Prism

Instructions

Before activating the laser array, you must predict the exact order in which crystals will be hit, identified by their sample IDs.

Example Test Case

Consider this crystal array configuration:

{
  "start": { "x": 0, "y": 0, "angle": 0 },
  "prisms": [
    { "id": 1, "x": 10, "y": 10, "angle": -90 },
    { "id": 2, "x": 10, "y": 0, "angle": 90 },
    { "id": 3, "x": 30, "y": 10, "angle": 45 },
    { "id": 4, "x": 20, "y": 0, "angle": 0 }
  ]
}

What's Happening

The laser starts at the origin (0, 0) and fires horizontally to the right at angle 0°. Here's the step-by-step beam path:

Step 1: The beam travels along the x-axis (y = 0) and first encounters Crystal #2 at position (10, 0). This crystal has a refraction angle of 90°, which means it bends the beam perpendicular to its current path. The beam, originally traveling at 0°, is now redirected to 90° (straight up).

Step 2: The beam now travels vertically upward from position (10, 0) and strikes Crystal #1 at position (10, 10). This crystal has a refraction angle of -90°, bending the beam by -90° relative to its current direction. The beam was traveling at 90°, so after refraction it's now at 0° (90° + (-90°) = 0°), traveling horizontally to the right again.

Step 3: From position (10, 10), the beam travels horizontally and encounters Crystal #3 at position (30, 10). This crystal refracts the beam by 45°, changing its direction to 45°. The beam continues into empty space beyond the array.

---

Source

FraSanga