** Introduction **

The interpolation algorithm, which I called **RGR** (**R**obust **G**eometric **R**esampling), is based on the same approach as SRALG.
Instead of searching for approximating functions, the assumed function would be approximated by a set of values calculated iteratively.
When enough values have been calculated to achieve the desired resulting set, the process can be terminated.
On each iteration it calculates the values of an interpolating vector-function that is defined between each pair of neighboring data points.
To calculate each vector I use a single **linear** equation that is representing a very simple geometric construction.
The algorithm has one parameter **k** controlling the shape of the resulting curve (or surface in the two-dimensional case).
Similar to GRI, Robust Geometric Resampling was intended mainly for image scaling. Like any other method (linear, cubic etc.) it could be applied first in one direction, and then again in the other direction.
In this regular grid case RGR calculation goes more efficient and every one of the iterations actually realizes an upsampling with the scale factor 2.

**How does it work? **

**Demo on image**

On the pictures below you can see the results of biRGR (bidirectional version of RGR) working on image compared with the standard solutions. They are very similar to the results of bicubic.

## Cut #1 | |||

## linear |
## cubic |
## RGR |
## lanczos3 |

## Cut #2 | |||

## linear |
## cubic |
## RGR |
## lanczos3 |

## Cut #3 | |||

## linear |
## cubic |
## RGR |
## lanczos3 |

© Dmitry Grilikhes, 2013.