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Notes on the Mathematics of the PHIGS Viewing Pipeline
Author(s) -
Krammer Gergely
Publication year - 1989
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.1989.tb00488.x
Subject(s) - conic section , clipping (morphology) , transformation matrix , homogeneous coordinates , computer science , transformation (genetics) , representation (politics) , mathematics , projective space , computer graphics (images) , pure mathematics , projective test , geometry , philosophy , linguistics , physics , biochemistry , kinematics , chemistry , classical mechanics , politics , political science , law , gene
It is well known that homogeneous linear matrix transformations of the projective space may be efficiently used for the representation and the execution of common geometrical transformations but the general class of such transformations include also matrices which may cause numerical problems by transforming certain finite geometrical objects to infinity Different methods have been developed for handling such cases and this paper presents a new one called‘UW clipping’which is based on some interesting properties of projective transformations. Furthermore the paper introduces die concept of ‘conic sectors’ as a generalisation to half‐planes and halfspaces respectively, with the invariance property that such sectors are mapped onto other such sectors by projective transformations, and thus enable the transformation of clipping halfplanes and halfspaces. Finally the possibility of transforming die rectangular clipping box into the object space is investigated.