Algorithmic Foundation of Multi-Scale Spatial Representation by Zhilin Li

By Zhilin Li

With the common use of GIS, multi-scale illustration has develop into an immense factor within the realm of spatial facts dealing with. targeting geometric variations, this source offers complete insurance of the low-level algorithms on hand for the multi-scale representations of alternative forms of spatial positive aspects, together with aspect clusters, person strains, a category of strains, person parts, and a category of parts. It additionally discusses algorithms for multi-scale illustration of 3D surfaces and 3-D positive aspects. Containing over 250 illustrations to complement the dialogue, the ebook presents the latest study effects, corresponding 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)

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In row 1 x0, y0 is the center of the circle and r is the radius. 4 Representation of spatial features in vector and raster spaces. 1 Mathematical Functions for Geometric Elements Geometric elements Mathematical function 1 Straight line (Ln) ax + by + c = 0 2 Plane (Pl) ax + by + cz + d = 0 3 Curved line (Cl) y = a + bx + cx 2 + .... 4 Circle (Cr) ( x − x 0 )2 + ( y − y0 )2 = r 2 5 Curved surface (Cs) z = a0 + a1 x + b1 y + a2 x 2 + b2 y 2 + ... 1) where L is the length along the curved line, sometimes called the arc length.

In computing literature, curve approximation and corner detection are the two operations used to retain critical points and remove less important points. In the author’s viewpoint, point reduction should not be part of the operations for multi-scale representation because traditional generalization has nothing to do with point reduction (Li, 1993). Point-reduction algorithms try to make best approximations of the original line with a minimum number of points. It must be emphasized here that no scale change is involved in such an operation.

From Chapter 4 on, algorithms for multi-scale spatial representations will be presented. 4. Chapter 4 is dedicated to the multi-scale representation of point features. The elimination of individual point features is an easy operation and there is no need of any algorithm. The displacement of a point feature is similar to displacement of a line or an area feature and will be discussed in Chapter 11, which is dedicated to the topic of displacement. The magnification of a point feature means the enlargement of a small area feature and will be discussed in Chapter 9.

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