Download A Formal Model of Visualization in Computer Graphics Systems by Tamiya Onodera PDF

By Tamiya Onodera

ISBN-10: 3540523952

ISBN-13: 9783540523956

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Let 7 = (G, M, M ) be a correspondence on M. W h e n 7 is a correspondence, the mappiug :r = (G, 2 M, 2 M) is naturally derived by the rule, n i=1 is called the power se~ ez~ensiort of 3'. The ®-closure of a set S, denoted by S*, is defined as S U (S ® S) U (S ® S ® S) .... When 3' is a mapping, the mapping 7* = (G, M*, M*) can be defined by the rule ( m l , ... , m . ) e M" ~-~ ( 3 " ( m l ) , . . , ~(m,)). 3" is called the ®-closure ezlertsiort of 3". The last extension of a correspondence is for a set of correspondences.

The system is called a graphical nucleus. The objects involved within a visuafizing net, geometries and pictures, are conceptual at the net's level of abstraction. How can they be specified? The first section deals with this subject and gives definitions to the concept of a graphical primitive. The important property of a graphical primitive, called soundness, is also identified. After defining a graphical nucleus, we formally investigate its implementability, where the primitives with the soundness property play a central role.

4 . 6 . 5 . 0 . 1. [] A point is represented by a dotted pair of its x and y coordinates in pNucleus. , ~rpt, and lrzat. The syntax of G-expressions is as follows: (*line {} {}) (*point {} {}) 52 CHAPTER 5. 1 (*lattice {}) These denote a line geometry, a point geometry, and a lattice geometry, respectively. Since Claim 1 insists that restrictive transformations must be accumulated, the syntax is determined so that each G-expresslon can maintain restrictive transformations by appending restrictive geometries specifying them.

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