Fix shape outline normal computation

The previous implementation could fail to determine if normals had to be
flipped or not: it assumed the first vertex position was strictly inside
the shape. This position being set to the bounding box's center, it is
possible for it be on an edge of the shape (consider a right triangle).

src/SFML/Graphics/Shape.cpp

@@ -34,12 +34,14 @@
 namespace
 {
 // Compute the normal of a segment
-sf::Vector2f computeNormal(const sf::Vector2f& p1, const sf::Vector2f& p2)
+sf::Vector2f computeNormal(const sf::Vector2f& p1, const sf::Vector2f& p2, bool flipped)
 {
     sf::Vector2f normal = (p2 - p1).perpendicular();
     const float  length = normal.length();
     if (length != 0.f)
         normal /= length;
+    if (flipped)
+        normal = -normal;
     return normal;
 }
 } // namespace
@@ -296,6 +298,15 @@ void Shape::updateOutline()
     const std::size_t count = m_vertices.getVertexCount() - 2;
     m_outlineVertices.resize((count + 1) * 2);
 
+    // Determine if points are defined clockwise or counterclockwise. This will impact normals computation.
+    const bool flipNormals = [this, count]()
+    {
+        float twiceArea = 0.f;
+        for (std::size_t i = 0; i < count; ++i)
+            twiceArea += m_vertices[i + 1].position.cross(m_vertices[i + 2].position);
+        return twiceArea >= 0.f;
+    }();
+
     for (std::size_t i = 0; i < count; ++i)
     {
         const std::size_t index = i + 1;
@@ -305,16 +316,9 @@ void Shape::updateOutline()
         const Vector2f p1 = m_vertices[index].position;
         const Vector2f p2 = m_vertices[index + 1].position;
 
-        // Compute their normal
-        Vector2f n1 = computeNormal(p0, p1);
-        Vector2f n2 = computeNormal(p1, p2);
-
-        // Make sure that the normals point towards the outside of the shape
-        // (this depends on the order in which the points were defined)
-        if (n1.dot(m_vertices[0].position - p1) > 0)
-            n1 = -n1;
-        if (n2.dot(m_vertices[0].position - p1) > 0)
-            n2 = -n2;
+        // Compute their normal pointing towards the outside of the shape
+        const Vector2f n1 = computeNormal(p0, p1, flipNormals);
+        const Vector2f n2 = computeNormal(p1, p2, flipNormals);
 
         // Combine them to get the extrusion direction
         const float    factor = 1.f + (n1.x * n2.x + n1.y * n2.y);