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

By Tamiya Onodera

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16 holds. We assume that i=2 without loss of generality. 4(a) shows a picture p and two survergent correspondences rl and r2; p assigns a single color in C to a circular region in U, while rl and r2 are simply translations of a square. We intentionally make the domain of p not equal to that of rl, and the images of rx and r2 overlapping. 4(b) and (c). The image of r~ obscures the one of r2 in r2 • ra, and this causes a circle to be partly obscured in (r2 @ ra)'(p). On the other hand, the domains of ~,(p) and ;~(p) are disjoint, and that of ~2(p) + ~,(p) consists of two full circles.

The closure point is initialized to the first point in the sequence and is reset to the successor when the keyword c l o s e is encountered. 3 . 7 . 7 . 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.

The system of pNucleus contains the following set of primitives: II,, = {~ .... } II~ = {%i**} where 7rt,,, 7r..... 2 and the others are defined as follows: 7rpt simply generates from a sequence of points the geometry consisting of the specified points. ~rtat generates from a sequence of three points P1,P2, and P3 the lattice whose reference point is P1 and whose width vector and height vector are P1P2 and P1P3, respectively. The primitives of 7rrt and 7rz~t are originally meant for polymarker drawing and fillarea drawing, respectively.

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