Abstract
AbstractThe 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.
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