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1 . 8 . 9))) The function *matrix*rot is a utility function to generate the transformation matrix for a rotation through the angle specified in its parameter. 4. P I C T U R E S AND PICTURE T R A N S F O R M A T I O N S ( * l i n e (0 . 0) ( - 0 . 1 . 9 53 . 8)) The geometry is validly rotated by rotating each point in the sequence, because of the sound property o f * l i n e . [] The restrictive geometry transformation *rtran*geom is realized to return a G-expression simply by appending the restrictive geometry to a given G-expresslon.

Together with this, Claim 2 shows that we have to implement a procedure that rasterizes a picture whose form is (id I ~,(g,))-(~(g))(~, ~ Hg,~ c II~). 4. OPTIMIZATION CONSIDERATIONS 47 The restrictive transformations also remain here. 4 Optimization Considerations In this section we discuss how to simplify or optimize an implementation of a graphical nucleus. The two procedures in the previous section can be simplified when we take advantage of the fact that, in most graphics systems, not all kinds of geometry are necessarily used to specify a restrictive transformation.

G-expressions will be described in the next section. The two picture transformations, geometric and restrictive, are represented by the following expressions, respectively: (*gtran*pict ' ' < p i c t u r e > ) (*rtran*pict ' ' < p i c t u r e > ) . 4. The other two transformations are as follows: (*pict*tran ' ' ') (*pict*sum {' }) The invocation of plctorlallzing transformation replicates the pattern given by < p i c t u r e name> along the geometry; the way of replicating is controlled by the control list.

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