program RectangleOverlap;
{
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.
}
type
Rect = record
x: Double; // top-left X
y: Double; // top-left Y
w: Double; // width
h: Double; // height
end;
{
Returns true if rectangles A and B overlap.
}
function rectanglesOverlap(const A, B: Rect): Boolean;
var
A_left, A_right, A_top, A_bottom: Double;
B_left, B_right, B_top, B_bottom: Double;
begin
// Compute edges of A
A_left := A.x;
A_right := A.x + A.w;
A_top := A.y;
A_bottom := A.y + A.h;
// Compute edges of B
B_left := B.x;
B_right := B.x + B.w;
B_top := B.y;
B_bottom := B.y + B.h;
// Separating conditions:
if (A_right <= B_left) then begin
rectanglesOverlap := False; // A is left of B
Exit;
end;
if (B_right <= A_left) then begin
rectanglesOverlap := False; // B is left of A
Exit;
end;
if (A_bottom <= B_top) then begin
rectanglesOverlap := False; // A is above B
Exit;
end;
if (B_bottom <= A_top) then begin
rectanglesOverlap := False; // B is above A
Exit;
end;
rectanglesOverlap := True; // Otherwise, they overlap
end;
var
A, B, C: Rect;
begin
A.x := 10; A.y := 10; A.w := 30; A.h := 20; // Example rectangle A
B.x := 25; B.y := 15; B.w := 40; B.h := 25; // Overlaps A
C.x := 100; C.y := 100; C.w := 10; C.h := 10; // Does not overlap A
if rectanglesOverlap(A, B) then
WriteLn('A vs B overlap? YES')
else
WriteLn('A vs B overlap? NO');
if rectanglesOverlap(A, C) then
WriteLn('A vs C overlap? YES')
else
WriteLn('A vs C overlap? NO');
end.
{
run:
A vs B overlap? YES
A vs C overlap? NO
}
