Open AccessTRANSFORMATIONS WHICH RENDER CURVES PARALLEL 1
Author(s) -
Levine Michael V.
Publication year - 1968
Publication title -
ets research bulletin series
Language(s) - English
Resource type - Journals
eISSN - 2333-8504
pISSN - 0424-6144
DOI - 10.1002/j.2333-8504.1968.tb00380.x
Subject(s) - rendering (computer graphics) , family of curves , transformation (genetics) , mathematics , set (abstract data type) , computer science , geometry , artificial intelligence , biochemistry , chemistry , gene , programming language
Eight examples are given to indicate the desirability of having a general theory treating sets of curves which can be transformed into parallel curves. With this theory it is shown that a set of curves can be rendered parallel if and only if every pair of functions in the completion of a particular group associated with the curves is uncrossed. Under general conditions any two transformations rendering a set of curves parallel are related by a linear transformation. Methods for calculating transformations are proposed. Several structural properties of sets of curves which can be rendered parallel are proven.