Radial Transformations

These one-dimensional grids can be transformed to other kinds of intervals using the radial transform module.

Transform	Domain	Co-Domain	\(r(x)\)
BeckeRTransform	\([-1,1]\)	\([r_{min},\infty)\)	\(r_i = R \frac{1 + x_i}{1 - x_i} + r_{min}\)
LinearFiniteRTransform	\([-1,1]\)	\([r_{min},r_{max}]\)	\(r_i = \frac{r_{max} - r_{min}}{2} (1 + x_i) + r_{min}\)
InverseRTransform	Co-Domain	Domain	\(x_i(r_i)\)
IdentityRTransform	Domain	Domain	\(x_i\)
LinearInfiniteRTransform	\([0,\infty)\)	\([r_{min},r_{max})\)	\(r_i = \frac{r_{max} - r_{min}}{N - 1} x_i + r_{min}\)
ExpRTransform	\([0,\infty)\)	\([r_{min},r_{max}]\)	\(r = r_{min} e^{x \log\left(\frac{r_{max}}{r_{min}} / (N - 1)\right)}\)
PowerRTransform	\([0,\infty)\)	\([r_{min},r_{max}]\)	\(r = r_{min} (x + 1)^{\frac{\log(r_{max}) - \log(r_{min})}{N}}\)
HyperbolicRTransform	\([0,\infty)\)	\([0,\infty)\)	\(r_i = \frac{a x_i}{1 - bx_i}\)
MultiExpRTransform	\([-1,1]\)	\([r_{min},\infty)\)	\(r_i = -R \log\left(\frac{x_i + 1}{2}\right) + r_{min}\)
KnowlesRTransform	\([-1,1]\)	\([r_{min},\infty)\)	\(r_i = r_{min} - R \log\left(1 - 2^{-k}(x_i + 1)^k\right)\)
HandyRTransform	\([-1,1]\)	\([r_{min},\infty)\)	\(r_i = R \left(\frac{1+x_i}{1-x_i}\right)^m + r_{min}\)
HandyModRTransform	\([-1,1]\)	\([r_{min},r_{max}]\)	\(r_i = \frac{(1+x_i)^m (r_{max} - r_{min})}{2^m(1 - 2^m + r_{max} - r_{min}) - (1+x_i)^m(r_{max}-r_{min}-2^m)} + r_{min}\)