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- is the acute angle between two adjacent sides of the rhombus
- one side lies along the positive -axis, with a vertex at the origin
- the small rhombuses are numbered from the origin, in rows, so that R1 - R50 lie along the -axis.
Then let's suppose that the point lies in the rhombus which is in the column and the row. Then, with the assumption I've made above, this is rhombus number . It now remains to find the values of and .
Next, you will need to make a decision about what to do if lies on one or more of the edges of one of the small rhombuses. In my working below, I have in this case taken the rhombus to the right and/or above the point.
In the diagram, then, you will see that the rhombus containing is bounded by four lines, whose equations I have shown. The point therefore satisfies the following inequalities:The values of and that satisfy these inequalities can be expressed using the floor function, where , is the largest integer less than or equal to . Then (if my working is correct - I have checked it with some simple data, but you need to check this with some data of your own) we get: