By Zhilin Li
With the common use of GIS, multi-scale illustration has develop into a tremendous factor within the realm of spatial facts dealing with. concentrating on geometric ameliorations, this source offers entire assurance of the low-level algorithms to be had for the multi-scale representations of other sorts of spatial gains, together with element clusters, person traces, a category of strains, person components, and a category of components. It additionally discusses algorithms for multi-scale illustration of three-D surfaces and 3D beneficial properties. Containing over 250 illustrations to complement the dialogue, the e-book presents the newest examine effects, similar to raster-based paintings, set of rules advancements, snakes, wavelets, and empirical mode decomposition.
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Additional info for Algorithmic Foundation of Multi-Scale Spatial Representation (2006)(en)(280s)
5a is a curved line formed by a set of points. Such a line is sometimes called a polyline. 5b shows the decomposition of the polyline line into two monotonic functions. In any algorithm for geometric transformations, some kinds of geometric parameters must be used as criteria. 5 Representation of a line in parametric form. 2 Some Commonly Used Geometric Parameters Geometric parameter Mathematical function 1 Distance between two points d ( P1 , P2 ) = ( x1 − x 2 )2 + ( y1 − y2 )2 2 Distance from point P to line Ln d ( P, Ln) = 3 Distance from point P to plane Pl d ( P, Pl ) = 4 Slope between two points tan α = 5 Curvature of a curved line c( x , y) = 6 Angle (ω) formed by two sides (a and b) of a triangle conω = a2 + b2 − c2 2ab 7 Area formed by N points A( P1 , P2 PN ) = ax1 + by1 + c a2 + b2 ax1 + by1 + cz + d a2 + b2 + c2 y2 − y1 x 2 − x1 d 2 y/dx 2 [1 + (dy/dx )2 ]3/ 2 ( 1 N ∑ y × xi +1 − xi × yi +1 2 i =1 i ) not exceptions.
7. However, some terms may have slightly different meanings. For example, exaggeration has been used to refer to enlarging the size of the doors of a building instead of the building itself (Bai and Chen, 2001). Such exaggeration will be defined as partial exaggeration in this context. In addition, bunching and injoining have been in use (Bai and Chen, 2001), but they are similar to the typification and aggregation operations for 2-D representations. In essence, there is not much difference between the operations used for 2-D and 3-D representations.
Relocation: Moving more than one feature around normally to solve a conflict problem. Structural simplification: Retaining the structure of area patches by selecting important ones and omitting less important ones. , buildings) aligned in rows and columns. , 2005): metric and visual. In metric multi-scale representation, the features on the same representation have the same scale. Filtering and pyramid structuring are the methods commonly used (de Floriani, 1989). Scale-driven generalization has also been discussed by Li and Li (1999) and Li et al.
Algorithmic Foundation of Multi-Scale Spatial Representation (2006)(en)(280s) by Zhilin Li