Thursday, January 21, 2016

[cosdhdgu] Rectangular and elliptical bar codes

Create a 2D rectangular bar code format (not just square like QR).  Goal is to encode as much data as possible into arbitrary rectangular areas.  One method is simply to start with a square bar code and perform a rectangle-square dissection: https: // www . math . nmsu . edu / ~breakingaway / Lessons / R2S / R2S.html: "Consider a rectangle ABDC with sides a and b such that a < b < 2*a. We show one way to cut it into three pieces and rearrange them into a square.  Compute s = sqrt(a*b). Open a compass to length s, put the center at corner A of the rectangle, and mark point X on side CD. The distance AX is s. Draw the line AX. Draw another line (using an index card) BY, perpendicular to AX. Cut out the rectangle ABDC, cut the line AX, and cut the line YB. In order to get a square in slanted position, move the left triangle to the right, and move the top triangle to the bottom right. Remark: Notice that the length BY is also s."

Previously, multiple QR codes on a page.

Create a 2D elliptical bar code format, fitting data into the interior of an ellipse.  Or superellipse.  The motivation is, the corners of a physical object (e.g., a card) with a barcode on it are more likely to encounter wear and destruction.  QR codes are especially vulnerable because their key alignment symbols are in the corners.

Alternatively, design a rectangular bar code format that assumes in its error model that bits written near the corners are less reliable than bits elsewhere.

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