From: Ben Harris <bjh21@bjh21.me.uk>
Date: Sun, 22 Mar 2020 00:26:27 +0000 (+0000)
Subject: NOTES on good bitmap sizes.  Conclusion: 20, 60, and 100 are good.
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NOTES on good bitmap sizes.  Conclusion: 20, 60, and 100 are good.
---

diff --git a/NOTES b/NOTES
index fce711c..fbfa9a1 100644
--- a/NOTES
+++ b/NOTES
@@ -498,3 +498,32 @@ http://www.twardoch.com/download/polishhowto/
 ẞ:
 https://typography.guru/journal/capital-sharp-s-designs/
 https://typography.guru/journal/how-to-draw-a-capital-sharp-s-r18/
+
+Good bitmap sizes for Bedstead fulfill two characteristics:
+
+1: An integer number of output pixels per Bedstead pixel (so
+horizontal and vertical lines work).
+
+2: Edges of diagonals don't pass through pixel centres (so no doubt
+whether any pixel is in or out).
+
+The first requires that the height be 10n for integer n.
+
+The second requires that the height _not_ be 40n for integer n.
+
+So good sizes are 10, 20, 30, 50, 60, 70, 90, 100, etc.
+
+The best sizes would be those where the area of a (long) diagonal line
+is correct.  The outline version has an area of 1 - (0.25^2) + (0.75^2) =
+1.5/pixel.  Others:
+
+size | area/diagonal pixel
+-----|--------------------
+10   | 1
+20   | 1+1/2 = 1.5
+30   | 1+6/9 = 1.67
+50   | 1+10/25 = 1.4
+60   | 1+18/36 = 1.5
+70   | 1+28/49 = 1.57
+90   | 1+36/81 = 1.44
+100  | 1+50/100 = 1.5