Parking Rectangle Algorithm Step-by-Step

Step 1: Input Parameters

Starting with:

v = [x, y] (street center)
θ = angle from north
B = [K, H, W] (dimensions)

Step 2: Generate Base Rectangle

Applying vertex template matrix:

M = [
  [1, 0, 0],
  [1, 1, 0],
  [1, 1, 1],
  [1, 0, 1]
]

Step 3: Apply Rotation

Rotating by angle θ using:

R(θ) = [
  [cos(θ), -sin(θ)],
  [sin(θ), cos(θ)]
]

Step 4: Convert to Geographic Coordinates

Applying normalization matrix G:

G = [
  [g_lat, 0],
  [0, g_lon]
]

Step 5: Generate Final Rectangles

Creating symmetric rectangles R₁ and R₂