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. 2019 Apr 30;75(Pt 3):593–599. doi: 10.1107/S2053273319002729

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© Lawrence C. Andrews et al. 2019

This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.

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This an example of a one-boundary tunneled mirrored boundary distance calculation. As with Fig. 1 ▸ the 24 reflections are not shown. Both points and are Selling reduced. The image is the three-dimensional, all-negative octant of the three axes, , , and ; the reduction is done along the axis, and and are the two scalars that will be interchanged. The points are shown above the / plane, with their projections onto that plane marked with a circled ‘X’. The Euclidean distance from to is shown as a dotted line. Let mp be the mirror point on the boundary going from to via the boundary. Then the shortest distance from to mp to is also shown as a dotted line. The transformed image of mp is mpx. The distance between and mp is the same as the distance between a transformed and mpx. There is a no-cost tunnel from mp to mpx. So the total alternative distance for this case is the distance between and mp plus the distance from mpx to (shown as a dashed line).

Inline graphic — This an example of a one-boundary tunneled mirrored boundary distance calculation. As with Fig. 1 ▸ the 24 reflections are not shown. Both points and are Selling reduced. The image is the three-dimensional, all-negative octant of the three axes, , , and ; the reduction is done along the axis, and and are the two scalars that will be interchanged. The points are shown above the / plane, with their projections onto that plane marked with a circled ‘X’. The Euclidean distance from to is shown as a dotted line. Let mp be the mirror point on the boundary going from to via the boundary. Then the shortest distance from to mp to is also shown as a dotted line. The transformed image of mp is mpx. The distance between and mp is the same as the distance between a transformed and mpx. There is a no-cost tunnel from mp to mpx. So the total alternative distance for this case is the distance between and mp plus the distance from mpx to (shown as a dashed line).