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

$$[0,\infty)$$

$$[r_{min},r_{max}]$$

$$r = r_{min} e^{x \log\bigg(\frac{r_{max}}{r_{min} / (N - 1)} \bigg)},$$

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

$$[-1,1]$$

$$[r_{min},r_{max}]$$

$$r_i = \frac{(1+x_i)^m (r_{max} - r_{min})} { 2^m (1 - 2^m + r_{max} - r_{min}) - (1 + x_i)^m (r_{max} - r_{min} - 2^m )} + r_{min}$$