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An analysis of a cubic isoparametric transformation
Author(s) -
Woodford G.,
Mitchell A. R.,
McLeod R.
Publication year - 1978
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620121009
Subject(s) - mathematics , transformation (genetics) , boundary (topology) , jacobian matrix and determinant , point (geometry) , variety (cybernetics) , geometry , mathematical analysis , pure mathematics , biochemistry , chemistry , gene , statistics
The general nine point isoparametric transformation is analysed with respect to a triangle with two straight sides and one curved side. Point placements are determined on the curved side which ensure that the Jacobian of the transformation remains positive inside and on the boundary of the triangle. Special cases of the transformation are considered which lead to implied curves of the form of symmetric cubics, parabolas, and explicit cubics respectively, thus enabling isoparametric transformations to match a variety of boundary shapes.