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

By Tamiya Onodera

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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.

4. 4. Since Gr 3'2 $ 3", = {(a, 1), (b, 2)}, Gr 3'2 o (3"~ ~ 3'~) = {(a, ~), (b, ~)}. On the other hand, since Gr 3"2 o 3"2 = {(a, z)) and Or 72 o 3'x = {(b, z)}, Gr (3'~ o3"~) ~ (3'203",) = {(a, ~)}. 4 Extensions of Correspondences In this subsection we define three extensions of a correspondence on a set. 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) ....

Each visualizing net is presented in a DAG representation, for clarity. CHAPTER 3. FORMAL MODEL OF VISUALIZATION 34 normalization / a sequence of points transformation---_~ M x G segment ~ tg transformation --~ M x G Itg workstation _MxG transformation'J~ i tg GxG ~tr line type _ . ~ P x G tp line color tR . 6. According to the GKS document, three geometric transformations - - normalization transformation, workstation transformation, and segment transformation - - take place at the stage of the geometry transformations, although GKS has no distinct concepts of geometry and picture.

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