147 | | Any value of θ,,ij,, which is not plus or minus 90 degrees indicates that shearing parallel to the i axis is required. This produces diamond shaped (non-rectangular) pixels in the output. In this section, we calculate a value for k,,i,, from the specific value of θ,,ij,,. We do this using the configuration in the following diagram: |

| 147 | Any value of θ,,ij,, which is not plus or minus 90 degrees indicates that shearing parallel to the i axis is required. This produces diamond shaped (non-rectangular) pixels in the output. In this section, we calculate a value for k,,i,, from the provided value for θ,,ij,,. Note that since the rotation of the entire grid does not affect the angle between the two basis vectors (because they are both rotated by the same amount), we solve for k,,i,, in the non-rotated system. |

| 148 | |

| 149 | The '''j,,b,,''' basis vector is represented as follows: |

| 150 | |

| 151 | [[Image(basisvector_j.png)]] |

| 152 | |

| 153 | Illustrated, the '''j,,b,,''' basis vector looks like this: |