Lesson 31 · The eight mask patterns - Build a QR Code Encoder

The eight mask patterns

A raw data pattern can have large blank areas or runs that confuse a scanner, so QR flips modules in a regular pattern to break them up. There are eight such mask patterns; today you write all eight conditions and apply one to the data region.

The goal

Define the eight mask conditions and apply a mask by flipping data modules where its condition holds.

Start here - the target

TO DO

Scenario: Masks flip only the data region

Giventhe eight mask conditions indexed 0-7, each a formula over a module's row and column

Whenthe conditions are evaluated at sample coordinates

Thenmask 0 ((row+col) mod 2 == 0) is true at (0,0) and false at (0,1); mask 1 (row mod 2 == 0) is true at (0,5) and false at (1,5); mask 6 (((row*col) mod 2 + (row*col) mod 3) == 0) is true at (2,3) and false at (5,3)

Andapplying a mask flips (dark to light and back) every data module whose condition is true, and never touches a function or reserved module

Background

The unmasked data grid is correct but often ugly: a stretch of zeros makes a big light patch, and a scanner can lose its place in it. A mask fixes this by flipping modules in a fixed geometric pattern, breaking up runs and balancing dark and light. There are exactly eight masks, numbered 0 to 7, each defined by a boolean condition over a module’s coordinates. Where the condition is true, that module is inverted.

Crucially, a mask applies only to data modules - finder patterns, timing, the dark module, and the reserved format area are never masked, because their fixed shapes must survive. So applyMask walks the placeable modules only and flips those whose condition holds. Masking is reversible (flip twice and you are back), which is exactly how a scanner undoes it after reading the mask number from the format information. You do not pick a mask yet: the next four lessons build the scoring that decides which of the eight leaves the cleanest symbol.

Make it work

// Condition is true -> flip that data module.
var masks = []func(r, c int) bool{
  func(r, c int) bool { return (r+c)%2 == 0 },
  func(r, c int) bool { return r%2 == 0 },
  func(r, c int) bool { return c%3 == 0 },
  func(r, c int) bool { return (r+c)%3 == 0 },
  func(r, c int) bool { return (r/2+c/3)%2 == 0 },
  func(r, c int) bool { return (r*c)%2+(r*c)%3 == 0 },
  func(r, c int) bool { return ((r*c)%2+(r*c)%3)%2 == 0 },
  func(r, c int) bool { return ((r+c)%2+(r*c)%3)%2 == 0 },
}

CheckpointDONE

You can apply any of the eight masks to the data region. Commit and stop here.