PolyMap Attributes

IterInverse

Provide an iterative inverse transformation? (bool)

This attribute indicates whether the inverse transformation of the uninverted PolyMap should be implemented via an iterative Newton-Raphson approximation that uses the forward transformation to transform candidate input positions until an output position is found which is close to the required output position. False by default.

Note, the term "inverse transformation" here refers to the inverse transformation of the original PolyMap, ignoring any subsequent inversions. Also, "input" and "output" refer to the inputs and outputs of the original PolyMap.

Note: if IterInverse is true then the iterative inverse is used by applyInverse, even if inverse coefficients are also supplied.

The NIterInverse and TolInverse attributes provide parameters that control the behaviour of the inverse approximation method.

The iterative inverse returns nan axis values at positions for which the inverse transformation is undefined. For instance, if the forward transformation is y = x*x, the iterative inverse will return x = nan at y = -1. If the inverse transformation is multiply defined, the position returned by the iterative inverse will be the position of the solution that is closest to the supplied position. For instance, using the above example, y = x*x, the iterative inverse will return x = +2 at y = 4, because x = +2 is the closest solution to 4 (the other solution is x = -2).

NIterInverse

Maximum number of iterations for the iterative inverse transformation. (int)

This attribute controls the iterative inverse transformation used if the IterInverse attribute is non-zero.

Its value gives the maximum number of iterations of the Newton-Raphson algorithm to be used for each transformed position. The default value is 4. See also attribute TolInverse.

TolInverse

Target relative error for the iterative inverse transformation. (double)

This attribute controls the iterative inverse transformation used if the IterInverse attribute is non-zero.

Its value gives the target relative error in teh axis values of each transformed position. Further iterations will be performed until the target relative error is reached, or the maximum number of iterations given by attribute NIterInverse is reached.

The default value is 1.0E-6.