2d trilateration

Question

I am writing some code to participate in an AI challenge. The main objective for the AI challenge is to take a simulated robot and navigate it through a maze to a destinatio

Answer 1

As the Wikipedia trilateriation article describes, you compute (x,y) coordinates by successively calculating: e_x, i, e_y, d, j, x, y. You have to be familiar with vector notation, so, for example, e_x = (P2 - P1) / ‖P2 - P1‖ means:

• e_x,x = (P2_x - P1_x) / sqrt((P2_x - P1_x)² + (P2_y - P1_y)²)
• e_x,y = (P2_y - P1_y) / sqrt((P2_x - P1_x)² + (P2_y - P1_y)²)

Your data is:

• P1 = (39, 28); r₁ = 8
• P2 = (13, 39); r₂ = 11
• P3 = (16, 40); r₃ = 8

The calculation steps are:

1. e_x = (P2 - P1) / ‖P2 - P1‖
2. i = e_x(P3 - P1)
3. e_y = (P3 - P1 - i · e_x) / ‖P3 - P1 - i · e_x‖
4. d = ‖P2 - P1‖
5. j = e_y(P3 - P1)
6. x = (r₁² - r₂² + d²) / 2d
7. y = (r₁² - r₃² + i² + j²) / 2j - ix / j