map_boy_to_street.md

Map Boy To Kids Room

• R135

[ [ -0.707106781187, 0.707106781187,  0 ]
  [ -0.707106781187, -0.707106781187, 0 ]
  [        0,               0,        1 ] ]

• T4,2

[ [ 1, 0, 0 ]
  [ 0, 1, 0 ]
  [ 4, 2, 1 ] ]

Map Kids Room To House

• R−90

[ [ 0, -1, 0 ]
  [ 1, 0,  0 ]
  [ 0, 0,  1 ] ]

• S½,½

[ [ 0.5,  0,  0 ]
  [  0,  0.5, 0 ]
  [  0,   0,  1 ] ]

• T2,4

[ [ 1, 0, 0 ]
  [ 0, 1, 0 ]
  [ 2, 4, 1 ] ]

Map House To Street

• T0,−6

[ [ 1,  0,  0 ]
  [ 0,  1,  0 ]
  [ 0, -6, 1 ] ]

• S1,−1

[ [ 1, 0,  0 ]
  [ 0, -1, 0 ]
  [ 0, 0,  1 ] ]

• S⅔,⅔

[ [ 0.666666666667,        0,        0 ]
  [       0,         0.666666666667, 0 ]
  [       0,               0,        1 ] ]

Result

Mb→s = Ls→b = Lk→b Lh→k Ls→h
      = (R135 T4,2) (R−90 S½,½ T2,4) (T0,−6 S1,−1 S⅔,⅔)
      = [ [ 0.2357,  -0.2357, 0 ]
          [ -0.2357, -0.2357, 0 ]
          [    2,    2.6667,  1 ] ]

This follows row-vector convention. Transpose and reverse the order of multiplication to get the same result in column-vector convention.