By Guillaume Damiand, Pascal Lienhardt
Combinatorial Maps: effective info constructions for special effects and photograph Processing Комбинаторные карты: эффективные структуры данных для компьютерной графики и обработки изображений. Combinatorial Maps: effective information buildings for special effects and photograph Processing gathers very important principles concerning combinatorial maps and explains how the maps are utilized in geometric modeling and photograph processing. mirknig.com It specializes in subclasses of combinatorial maps: n-Gmaps and n-maps. compatible for researchers and graduate scholars in geometric modeling, computational and discrete geometry, special effects, and picture processing and research, the e-book provides the information constructions, operations, and algorithms which are important in dealing with subdivided geometric items. It indicates find out how to learn info constructions for the specific illustration of subdivided geometric items and describes operations for dealing with the constructions. The booklet additionally illustrates result of the layout of knowledge constructions and operations.
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Fig. 9). So a paper surface can be made of a single face, or by many faces glued by identifying several pairs of edges. e. partitioned) into vertices, edges and faces. Incidence and adjacency relations The “boundary” relation corresponds to the incidence relation: more precisely, an edge (resp. a vertex) which belongs to the boundary of a face is incident to the face, and conversely, the face is incident to the edge (resp. to the vertex). e. the vertex meets the edge), the vertex and the edge are incident to each other.
For instance (cf. Fig. 3), all curves without boundary are homeomorphic, and all are homeomorphic to the unit 1-dimensional sphere S11 (O), where O = (0, 0) ∈ R2 ; since any point x ∈ S11 (O) has a neighborhood which is homeomorphic to I1 =] − 1, 1[⊂ R, any point of any curve without boundary satisfies the same property. Similarly, all curves with boundary are homeomorphic, and all are homeomorphic to I¯1 = [−1, 1] ⊂ R. Intuitively, A and B are homeomorphic if you can deform continuously A in order to get B.
Is a point, a 1-simplex is a line segment, a 2-simplex is a triangle, a 3-simplex is a tetrahedron, etc. Quasi-manifolds, manifolds, pseudo-manifolds and orientability Let closed n-cells be homeomorphic to n-simplices (cf. Figs. e. a closed n-cell contains an n-cell and its boundary, made of k-cells (0 ≤ k < n). We can construct n-dimensional quasi-manifolds by taking such closed n-cells and by identifying pairs of free (n − 1)-cells (and their boundaries). The identification operation can be defined by considering a homeomorphism between the two free (n − 1)-cells, extending it on the boundaries of the (n − 1)-cells by continuity, and then by identifying any points associated by the “extended homeomorphism”: cf.
Combinatorial Maps Efficient Data Structures for Computer Graphics and Image Processing by Guillaume Damiand, Pascal Lienhardt