/*
Axis‑aligned rectangles are simply rectangles whose edges are parallel to the
coordinate axes — meaning their sides are horizontal and vertical.
That single assumption makes the overlap test dramatically simpler and faster.
*/
/*
Rectangle overlap detection (axis-aligned)
Each rectangle is defined by:
- x, y : coordinates of its top-left corner
- w, h : width and height
Two rectangles DO NOT overlap if any separating condition is true:
- One is completely to the left of the other
- One is completely to the right of the other
- One is completely above the other
- One is completely below the other
Otherwise, they overlap.
This is the standard O(1) test for axis-aligned rectangles.
*/
struct Rect {
var x: Double // top-left X
var y: Double // top-left Y
var w: Double // width
var h: Double // height
}
/*
Returns true if rectangles A and B overlap.
*/
func rectanglesOverlap(_ A: Rect, _ B: Rect) -> Bool {
// Compute edges of A
let A_left: Double = A.x
let A_right: Double = A.x + A.w
let A_top: Double = A.y
let A_bottom: Double = A.y + A.h
// Compute edges of B
let B_left: Double = B.x
let B_right: Double = B.x + B.w
let B_top: Double = B.y
let B_bottom: Double = B.y + B.h
// Separating conditions:
if A_right <= B_left { return false } // A is left of B
if B_right <= A_left { return false } // B is left of A
if A_bottom <= B_top { return false } // A is above B
if B_bottom <= A_top { return false } // B is above A
return true // Otherwise, they overlap
}
let A = Rect(x: 10, y: 10, w: 30, h: 20) // Example rectangle A
let B = Rect(x: 25, y: 15, w: 40, h: 25) // Overlaps A
let C = Rect(x: 100, y: 100, w: 10, h: 10) // Does not overlap A
print("A vs B overlap? \(rectanglesOverlap(A, B) ? "YES" : "NO")")
print("A vs C overlap? \(rectanglesOverlap(A, C) ? "YES" : "NO")")
/*
run:
A vs B overlap? YES
A vs C overlap? NO
*/
