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geometry_polynomial index $a_0$ $a_1$ ...$a_n$ x_0 x_1 y_0 y_1 tolerance

This data item defines a polynomial in space if 2D or 3D. Other data items can check if nodes are located on this geometry. In 2D it is the curve $y = a_0 + a_1 x + a_2 x^2 + \ldots $. In 3D it is the surface $z = a_0 + a_1 x + a_2 y + a_3 x^2 + a_4 xy +
a_5 y^2 + a_6 x^3 + a_7 x^2 y + a_8 x y^2 + a_9 y^3 + \ldots $. In 2D $x_0-x_1$ defines the domain of $x$. In 3D $x_0-x_1$ defines the domain of $x$ and $y_0-y_1$ defines the domain of $y$. All node with a distance (that is the $y$-distance in 2D or the $z$-distance in 3D) not more than tolerance are considered to be part of the polynomial.

tochnog 2001-09-02