This interpolation algorithm, the so called "thin plate spline" (TPS), was borrowed from material physics and was introduced to morphometrics by Fred Bookstein. While Thompson's deformation grids where drawn by hand, the geometric morphometric toolkit provides a formal algorithm to calculate such grids based on homologous landmark configurations. D'Arcy Thompson's Cartesian transformation of a human skull to the skull of a chimpanzee. From Dürer (1528).ĭ'Arcy Thompson revisits this approach with his "Cartesian transformations", which emphasize not the single specimen's geometry but rather on the mapping function from one form onto others. One head with a standard grid (left) and three transformations onto other facial "types". Deformation grids illustrate and formalize shape differences between geometrical objects - an idea dating back to the Renaissance when Albrecht Dürer described the variation of human faces in his 1528 book "Vier Bücher von menschlicher Proportion".
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