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

By Tamiya Onodera

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5. 3 . I))) *A ,(*mat*seal . 2)) . 8 . 2))) . 5. The picture referred to as *A was defined within [0, 1] × [0, 1]. 1), accordingly. 2 Pictorlalizing a Lattice Geometry When a supplied geometry is a lattice geometry, the returned P-expression is considered to represent the picture constructed by pasting the pattern to each cell of a lattice geometry. This pasting is done through affine transformations, each of which maps the pa~ern recLangle to a parallelogram of a ceil. The default pattern rectangle is [0: 1] x [0, 1].

The requirement for soundness is relevant to the implementability discussed in the next section. If we imitate the title of the famous book on algorithms and data structures by N. " The organization of its visualizing net is variable and is not dependent on a primitive. This orthogonality of a visual net and primitives makes a graphical nucleus open: adding a new geometric or pictorial primitive causes no problem. The generality of attribute rendering in a graphical nucleus, which is brought about by regarding attribute renditions as pictorializing transformations in a unified manner, make it much more descriptive than conventional systems.

We regard the values of these attributes as collectively specifying one picture, which is one input to the pictorializing transformation. Together with the other input of the line geometry, the pictoriMizing transformation first constructs a replication: it generates a number of nonsingular affine transformations to 'paste' thz selected picture along that geometry. It then transforms the pictlzre by means of this constructed replication. Note that our formalization of attribute rendering is at the level of abstraction where it is unnecessary to describe such details as the set of attributes of a graphical primitive.

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