(Stop reading now - This is your only warning)
Ok, I'm struggling on some algebra here for a Script-fu plug-in I'm working on.
The plug-in is an automation of this rounded corners tutorial:
http://gug.sunsite.dk/tutorials/rounded-corners
Essentially, this tutorial blurs a black and white image w/90 degree corners,
and then applies levels to bring the blurred edges back to a tight curved edge
(i.e., the technique rounds all corners in a black/white image). The level
tool's black input slider and the white input slider must adjust in relation to
the blur radius, and that's where I'm stuck.
The tutorial uses levels 119 (black slider) and 135 (white slider), which works
fine for a blur radius of 20px. However, to use a different blur radius (to
achieve greater/lesser rounding of corners), the black and white input sliders
must adjust appropriately. For example, if I do a blur radius of only 10px,
111 (black) and 142 (white) give the desired result (i.e., a tight rounded
corner with all excess blur removed).
Now I did some manual sampling of different blur radius to see if I could find
a relation between the blur radius and the black/white slider settings. My
results make what looks like a y=1/x^2 type graph, but it needs a little
tweaking.
Here's my data.
Radius Black White diff (White - Black)
0 0 255 255
2 70 183 113
4 93 160 67
6102 151 49
8108 145 37
10 111 142 31
12 114 139 25
14 115 138 23
16 117 136 19
18 118 135 17
20 119 134 15
22 119 134 15
24 120 133 13
26 120 133 13
28 121 132 11
30 121 132 11
32 121 132 11
34 122 131 9
36 122 131 9
38 122 131 9
40 122 131 9
42 123 130 7
44 123 130 7
46 123 130 7
48 123 130 7
50 123 130 7
52 123 130 7
54 123 130 7
56 124 129 5
58 124 129 5
60 124 129 5
62 124 129 5
64 124 129 5
66 124 129 5
68 124 129 5
70 124 129 5
72 124 129 5
74 124 129 5
76 124 129 5
78 124 129 5
80 124 129 5
82 125 129 4
84 125 129 4
86 125 128 3
88 125 128 3
90 125 128 3
I've made a spreadsheet to graph this data (i.e., add to the confusion).
http://epierce.freeshell.org/gimp/selection_rounded_stats.gnumeric
Now if I can just figure out the relationship (i.e., equation) between the
radius (1st column) and the diff (4th column), that should be all I need to
determine what the black/white slider settings should be for all cases. My
best stab is 'diff=(1/radius^2)*255*radius'. But this produces slightly skewed
results.
Anyway, thanks for reading!
Eric P.
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