Symmetric tags

A method of generating an interface surface, including the steps of:

• receiving, in a printer, user data;
• generating machine-readable coded data incorporating the user data, the machine-readable coded data being arranged in accordance with a layout having mirror symmetry and n-fold rotational symmetry, where n is at least two, the layout including n identical first sub-layouts rotated 1/n revolutions apart about a center of rotational symmetry of the layout, the layout further including n identical second sub-layouts rotated 1/n revolutions apart about a center of rotational symmetry of the layout, each second sub-layout being a reflection of a corresponding one of the first sub-layouts, the coded data being arranged in accordance with each sub-layout including rotation-indicating data that distinguishes the rotation of that sub-layout from the rotation of at least one other sub-layout within the layout, the coded data being arranged in accordance with each sub-layout further including reflection-indicating data that distinguishes the reflection of that sub-layout from the reflection of its corresponding reflected sub-layout;
• and
• printing the coded data onto a substrate.

A method of using a sensing device to read machine-readable coded data, the machine-readable coded data being disposed on or in a substrate in accordance with a layout having mirror symmetry and n-fold rotational symmetry, where n is at least two, the layout including n identical first sub-layouts rotated 1/n revolutions apart about a center of rotational symmetry of the layout, the layout further including n identical second sub-layouts rotated 1/n revolutions apart about a center of rotational symmetry of the layout, each second sub-layout being a reflection of a corresponding one of the first sub-layouts, the coded data disposed in accordance with each sub-layout including rotation-indicating data that distinguishes the rotation of that sub-layout from the rotation of at least one other sub-layout within the layout, the coded data disposed in accordance with each sub-layout further including reflection-indicating data that distinguishes the reflection of that sub-layout from the reflection of its corresponding reflected sub-layout,

• the method including the steps of:
• (a) reading, using the sensing device, the coded data of the layout;
• (b) decoding the coded data of at least one of the sub-layouts of the layout, thereby determining at least the rotation-indicating data and reflection-indicating data of that sub-layout;
• and
• (c) using the rotation-indicating data and reflection-indicating data to interpret the meaning of at least some of the coded data.