Clarify for myself how the line-point intersection check works

src/engine/collision.cpp

@@ -116,19 +116,44 @@ namespace egn{
 		return false;
 	}
 	bool check_collision(const line& l, const point& r, float epsilon){
+		/*
+		          C (the point)
+		          .
+		         /|
+		        / |
+		       /  |
+		      /   |
+		    .-----------------.
+		    A     b           B
+		 (line start)       (line end)
+
+			L(t) = A + t*(B - A)
+			ab = (B - A)
+			ac = (C - A)
+			solve for b
+			L(b) = A + b*(ab)
+			b = (ac * ab) / (ab * ab)
+			u = ab / |ab|
+			dist = |C - L(b)|
+		*/
 		math::vec3<float> ab = (l.point2 - l.point1);
 		math::vec3<float> ac = (r - l.point1);
 
 		//check if point is within the line segment
-		float c1 = ac * ab;
-		if(c1 < (0 - epsilon))
-			return false;
-		float c2 = ab * ab;
-		if(c2 < (c1 - epsilon))
+		//don't need to divide b by (ab * ab) to check if it's less than 0
+		float b = ac * ab;
+		if(b < (0 - epsilon))
 			return false;
 
-		//check if the point is zero distance from the line
-		float b = c1 / c2;
+		//don't need to divide b by (ab * ab) to check if it's greater than (ab * ab)
+		float ab2 = ab * ab;
+		if(b > (ab2 + epsilon))
+			return false;
+
+		//now divide once we know that the point is within this line segment
+		b = b / ab2;
+
+		//check if the point is zero(ish) distance from the line
 		math::vec3<float> pb = l.point1 + (ab * b);
 		return math::fuzzy_eq(r - pb, math::vec3<float>(math::zero_initialize), epsilon);
 	}