diff --git a/examples/Demo/Source/Demos/AudioPlaybackDemo.cpp b/examples/Demo/Source/Demos/AudioPlaybackDemo.cpp
index 57139d7c2d..9d2e4c652a 100644
--- a/examples/Demo/Source/Demos/AudioPlaybackDemo.cpp
+++ b/examples/Demo/Source/Demos/AudioPlaybackDemo.cpp
@@ -190,7 +190,10 @@ private:
 
     float timeToX (const double time) const
     {
-        return getWidth() * (float) ((time - visibleRange.getStart()) / (visibleRange.getLength()));
+        if (visibleRange.getLength() <= 0)
+            return 0;
+
+        return getWidth() * (float) ((time - visibleRange.getStart()) / visibleRange.getLength());
     }
 
     double xToTime (const float x) const
diff --git a/modules/juce_graphics/geometry/juce_Path.cpp b/modules/juce_graphics/geometry/juce_Path.cpp
index ac54f3195f..c0aef9ec26 100644
--- a/modules/juce_graphics/geometry/juce_Path.cpp
+++ b/modules/juce_graphics/geometry/juce_Path.cpp
@@ -88,43 +88,19 @@ void Path::PathBounds::reset() noexcept
     pathXMin = pathYMin = pathYMax = pathXMax = 0;
 }
 
-void Path::PathBounds::reset (const float x, const float y) noexcept
+void Path::PathBounds::reset (float x, float y) noexcept
 {
     pathXMin = pathXMax = x;
     pathYMin = pathYMax = y;
 }
 
-void Path::PathBounds::extend (const float x, const float y) noexcept
+void Path::PathBounds::extend (float x, float y) noexcept
 {
-    pathXMin = jmin (pathXMin, x);
-    pathXMax = jmax (pathXMax, x);
-    pathYMin = jmin (pathYMin, y);
-    pathYMax = jmax (pathYMax, y);
-}
-
-void Path::PathBounds::extend (const float x1, const float y1, const float x2, const float y2) noexcept
-{
-    if (x1 < x2)
-    {
-        pathXMin = jmin (pathXMin, x1);
-        pathXMax = jmax (pathXMax, x2);
-    }
-    else
-    {
-        pathXMin = jmin (pathXMin, x2);
-        pathXMax = jmax (pathXMax, x1);
-    }
+    if (x < pathXMin)      pathXMin = x;
+    else if (x > pathXMax) pathXMax = x;
 
-    if (y1 < y2)
-    {
-        pathYMin = jmin (pathYMin, y1);
-        pathYMax = jmax (pathYMax, y2);
-    }
-    else
-    {
-        pathYMin = jmin (pathYMin, y2);
-        pathYMax = jmax (pathYMax, y1);
-    }
+    if (y < pathYMin)      pathYMin = y;
+    else if (y > pathYMax) pathYMax = y;
 }
 
 //==============================================================================
@@ -240,7 +216,7 @@ void Path::preallocateSpace (int numExtraCoordsToMakeSpaceFor)
 
 void Path::startNewSubPath (const float x, const float y)
 {
-    JUCE_CHECK_COORDS_ARE_VALID (x, y);
+    JUCE_CHECK_COORDS_ARE_VALID (x, y)
 
     if (data.isEmpty())
         bounds.reset (x, y);
@@ -257,7 +233,7 @@ void Path::startNewSubPath (Point<float> start)
 
 void Path::lineTo (const float x, const float y)
 {
-    JUCE_CHECK_COORDS_ARE_VALID (x, y);
+    JUCE_CHECK_COORDS_ARE_VALID (x, y)
 
     if (data.isEmpty())
         startNewSubPath (0, 0);
@@ -274,8 +250,8 @@ void Path::lineTo (Point<float> end)
 void Path::quadraticTo (const float x1, const float y1,
                         const float x2, const float y2)
 {
-    JUCE_CHECK_COORDS_ARE_VALID (x1, y1);
-    JUCE_CHECK_COORDS_ARE_VALID (x2, y2);
+    JUCE_CHECK_COORDS_ARE_VALID (x1, y1)
+    JUCE_CHECK_COORDS_ARE_VALID (x2, y2)
 
     if (data.isEmpty())
         startNewSubPath (0, 0);
@@ -294,16 +270,15 @@ void Path::cubicTo (const float x1, const float y1,
                     const float x2, const float y2,
                     const float x3, const float y3)
 {
-    JUCE_CHECK_COORDS_ARE_VALID (x1, y1);
-    JUCE_CHECK_COORDS_ARE_VALID (x2, y2);
-    JUCE_CHECK_COORDS_ARE_VALID (x3, y3);
+    JUCE_CHECK_COORDS_ARE_VALID (x1, y1)
+    JUCE_CHECK_COORDS_ARE_VALID (x2, y2)
+    JUCE_CHECK_COORDS_ARE_VALID (x3, y3)
 
     if (data.isEmpty())
         startNewSubPath (0, 0);
 
     data.add (cubicMarker, x1, y1, x2, y2, x3, y3);
-    bounds.extend (x1, y1, x2, y2);
-    bounds.extend (x3, y3);
+    bounds.extend (x1, y1, x2, y2, x3, y3);
 }
 
 void Path::cubicTo (Point<float> controlPoint1,
@@ -858,6 +833,7 @@ void Path::applyTransform (const AffineTransform& transform) noexcept
         if (isMarker (type, moveMarker))
         {
             transform.transformPoint (d[0], d[1]);
+            JUCE_CHECK_COORDS_ARE_VALID (d[0], d[1])
 
             if (firstPoint)
             {
@@ -874,20 +850,25 @@ void Path::applyTransform (const AffineTransform& transform) noexcept
         else if (isMarker (type, lineMarker))
         {
             transform.transformPoint (d[0], d[1]);
+            JUCE_CHECK_COORDS_ARE_VALID (d[0], d[1])
             bounds.extend (d[0], d[1]);
             d += 2;
         }
         else if (isMarker (type, quadMarker))
         {
             transform.transformPoints (d[0], d[1], d[2], d[3]);
+            JUCE_CHECK_COORDS_ARE_VALID (d[0], d[1])
+            JUCE_CHECK_COORDS_ARE_VALID (d[2], d[3])
             bounds.extend (d[0], d[1], d[2], d[3]);
             d += 4;
         }
         else if (isMarker (type, cubicMarker))
         {
             transform.transformPoints (d[0], d[1], d[2], d[3], d[4], d[5]);
-            bounds.extend (d[0], d[1], d[2], d[3]);
-            bounds.extend (d[4], d[5]);
+            JUCE_CHECK_COORDS_ARE_VALID (d[0], d[1])
+            JUCE_CHECK_COORDS_ARE_VALID (d[2], d[3])
+            JUCE_CHECK_COORDS_ARE_VALID (d[4], d[5])
+            bounds.extend (d[0], d[1], d[2], d[3], d[4], d[5]);
             d += 6;
         }
     }
diff --git a/modules/juce_graphics/geometry/juce_Path.h b/modules/juce_graphics/geometry/juce_Path.h
index 96b231efe5..969be61f11 100644
--- a/modules/juce_graphics/geometry/juce_Path.h
+++ b/modules/juce_graphics/geometry/juce_Path.h
@@ -812,7 +812,13 @@ private:
         void reset() noexcept;
         void reset (float, float) noexcept;
         void extend (float, float) noexcept;
-        void extend (float, float, float, float) noexcept;
+
+        template <typename... Coords>
+        void extend (float x, float y, Coords... coords) noexcept
+        {
+            extend (x, y);
+            extend (coords...);
+        }
 
         float pathXMin = 0, pathXMax = 0, pathYMin = 0, pathYMax = 0;
     };
diff --git a/modules/juce_gui_basics/drawables/juce_DrawableRectangle.cpp b/modules/juce_gui_basics/drawables/juce_DrawableRectangle.cpp
index 52a24ecd92..cd61718d43 100644
--- a/modules/juce_gui_basics/drawables/juce_DrawableRectangle.cpp
+++ b/modules/juce_gui_basics/drawables/juce_DrawableRectangle.cpp
@@ -71,7 +71,7 @@ void DrawableRectangle::rebuildPath()
 {
     if (bounds.isDynamic() || cornerSize.isDynamic())
     {
-        Drawable::Positioner<DrawableRectangle>* const p = new Drawable::Positioner<DrawableRectangle> (*this);
+        auto p = new Drawable::Positioner<DrawableRectangle> (*this);
         setPositioner (p);
         p->apply();
     }
@@ -95,11 +95,11 @@ void DrawableRectangle::recalculateCoordinates (Expression::Scope* scope)
     Point<float> points[3];
     bounds.resolveThreePoints (points, scope);
 
-    const float cornerSizeX = (float) cornerSize.x.resolve (scope);
-    const float cornerSizeY = (float) cornerSize.y.resolve (scope);
+    auto cornerSizeX = (float) cornerSize.x.resolve (scope);
+    auto cornerSizeY = (float) cornerSize.y.resolve (scope);
 
-    const float w = Line<float> (points[0], points[1]).getLength();
-    const float h = Line<float> (points[0], points[2]).getLength();
+    auto w = Line<float> (points[0], points[1]).getLength();
+    auto h = Line<float> (points[0], points[2]).getLength();
 
     Path newPath;
 
@@ -154,7 +154,7 @@ void DrawableRectangle::ValueTreeWrapper::setCornerSize (const RelativePoint& ne
 
 RelativePoint DrawableRectangle::ValueTreeWrapper::getCornerSize() const
 {
-    return RelativePoint (state [cornerSize]);
+    return RelativePoint (state[cornerSize]);
 }
 
 Value DrawableRectangle::ValueTreeWrapper::getCornerSizeValue (UndoManager* undoManager)