CAD Geometry: Point-in-Polygon Ray Casting Algorithm

In computer-aided mechanical design (CAD/CAM), determine whether a 2D query point `(px, py)` lies strictly inside a non-self-intersecting closed polygon using the **Ray Casting Algorithm (Crossing Number Rule)**. Cast a horizontal ray extending from the point toward $+\infty$. Count how many polygon edges intersect the ray: - If the intersection count is odd, the point is inside (`true`). - If even, the point is outside (`false`). ### Input Format - First line contains two floats: `px py` (query point coordinates). - Second line contains an integer `n` (number of polygon vertices). - The next `n` lines each contain two floats: `x y` (vertex coordinates in counter-clockwise order). ### Output Format - Print `true` or `false`. ### Constraints - `3 <= n <= 1000` - `-1000.0 <= x, y, px, py <= 1000.0`