Diskussion:Exploring a Design Space for Patterns and Tilings Competition 2015
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is it possible to make a overlap measure that can be computed given the result pattern image and the command list without the m intermediate steps?
Given is a pattern image $P with width $w_P and height $h_P; the number of pixel in $P is $wh_P = $w_P * $h_P and the number of non-transparent pixel in $P is $p; Gap Measure: number of transparent pixel in an image: here $gap_P;
Case 1: Given is one prototile in an image $S (with width $w_S and height $h_S) with transparent background; the number of pixel in $S is $wh_S = $w_S * $h_S and the number of non-transparent pixel in $S is $s;
The given command list consists of m 5-tuple which means that $S is composed m times over the pattern image with results in a composing list @C_S = ($S | j = 1, …, m).
The overlap after m composings is the sum of the non-transparent pixels of all elements in @C_S (which is m * $s because all elements in @C_S are the same image $S) minus the number of non-transparent pixel in $P after the m composings ($p_m): $overlap_m = m * $s - $p_m
Case 2: Given are n prototiles in images @S = ($S_i | i = 1, …, n) with transparent background; the number of pixel in $S_i is $wh_S_i = $w_S_i * $h_S_i and the number of non-transparent pixel in $S is $s_i;
The given command list consists of m 5-tuple which means that a selection of different elements of @S are composed over the pattern image and every image in @S is at least used one time. The composing list @C_S = ($S_i_j | j = 1, …, m) respresents one possible combination of such a composing pipeline.
The overlap after m composings is the sum of the non-transparent pixels of all elements in @C_S ($s_j, j = 1, …, m) minus the number of non-transparent pixel in $P after the m composings ($p_m): $overlap_m = Σj=1->m $s_j - $p_m.
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