[GL] Use exact predicate for 2D orientation.

The predicate is correct but slower than the homegrown solution.

GeoLib/AnalyticalGeometry.cpp

@@ -44,25 +44,15 @@ double getOrientation2d(MathLib::Point3d const& a,
 
 namespace GeoLib
 {
-Orientation getOrientation(const double& p0_x, const double& p0_y, const double& p1_x,
-                           const double& p1_y, const double& p2_x, const double& p2_y)
-{
-    double h1((p1_x - p0_x) * (p2_y - p0_y));
-    double h2((p2_x - p0_x) * (p1_y - p0_y));
-
-    double tol(std::numeric_limits<double>::epsilon());
-    if (fabs(h1 - h2) <= tol * std::max(fabs(h1), fabs(h2)))
-        return COLLINEAR;
-    if (h1 - h2 > 0.0)
-        return CCW;
-
-    return CW;
-}
-
 Orientation getOrientation(const GeoLib::Point* p0, const GeoLib::Point* p1,
                            const GeoLib::Point* p2)
 {
-    return getOrientation((*p0)[0], (*p0)[1], (*p1)[0], (*p1)[1], (*p2)[0], (*p2)[1]);
+    double const orientation = ExactPredicates::getOrientation2d(*p0, *p1, *p2);
+    if (orientation > 0)
+        return CCW;
+    if (orientation < 0)
+        return CW;
+    return COLLINEAR;
 }
 
 bool parallel(MathLib::Vector3 v, MathLib::Vector3 w)
@@ -380,8 +370,8 @@ std::vector<MathLib::Point3d> lineSegmentIntersect2d(
     GeoLib::Point const& c{cd.getBeginPoint()};
     GeoLib::Point const& d{cd.getEndPoint()};
 
-    double const orient_abc(ExactPredicates::getOrientation2d(a, b, c));
-    double const orient_abd(ExactPredicates::getOrientation2d(a, b, d));
+    double const orient_abc(getOrientation(a, b, c));
+    double const orient_abd(getOrientation(a, b, d));
 
     // check if the segment (cd) lies on the left or on the right of (ab)
     if ((orient_abc > 0 && orient_abd > 0) || (orient_abc < 0 && orient_abd < 0)) {
@@ -497,8 +487,8 @@ std::vector<MathLib::Point3d> lineSegmentIntersect2d(
     }
 
     // check if the segment (ab) lies on the left or on the right of (cd)
-    double const orient_cda(ExactPredicates::getOrientation2d(c, d, a));
-    double const orient_cdb(ExactPredicates::getOrientation2d(c, d, b));
+    double const orient_cda(getOrientation(c, d, a));
+    double const orient_cdb(getOrientation(c, d, b));
     if ((orient_cda > 0 && orient_cdb > 0) || (orient_cda < 0 && orient_cdb < 0)) {
         return std::vector<MathLib::Point3d>();
     }

GeoLib/AnalyticalGeometry.h

@@ -37,20 +37,13 @@ enum Orientation
 };
 
 /**
- * computes the orientation of the three 2D-Points given by their coordinates
- * p0_x, p0_y, p1_x, p1_y, p2_x and p2_y
- * \returns CW (clockwise), CCW (counterclockwise) or COLLINEAR (points are on a line)
+ * Computes the orientation of the three 2D-Points.
+ * \returns CW (clockwise), CCW (counterclockwise) or COLLINEAR (points are on a
+ * line)
  */
-Orientation getOrientation (const double& p0_x, const double& p0_y,
-    const double& p1_x, const double& p1_y,
-    const double& p2_x, const double& p2_y);
-
-/**
- * wrapper for getOrientation ()
- */
-Orientation getOrientation (const GeoLib::Point* p0,
-                            const GeoLib::Point* p1,
-                            const GeoLib::Point* p2);
+Orientation getOrientation(const GeoLib::Point* p0,
+                           const GeoLib::Point* p1,
+                           const GeoLib::Point* p2);
 
 /**
  * compute a supporting plane (represented by plane_normal and the value d) for the polygon