths, y at odd depths) Two descendents (binary treE) left and right. HOW TO: Each leaf node contains one vertex. A vertex leaf node cannot contain edges not incident with that vertex For a nonvertex leaf node, can only contain one edge part |
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Original R tree |
Multidimensional extension of the Btree -indexing rectangles in 2D space -Balanced tree, avoids overflow or underflow of disk block Each node in the tree represents a rectangle -leaf nodes contain unit rectangles -internal nodes contain smallest rectangle enclosing its descendants. (saves searching time) Overlap of rectangles along a tier likely. |
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R + tree |
Doesnt not permit overlapping in non leaf rectangles. - partitions rectangles and stores each in different part of tree. Complex insertion and deletion Loss of tree balance More nodes and duplicate entries |
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What is linear referencing? |
Linear referencing is the method of storing gepgraphic locations by using relative positions along a measured linear feature |
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What is a fractal |
a never ending pattern. |
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three applications of Linear referencing systems? |
Transportation Rivers Coast |
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three example modes of operation of Linear referencing systems |
Distance to discrete point distance to where a continuous attribute changes in value Start and end distances of a segment |
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What is dynamic segmentation |
The process of computing the map locations of linearly referenced data (for example, attributes stored in a table) at run time so they can be displayed on a map, queried, and analyzed using a GIS |
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Interpolation. define. |
the procedure that estimates the values of properties at unsampled locations covered by existing observations. Most data is sampled. Need to fill the gaps.. |
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Spatial Interpolation: Point Interpolation: Global : Trend Surfaces |
Trend Surfaces: Uses a polynomial regression to fit leastsquares surface to data points. |
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Local interpolation methods |
eg Inverse Distance Weighting Assume space is correlated. Values nearby are independent, used to predict nearby values. |
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Common problems of point interpolation methods |
Input data uncertainty: -too few data points -limited or clustered spatial coverage -uncertainty about location/value Edge effects: -need data points outside study area -improve interpolation and avoid distortion at boundaries. |
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toblers approach to area interpolation |
Method assumes the existence of a smooth density funciton which takes into account the effect of adjacent source zones. |
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IDW asumptions |
Inverse Distance Weighting: Assumes space is correlated, so values of nearby points can be predicted. |
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IDW basic pseudocode |
-compute distance between sample points and other points. - define weighting as (1/distance)^p -sum weighted balue of each observation - normalise the result by the sum of the weights. |
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IDW effects of p |
the higher p is, the quicker the weighting diminishes with distance. value of 0, same weighting for all distance ==~~ mean basically. |
