Figure 9

Here we show all of the stars through all 16 pixels of the same array as Figure 8, but with 5 evenly spaced views for which the tangent is irrational, except for 0°. The total number of unique rays is thus 68. With a slight rotation all of the rays could have irrational tangents, raising the number of unique rays to T = MN ² = 5 × 16 = 80. Thus 85% of the possible rays with this star are unique, and with the rotation this would rise to 100%. Of course, with truncation of rays to staircase functions, as we have done for the sake of computational speed, many of the otherwise distinct rays end up with the same staircase function. This would not be the case if weights between 0 and 1, rather than 0 or 1 only, were used [31].