Bevel shape outline corners beyond threshold

include/SFML/Graphics/Shape.hpp

@@ -127,6 +127,24 @@ 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
+    ///
+    /// The edges of the shape's outline around sharp angles can meet
+    /// well beyond the outline thickness. When the ratio between the
+    /// miter length (distance between the outline's tip and the shape's
+    /// corner) and the outline thickness exceeds the given limit, then
+    /// the join is converted from a miter to a bevel.
+    /// The miter limit must be greater than or equal to 1.
+    /// By default, the miter limit is 4.
+    ///
+    /// \param miterLimit New miter limit
+    ///
+    /// \see getMiterLimit
+    ///
+    ////////////////////////////////////////////////////////////
+    void setMiterLimit(float miterLimit);
+
     ////////////////////////////////////////////////////////////
     /// \brief Get the source texture of the shape
     ///
@@ -181,6 +199,16 @@ 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
     ///
@@ -314,6 +342,7 @@ 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{4.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

@@ -31,18 +31,22 @@
 
 #include <algorithm>
 
+#include <cassert>
+#include <cmath>
+
 namespace
 {
-// Compute the normal of a segment
-sf::Vector2f computeNormal(const sf::Vector2f& p1, const sf::Vector2f& p2, bool flipped)
+// Compute the direction and normal unit vectors of a segment
+std::pair<sf::Vector2f, sf::Vector2f> computeDirectionAndNormal(const sf::Vector2f& p1, const sf::Vector2f& p2, bool flipped)
 {
-    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;
+        direction /= length;
+    sf::Vector2f normal = direction.perpendicular();
     if (flipped)
         normal = -normal;
-    return normal;
+    return {direction, normal};
 }
 } // namespace
 
@@ -120,7 +124,7 @@ const Color& Shape::getOutlineColor() const
 void Shape::setOutlineThickness(float thickness)
 {
     m_outlineThickness = thickness;
-    update(); // recompute everything because the whole shape must be offset
+    updateOutline();
 }
 
 
@@ -131,6 +135,22 @@ float Shape::getOutlineThickness() const
 }
 
 
+////////////////////////////////////////////////////////////
+void Shape::setMiterLimit(float miterLimit)
+{
+    assert(1.f <= miterLimit && "Shape::setMiterLimit(float) cannot set miter limit to a value lower than 1");
+    m_miterLimit = std::max(1.f, miterLimit);
+    updateOutline();
+}
+
+
+////////////////////////////////////////////////////////////
+float Shape::getMiterLimit() const
+{
+    return m_miterLimit;
+}
+
+
 ////////////////////////////////////////////////////////////
 Vector2f Shape::getGeometricCenter() const
 {
@@ -286,16 +306,17 @@ 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]()
@@ -306,31 +327,66 @@ void Shape::updateOutline()
         return twiceArea >= 0.f;
     }();
 
+    // In each iteration, d1 and n1 vectors will be the direction and normal of the segment before the current one.
+    auto [d1, n1] = computeDirectionAndNormal(m_vertices[count].position, m_vertices[1].position, flipNormals);
+
+    std::size_t outlineIndex = 0;
     for (std::size_t i = 0; i < count; ++i)
     {
         const std::size_t index = i + 1;
 
-        // Get the two segments shared by the current point
-        const Vector2f p0 = (i == 0) ? m_vertices[count].position : m_vertices[index - 1].position;
+        // Get the segment starting at the current point
         const Vector2f p1 = m_vertices[index].position;
         const Vector2f p2 = m_vertices[index + 1].position;
 
-        // 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);
-        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 its direction and normal pointing towards the outside of the shape
+        const auto [d2, n2] = computeDirectionAndNormal(p1, p2, flipNormals);
+
+        // 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     = 0.f <= d1.dot(n2) * m_outlineThickness;
+        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 float    sin       = std::sqrt(twoSin2 / 2.f);
+            const Vector2f direction = (n2 - n1) / twoSin2; // Length is 1 / sin
+            const Vector2f extrusion = (flipNormals != (0.f <= d1.dot(n2)) ? direction : -direction).perpendicular();
+
+            // Compute bevel corner position in (direction, extrusion) coordinates
+            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;
+        }
+
+        // Save direction and normal for the potential next iteration
+        d1 = d2;
+        n1 = n2;
     }
 
     // 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

@@ -56,6 +56,7 @@ TEST_CASE("[Graphics] sf::Shape")
         CHECK(triangleShape.getFillColor() == sf::Color::White);
         CHECK(triangleShape.getOutlineColor() == sf::Color::White);
         CHECK(triangleShape.getOutlineThickness() == 0.0f);
+        CHECK(triangleShape.getMiterLimit() == 4.0f);
         CHECK(triangleShape.getLocalBounds() == sf::FloatRect());
         CHECK(triangleShape.getGlobalBounds() == sf::FloatRect());
     }
@@ -88,6 +89,13 @@ TEST_CASE("[Graphics] sf::Shape")
         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});