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

By Tamiya Onodera

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7) c l o s e . 8 . 0 . 9 ) ) ) The system of pNucleus will evaluate this V-expression to the following G-expression: (*line (0 . 1 . 3 . 4 . 4) . 6 . 4) . 7 . 3 . 5 . 0 . 6 ) ) ) No actual restriction is performed by *rtran*geom; a restrictive geometry is merely appended. 4 Pictures and P i c t u r e Transformations This section presents the syntax of P-expressions and the method of realizing the picture transformations. We also describe picture-naming facilities, which add another type of P-expression to the pNucleus system.

EXTENSIONS OF CORRESPONDENCES M P M P --'~N M "Y2 ~'N ~1 (P) --- N P M M *N \ These sets are given priorities. 5: Diagram representing both sides in the equality of Theorem 4 Chapter 3 F o r m a l M o d e l of V i s u a l i z a t i o n This chapter first gives a formalization of basic concepts in computer graphics, resorting to the mathematical framework constructed in the previous chapter. After identifying the two distinct concepts of geometries and pictures, geometric transformations and restrictive transformations are defined for each.

All the primitives are carefully selected to be sound. CHAPTER 5. 2 Representation of Visualizing Nets This section introduces V-ezpre~sions, which are the pNucleus representation of a visualizing net. The component transformations of a visualizing net are realized by Lisp functions. The two geometry transformations, geometric and restrictive~ are invoked by the following expressions, respectively: (*gtran*geom ' ') (*rtran*geom ' < r e s t r i c t i v e geometry> ') .

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