From 4bb287eb705615695444c85ce70073ee91a37f75 Mon Sep 17 00:00:00 2001
From: lisyarus <lisyarus@gmail.com>
Date: Wed, 30 Sep 2020 07:22:27 +0300
Subject: [PATCH] Add n-dim versions of orientation(points) and add
 orientation(vectors)

---
 libs/geom/include/psemek/geom/orientation.hpp | 50 +++++++++++--------
 libs/geom/include/psemek/geom/sign.hpp        | 10 ++++
 2 files changed, 38 insertions(+), 22 deletions(-)

diff --git a/libs/geom/include/psemek/geom/orientation.hpp b/libs/geom/include/psemek/geom/orientation.hpp
index ab77c9aa..63303bdb 100644
--- a/libs/geom/include/psemek/geom/orientation.hpp
+++ b/libs/geom/include/psemek/geom/orientation.hpp
@@ -14,25 +14,6 @@
 namespace psemek::geom
 {
 
-	// TODO: generic implementation
-	template <typename T>
-#ifdef PSEMEK_GEOM_ROBUST_PREDICATES
-	std::enable_if_t<!std::is_floating_point_v<T>, sign_t>
-#else
-	sign_t
-#endif
-		orientation(point<T, 2> const & p0, point<T, 2> const & p1, point<T, 2> const & p2)
-	{
-		T const d = det(p1 - p0, p2 - p0);
-
-		if (d > T{})
-			return sign_t::positive;
-		else if (d < T{})
-			return sign_t::negative;
-		else
-			return sign_t::zero;
-	}
-
 #ifdef PSEMEK_GEOM_ROBUST_PREDICATES
 	template <typename T>
 	std::enable_if_t<std::is_floating_point_v<T>, sign_t>
@@ -59,10 +40,15 @@ namespace psemek::geom
 	}
 #endif
 
-	template <typename T>
-	sign_t orientation(point<T, 3> const & p0, point<T, 3> const & p1, point<T, 3> const & p2, point<T, 3> const & p3)
+	template <typename T, std::size_t N, typename ... Vectors>
+#ifdef PSEMEK_GEOM_ROBUST_PREDICATES
+	std::enable_if_t<!std::is_floating_point_v<T>, sign_t>
+#else
+	sign_t
+#endif
+	orientation(vector<T, N> const & v1, Vectors const & ... vs)
 	{
-		T const d = det(p0 - p3, p1 - p3, p2 - p3);
+		T const d = det(v1, vs...);
 
 		if (d > T{})
 			return sign_t::positive;
@@ -72,4 +58,24 @@ namespace psemek::geom
 			return sign_t::zero;
 	}
 
+	template <typename T, std::size_t N, typename ... Points>
+#ifdef PSEMEK_GEOM_ROBUST_PREDICATES
+	std::enable_if_t<!std::is_floating_point_v<T>, sign_t>
+#else
+	sign_t
+#endif
+	orientation(point<T, N> const & p0, Points const & ... ps)
+	{
+		auto o = orientation((ps - p0)...);
+
+		if constexpr ((N % 2) == 0)
+		{
+			return o;
+		}
+		else
+		{
+			return inverse(o);
+		}
+	}
+
 }
diff --git a/libs/geom/include/psemek/geom/sign.hpp b/libs/geom/include/psemek/geom/sign.hpp
index 3ba9fc4f..3255d1f4 100644
--- a/libs/geom/include/psemek/geom/sign.hpp
+++ b/libs/geom/include/psemek/geom/sign.hpp
@@ -23,4 +23,14 @@ namespace psemek::geom
 		return o;
 	}
 
+	inline sign_t inverse(sign_t s)
+	{
+		switch (s)
+		{
+		case sign_t::positive: return sign_t::negative;
+		case sign_t::zero: return sign_t::zero;
+		case sign_t::negative: return sign_t::positive;
+		}
+	}
+
 }