From 00a42f3d852184e34a4372b95b2339ba2bccaf26 Mon Sep 17 00:00:00 2001
From: Giulio Camuffo <giuliocamuffo@gmail.com>
Date: Wed, 9 Jan 2013 18:27:07 +0100
Subject: [PATCH] MATH: Fix Line2d intersection functions. Fix #682

---
 math/line2d.cpp | 28 ++++++++++++++--------------
 math/rect2d.cpp | 12 ++++++++++--
 2 files changed, 24 insertions(+), 16 deletions(-)

diff --git a/math/line2d.cpp b/math/line2d.cpp
index 89151149ea4..fcc875a9f38 100644
--- a/math/line2d.cpp
+++ b/math/line2d.cpp
@@ -32,8 +32,13 @@ Line2d::Line2d() :
 
 Line2d::Line2d(const Vector2d &direction, const Vector2d &point) {
 	Vector2d d = direction;
-	_a = d.getY() / d.getX();
-	_b = -1;
+	if (fabsf(d.getX()) > 0.0001f) {
+		_a = d.getY() / d.getX();
+		_b = -1;
+	} else {
+		_a = 1;
+		_b = 0;
+	}
 
 	if (_b == 0) {
 		_c = -point.getX();
@@ -76,23 +81,18 @@ bool Line2d::intersectsLine(const Line2d &line, Vector2d *pos) const {
 
 	float x, y;
 
-	if (d * b - a * e == 0 || a == 0) {
+	const float det = a * e - b * d;
+
+	if (fabsf(det) < 0.0001f) {
 		return false;
 	}
 
-	if (!pos) {
-		return true;
-	}
+	x = (-c * e + b * f) / det;
+	y = (-a * f + c * d) / det;
 
-	/*
-	 * {ax + by + c = 0 -> x = -(by + c) / a
-	 * {dx + ey + f = 0 -> y = (-dc + af) / (db - ae)
-	 */
+	if (pos)
+		*pos = Vector2d(x, y);
 
-	y = (-d * c + a * f) / (d * b - a * e);
-	x = -(b * y + c) / a;
-
-	*pos = Vector2d(x, y);
 	return true;
 }
 
diff --git a/math/rect2d.cpp b/math/rect2d.cpp
index 23cf34c80a2..4ce9b54091b 100644
--- a/math/rect2d.cpp
+++ b/math/rect2d.cpp
@@ -129,9 +129,17 @@ bool Rect2d::intersectsCircle(const Vector2d &center, float radius) const {
 	}
 }
 
+inline bool le(float a, float b) {
+	return (a < b || (fabsf(a - b) < 0.0001f));
+}
+
+inline bool ge(float a, float b) {
+	return (a > b || (fabsf(a - b) < 0.0001f));
+}
+
 bool Rect2d::containsPoint(const Vector2d &point) const {
-	return (point.getX() >= _topLeft.getX() && point.getX() <= _bottomRight.getX() &&
-	        point.getY() >= _topLeft.getY() && point.getY() <= _bottomRight.getY());
+	return ge(point.getX(), _topLeft.getX()) && le(point.getX(), _bottomRight.getX()) &&
+	       ge(point.getY(), _topLeft.getY()) && le(point.getY(), _bottomRight.getY());
 }
 
 Vector2d Rect2d::getCenter() const {