Add love.math.isConvex()

Checks whether a given polygon is convex or not.

src/modules/math/MathModule.cpp

@@ -20,6 +20,7 @@
 
 // LOVE
 #include "MathModule.h"
+#include "common/Vector.h"
 
 // STL
 #include <cmath>
@@ -159,5 +160,32 @@ vector<Triangle> Math::triangulate(const vector<vertex> &polygon)
 	return triangles;
 }
 
+bool Math::isConvex(const std::vector<vertex> &polygon)
+{
+	if (polygon.size() < 3)
+		return false;
+
+	// a polygon is convex if all corners turn in the same direction
+	// turning direction can be determined using the cross-product of
+	// the forward difference vectors
+	size_t i = polygon.size() - 2, j = polygon.size() - 1, k = 0;
+	Vector p(polygon[j].x - polygon[i].x, polygon[j].y - polygon[i].y);
+	Vector q(polygon[k].x - polygon[j].x, polygon[k].y - polygon[j].y);
+	float winding = p ^ q;
+
+	while (k+1 < polygon.size())
+	{
+		i = j; j = k; k++;
+		p.x = polygon[j].x - polygon[i].x;
+		p.y = polygon[j].y - polygon[i].y;
+		q.x = polygon[k].x - polygon[j].x;
+		q.y = polygon[k].y - polygon[j].y;
+
+		if ((p^q) * winding < 0)
+			return false;
+	}
+	return true;
+}
+
 } // math
 } // love

src/modules/math/MathModule.h

@@ -108,6 +108,14 @@ public:
 	 **/
 	std::vector<Triangle> triangulate(const std::vector<vertex> &polygon);
 
+	/**
+	 * Checks whether a polygon is convex.
+	 *
+	 * @param polygon Polygon to test.
+	 * @return True if the polygon is convex, false otherwise.
+	 **/
+	bool isConvex(const std::vector<vertex> &polygon);
+
 	/**
 	 * Calculate Simplex noise for the specified coordinate(s).
 	 *

src/modules/math/wrap_Math.cpp

@@ -148,6 +148,43 @@ int w_triangulate(lua_State *L)
 	return 1;
 }
 
+int w_isConvex(lua_State *L)
+{
+	std::vector<vertex> vertices;
+	if (lua_istable(L, 1))
+	{
+		size_t top = lua_objlen(L, 1);
+		vertices.reserve(top / 2);
+		for (size_t i = 1; i <= top; i += 2)
+		{
+			lua_rawgeti(L, 1, i);
+			lua_rawgeti(L, 1, i+1);
+
+			vertex v;
+			v.x = luaL_checknumber(L, -2);
+			v.y = luaL_checknumber(L, -1);
+			vertices.push_back(v);
+
+			lua_pop(L, 2);
+		}
+	}
+	else
+	{
+		size_t top = lua_gettop(L);
+		vertices.reserve(top / 2);
+		for (size_t i = 1; i <= top; i += 2)
+		{
+			vertex v;
+			v.x = luaL_checknumber(L, i);
+			v.y = luaL_checknumber(L, i+1);
+			vertices.push_back(v);
+		}
+	}
+
+	lua_pushboolean(L, Math::instance.isConvex(vertices));
+	return 1;
+}
+
 int w_noise(lua_State *L)
 {
 	float w, x, y, z;
@@ -192,6 +229,7 @@ static const luaL_Reg functions[] =
 	{ "randomnormal", w_randomnormal },
 	{ "newRandomGenerator", w_newRandomGenerator },
 	{ "triangulate", w_triangulate },
+	{ "isConvex", w_isConvex },
 	{ "noise", w_noise },
 	{ 0, 0 }
 };

src/modules/math/wrap_Math.h

@@ -35,6 +35,7 @@ int w_random(lua_State *L);
 int w_randomnormal(lua_State *L);
 int w_newRandomGenerator(lua_State *L);
 int w_triangulate(lua_State *L);
+int w_isConvex(lua_State *L);
 int w_noise(lua_State *L);
 extern "C" LOVE_EXPORT int luaopen_love_math(lua_State *L);