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Figure 3
This an example of a one-boundary tunneled mirrored boundary distance calculation. As with Fig. 1[link] the 24 reflections are not shown. Both points p1 and p2 are Selling reduced. The image is the three-dimensional, all-negative octant of the three [{\bf S^6}] axes, s1, s3, and s5; the reduction is done along the s1 axis, and s3 and s5 are the two scalars that will be interchanged. The points are shown above the s3/s5 plane, with their projections onto that plane marked with a circled `X'. The Euclidean distance from p1 to p2 is shown as a dotted line. Let mp be the mirror point on the boundary going from p1 to p2 via the boundary. Then the shortest distance from p1 to mp to p2 is also shown as a dotted line. The transformed image of mp is mpx. The distance between p1 and mp is the same as the distance between a transformed p1 and mpx. There is a no-cost tunnel from mp to mpx. So the total alternative distance for this case is the distance between p1 and mp plus the distance from mpx to p2 (shown as a dashed line).

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ISSN: 2053-2733
Volume 75| Part 3| May 2019| Pages 593-599
https://doi.org/10.1107/S2053273319002729
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