Bevel shape outline beyond threshold

include/SFML/Graphics/Shape.hpp

@@ -134,6 +134,37 @@ class SFML_GRAPHICS_API Shape : public Drawable, public Transformable
     ////////////////////////////////////////////////////////////
     void setOutlineThickness(float thickness);
 
+    ////////////////////////////////////////////////////////////
+    /// \brief Set the limit on the ratio between miter length and outline thickness
+    ///
+    /// Outline segments around each shape corner are joined either
+    /// with a miter or a bevel join.
+    /// - A miter join is formed by extending outline segments until
+    ///   they intersect. The distance between the point of
+    ///   intersection and the shape's corner is the miter length.
+    /// - A bevel join is formed by connecting outline segments with
+    ///   a straight line perpendicular to the corner's bissector.
+    ///
+    /// The miter limit is used to determine whether ouline segments
+    /// around a corner are joined with a bevel or a miter.
+    /// When the ratio between the miter length and outline thickness
+    /// exceeds the miter limit, a bevel is used instead of a miter.
+    ///
+    /// The miter limit is linked to the maximum inner angle of a
+    /// corner below which a bevel is used by the following formula:
+    ///
+    /// miterLimit = 1 / sin(angle / 2)
+    ///
+    /// The miter limit must be greater than or equal to 1.
+    /// By default, the miter limit is 10.
+    ///
+    /// \param miterLimit New miter limit
+    ///
+    /// \see getMiterLimit
+    ///
+    ////////////////////////////////////////////////////////////
+    void setMiterLimit(float miterLimit);
+
     ////////////////////////////////////////////////////////////
     /// \brief Get the source texture of the shape
     ///
@@ -188,6 +219,16 @@ class SFML_GRAPHICS_API Shape : public Drawable, public Transformable
     ////////////////////////////////////////////////////////////
     float getOutlineThickness() const;
 
+    ////////////////////////////////////////////////////////////
+    /// \brief Get the limit on the ratio between miter length and outline thickness
+    ///
+    /// \return Limit on the ratio between miter length and outline thickness
+    ///
+    /// \see setMiterLimit
+    ///
+    ////////////////////////////////////////////////////////////
+    float getMiterLimit() const;
+
     ////////////////////////////////////////////////////////////
     /// \brief Get the total number of points of the shape
     ///
@@ -315,6 +356,7 @@ class SFML_GRAPHICS_API Shape : public Drawable, public Transformable
     Color          m_fillColor{Color::White};    //!< Fill color
     Color          m_outlineColor{Color::White}; //!< Outline color
     float          m_outlineThickness{};         //!< Thickness of the shape's outline
+    float          m_miterLimit{10.f};           //!< Limit on the ratio between miter length and outline thickness
     VertexArray    m_vertices{PrimitiveType::TriangleFan};          //!< Vertex array containing the fill geometry
     VertexArray    m_outlineVertices{PrimitiveType::TriangleStrip}; //!< Vertex array containing the outline geometry
     FloatRect      m_insideBounds;                                  //!< Bounding rectangle of the inside (fill)

src/SFML/Graphics/Shape.cpp

@@ -32,18 +32,19 @@
 #include <algorithm>
 
 #include <cassert>
+#include <cmath>
 #include <cstddef>
 
 namespace
 {
-// Compute the normal of a segment
-sf::Vector2f computeNormal(const sf::Vector2f& p1, const sf::Vector2f& p2)
+// Compute the direction of a segment
+sf::Vector2f computeDirection(const sf::Vector2f& p1, const sf::Vector2f& p2)
 {
-    sf::Vector2f normal = (p2 - p1).perpendicular();
-    const float  length = normal.length();
+    sf::Vector2f direction = p2 - p1;
+    const float  length    = direction.length();
     if (length != 0.f)
-        normal /= length;
-    return normal;
+        direction /= length;
+    return direction;
 }
 } // namespace
 
@@ -121,7 +122,7 @@ const Color& Shape::getOutlineColor() const
 void Shape::setOutlineThickness(float thickness)
 {
     m_outlineThickness = thickness;
-    update(); // recompute everything because the whole shape must be offset
+    updateOutline();
 }
 
 
@@ -132,6 +133,22 @@ float Shape::getOutlineThickness() const
 }
 
 
+////////////////////////////////////////////////////////////
+void Shape::setMiterLimit(float miterLimit)
+{
+    assert(miterLimit >= 1.f && "Shape::setMiterLimit(float) cannot set miter limit to a value lower than 1");
+    m_miterLimit = miterLimit;
+    updateOutline();
+}
+
+
+////////////////////////////////////////////////////////////
+float Shape::getMiterLimit() const
+{
+    return m_miterLimit;
+}
+
+
 ////////////////////////////////////////////////////////////
 Vector2f Shape::getGeometricCenter() const
 {
@@ -282,17 +299,28 @@ void Shape::updateTexCoords()
 ////////////////////////////////////////////////////////////
 void Shape::updateOutline()
 {
-    // Return if there is no outline
-    if (m_outlineThickness == 0.f)
+    // Return if there is no outline or no vertices
+    if (m_outlineThickness == 0.f || m_vertices.getVertexCount() < 2)
     {
         m_outlineVertices.clear();
         m_bounds = m_insideBounds;
         return;
     }
 
     const std::size_t count = m_vertices.getVertexCount() - 2;
-    m_outlineVertices.resize((count + 1) * 2);
+    m_outlineVertices.resize((count + 1) * 2); // We need at least that many vertices.
+                                               // We will add two more vertices each time we need a bevel.
+
+    // 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;
+    }();
 
+    std::size_t outlineIndex = 0;
     for (std::size_t i = 0; i < count; ++i)
     {
         const std::size_t index = i + 1;
@@ -302,29 +330,55 @@ 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;
-
-        // Combine them to get the extrusion direction
-        const float    factor = 1.f + (n1.x * n2.x + n1.y * n2.y);
-        const Vector2f normal = (n1 + n2) / factor;
-
-        // Update the outline points
-        m_outlineVertices[i * 2 + 0].position = p1;
-        m_outlineVertices[i * 2 + 1].position = p1 + normal * m_outlineThickness;
+        // Compute their direction
+        const Vector2f d1 = computeDirection(p0, p1);
+        const Vector2f d2 = computeDirection(p1, p2);
+
+        // Compute their normal pointing towards the outside of the shape
+        const Vector2f n1 = flipNormals ? -d1.perpendicular() : d1.perpendicular();
+        const Vector2f n2 = flipNormals ? -d2.perpendicular() : d2.perpendicular();
+
+        // Decide whether to add a bevel or not
+        const float twoCos2            = 1.f + n1.dot(n2);
+        const float squaredLengthRatio = m_miterLimit * m_miterLimit * twoCos2 / 2.f;
+        const bool  isConvexCorner     = d1.dot(n2) * m_outlineThickness >= 0.f;
+        const bool  needsBevel         = twoCos2 == 0.f || (squaredLengthRatio < 1.f && isConvexCorner);
+
+        if (needsBevel)
+        {
+            // Make room for two more vertices
+            m_outlineVertices.resize(m_outlineVertices.getVertexCount() + 2);
+
+            // Combine normals to get bevel edge's direction and normal vector pointing towards the outside of the shape
+            const float    twoSin2   = 1.f - n1.dot(n2);
+            const Vector2f direction = (n2 - n1) / twoSin2; // Length is 1 / sin
+            const Vector2f extrusion = (flipNormals != (d1.dot(n2) >= 0.f) ? direction : -direction).perpendicular();
+
+            // Compute bevel corner position in (direction, extrusion) coordinates
+            const float sin = std::sqrt(twoSin2 / 2.f);
+            const float u   = m_miterLimit * sin;
+            const float v   = 1.f - std::sqrt(squaredLengthRatio);
+
+            // Update the outline points
+            m_outlineVertices[outlineIndex++].position = p1;
+            m_outlineVertices[outlineIndex++].position = p1 + (u * extrusion - v * direction) * m_outlineThickness;
+            m_outlineVertices[outlineIndex++].position = p1;
+            m_outlineVertices[outlineIndex++].position = p1 + (u * extrusion + v * direction) * m_outlineThickness;
+        }
+        else
+        {
+            // Combine normals to get the extrusion direction
+            const Vector2f extrusion = (n1 + n2) / twoCos2;
+
+            // Update the outline points
+            m_outlineVertices[outlineIndex++].position = p1;
+            m_outlineVertices[outlineIndex++].position = p1 + extrusion * m_outlineThickness;
+        }
     }
 
     // Duplicate the first point at the end, to close the outline
-    m_outlineVertices[count * 2 + 0].position = m_outlineVertices[0].position;
-    m_outlineVertices[count * 2 + 1].position = m_outlineVertices[1].position;
+    m_outlineVertices[outlineIndex++].position = m_outlineVertices[0].position;
+    m_outlineVertices[outlineIndex++].position = m_outlineVertices[1].position;
 
     // Update outline colors
     updateOutlineColors();

test/Graphics/Shape.test.cpp

@@ -60,6 +60,7 @@ TEST_CASE("[Graphics] sf::Shape", runDisplayTests())
         CHECK(triangleShape.getFillColor() == sf::Color::White);
         CHECK(triangleShape.getOutlineColor() == sf::Color::White);
         CHECK(triangleShape.getOutlineThickness() == 0.0f);
+        CHECK(triangleShape.getMiterLimit() == 10.0f);
         CHECK(triangleShape.getLocalBounds() == sf::FloatRect());
         CHECK(triangleShape.getGlobalBounds() == sf::FloatRect());
     }
@@ -100,6 +101,13 @@ TEST_CASE("[Graphics] sf::Shape", runDisplayTests())
         CHECK(triangleShape.getOutlineThickness() == 3.14f);
     }
 
+    SECTION("Set/get miter limit")
+    {
+        TriangleShape triangleShape({});
+        triangleShape.setMiterLimit(6.28f);
+        CHECK(triangleShape.getMiterLimit() == 6.28f);
+    }
+
     SECTION("Virtual functions: getPoint, getPointCount, getGeometricCenter")
     {
         const TriangleShape triangleShape({2, 2});
@@ -130,5 +138,13 @@ TEST_CASE("[Graphics] sf::Shape", runDisplayTests())
             CHECK(triangleShape.getLocalBounds() == Approx(sf::FloatRect({-7.2150f, -14.2400f}, {44.4300f, 59.2400f})));
             CHECK(triangleShape.getGlobalBounds() == Approx(sf::FloatRect({-7.2150f, -14.2400f}, {44.4300f, 59.2400f})));
         }
+
+        SECTION("Add beveled outline")
+        {
+            triangleShape.setMiterLimit(2);
+            triangleShape.setOutlineThickness(5);
+            CHECK(triangleShape.getLocalBounds() == Approx(sf::FloatRect({-7.2150f, -10.f}, {44.4300f, 55.f})));
+            CHECK(triangleShape.getGlobalBounds() == Approx(sf::FloatRect({-7.2150f, -10.f}, {44.4300f, 55.f})));
+        }
     }
 }