A Formal Model of Visualization in Computer Graphics Systems - download pdf or read online

By Tamiya Onodera

ISBN-10: 3540523952

ISBN-13: 9783540523956

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Example text

We also present the proofs, which is based upon induction on their structures, that is, on the production rules generating them. Claim 1 The geometry in a visualizing net is in the form of N~,(g,), ~here ~, e rig. i We prove the claim by induction on the structure of a geometry. Proof: STEPI: The arbitrary geometry generated by a geometric primitive takes the specified form. STEP2(A): Suppose the production rule G ---* t g ( M G ) is applied. ~(Ni ~,(g,)) =Ni ~(~,(9,)) (Prop. 1) =Ni ~,(m*(~,)) (soundness of ~) STEP2(B): Suppose the production rule G --* t , ( G G ) is applied.

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.

This modeling results from the careful reading of the corresponding part of the GKS document. The first transformation takes as a pattern the picture specified by the interior style index and replicates it along the lattice. The restrictive picture transformation then cfips the lattice against the geometry of the region specified by a point sequence. Following this, three geometric transformations and the additional restrictive transformation are performed in order. All the transformations occur in a sequence of picture transformations.

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


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