Download Combinatorial Maps Efficient Data Structures for Computer by Guillaume Damiand, Pascal Lienhardt PDF

By Guillaume Damiand, Pascal Lienhardt

Combinatorial Maps: effective info buildings for special effects and snapshot Processing Комбинаторные карты: эффективные структуры данных для компьютерной графики и обработки изображений. Combinatorial Maps: effective info buildings for special effects and snapshot Processing gathers vital principles on the topic of combinatorial maps and explains how the maps are utilized in geometric modeling and snapshot processing. It makes a speciality of subclasses of combinatorial maps: n-Gmaps and n-maps. appropriate for researchers and graduate scholars in geometric modeling, computational and discrete geometry, special effects, and snapshot processing and research, the publication offers the knowledge buildings, operations, and algorithms which are priceless in dealing with subdivided geometric items. It indicates the right way to learn info buildings for the specific illustration of subdivided geometric items and describes operations for dealing with the constructions. The publication additionally illustrates result of the layout of knowledge constructions and operations.

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Extra info for Combinatorial Maps Efficient Data Structures for Computer Graphics and Image Processing

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This is a structural operation, which consists in “expanding” vertices and edges into faces, the structure of the face depending on the structure of the replaced vertex or edge. For instance, a vertex incident to three edges is basically replaced with a triangular face; • then computing surfaces patches, which are associated with the chamfered cells: cf. Fig. 4(c). The structural relations between cells are also useful or necessary for many global operations. For instance, when simulating a traversal of a building, the adjacency relations between the represented rooms make it possible to control the traversal: obviously, it is not possible, when exiting a room, to enter a nonadjacent room.

By applying b times “making a boundary” to a disc, you get a sphere with b boundaries (a disc is thus a sphere with one boundary). If you apply “removing a boundary” to a M¨ obius strip, you get a projective plane. If you apply twice “making a twist” to a disc, you get a Klein bottle with one boundary: cf. Fig. 15(a) and Fig. 16(c). If you apply “removing a boundary” to a Klein bottle with one boundary, you get a Klein bottle: cf. Fig. 15(b). Note that if you apply “making a twist” several times, you can get a surface such that its orientability factor is greater than 2: we will see below that, thanks to the exchange theorem, there is no contradiction with the surface classification as stated at the beginning of this section.

See [1, 196, 180, 133] for introductions to topology. 1 Basic Topological Notions Some classical vocabulary is introduced here. 1 Basic Elements Balls: cf. Figs. 1(a), (b) and (c). Let Rn = {x = (x1 , . . , xn )|xi ∈ R, 1 ≤ i ≤ n} be the usual n − dimensional space. Let r ∈ R. 1 (a) B12 (O), where O = (0, 0). ¯ 2 (O). (b) B 1 (c) S11 (O). ¯ 2 (O). (d) N is a neighborhood of point a in B 1 • Srn−1 (x) = {y ∈ Rn |d(x, y) = r} is the (n − 1)-dimensional sphere of radius r around x in Rn . ¯ 1 (0) = I¯1 = [−1, 1] and S 0 = {−1, 1}.

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