Clean up lineIntersection

Author: simonlindholm

content/geometry/lineIntersection.h

@@ -5,10 +5,11 @@
  * Source: https://vlecomte.github.io/cp-geo.pdf
  * Description:\\
 \begin{minipage}{75mm}
-If a unique intersection point of the lines going through s1,e1 and s2,e2 exists {1, point} is returned. If no
-intersection point exists {0, (0,0)} is returned and if infinitely many exists {-1, (0,0)} is returned. The wrong
-position will be returned if P is Point<ll> and the intersection point does not have integer coordinates. Products of
-three coordinates are used in intermediate steps so watch out for overflow if using int or long long. \end{minipage}
+If a unique intersection point of the lines going through s1,e1 and s2,e2 exists \{1, point\} is returned.
+If no intersection point exists \{0, (0,0)\} is returned and if infinitely many exists \{-1, (0,0)\} is returned.
+The wrong position will be returned if P is Point<ll> and the intersection point does not have integer coordinates.
+Products of three coordinates are used in intermediate steps so watch out for overflow if using int or ll.
+\end{minipage}
 \begin{minipage}{15mm}
 \includegraphics[width=\textwidth]{content/geometry/lineIntersection}
 \end{minipage}
@@ -22,12 +23,11 @@ three coordinates are used in intermediate steps so watch out for overflow if us
 
 #include "Point.h"
 
-template <class P> pair<int, P> lineInter(P s1, P e1, P s2, P e2) {
-    auto d = (e1 - s1).cross(e2 - s2);
-    if (d == 0) // if parallel
-        return {-(s1.cross(e1, s2) == 0 || s2 == e2), P(0, 0)};
-    else {
-        double a1 = s2.cross(e2, s1), a2 = -s2.cross(e2, e1);
-        return {1, (s1 * a2 + e1 * a1) / (a1 + a2)};
-    }
+template<class P>
+pair<int, P> lineInter(P s1, P e1, P s2, P e2) {
+	auto d = (e1 - s1).cross(e2 - s2);
+	if (d == 0) // if parallel
+		return {-(s1.cross(e1, s2) == 0), P(0, 0)};
+	auto p = s2.cross(e1, e2), q = s2.cross(e2, s1);
+	return {1, (s1 * p + e1 * q) / d};
 }