The scaling behavior of viewing transformations

Author

Abi-Ezzi, Salim S. ; Shirman, Leon A.

Author_Institution

SunSoft, Mountain View, CA, USA

Volume

13

Issue

3

fYear

1993

fDate

5/1/1993 12:00:00 AM

Firstpage

48

Lastpage

54

Abstract

Using formal analysis of parallel and perspective viewing transformation behavior, closed-form form expressions are obtained for immediate evaluation of maximum, minimum, and average scales at a given point in space. While these are constant for parallel transformations, they vary from point to point for perspective transformations. The average scale of a transformation is expressed in ways useful for heuristic computations. The expressions indicate how transformations perform in general without providing guarantees. It is shown that these results apply to the dynamic tessellation of curved surfaces. The maximum scale of a transformation across a bounded region can guarantee that one will meet postviewing approximation thresholds specified in display coordinates, based on derivative bounds precomputed in modeling coordinates.<>

Keywords

computational geometry; computer graphics; bounded region; closed-form form expressions; curved surfaces; derivative bounds; display coordinates; dynamic tessellation; formal analysis; heuristic computations; perspective transformations; scaling behavior; viewing transformations; Computer displays; Equations; Geometry; Graphics; Lighting control; Reduced instruction set computing; Rendering (computer graphics); Sampling methods; Sparse matrices; Very large scale integration;

fLanguage

English

Journal_Title

Computer Graphics and Applications, IEEE

Publisher

ieee

ISSN

0272-1716

Type

jour

DOI

10.1109/38.210491

Filename

210491