Commit aecbfe1ba775d683f3395f0f9214a394feb8b63b

David Bevan 2011-07-02T12:09:52

[ftstroke] Major revision. The main problems ----------------- o If FT_STROKER_LINEJOIN_BEVEL was specified, unlimited miter joins (not bevel joins) were generated. Indeed, the meanings of `miter' and `bevel' were incorrectly reversed (consistently) in both the code and comments. o The way bevel joins were constructed (whether specified explicitly, or created as a result of exceeding the miter limit) did not match what is required for stroked text in PostScript or PDF. The main fixes -------------- o The behaviour of FT_STROKER_LINEJOIN_BEVEL has been corrected. o A new line join style, FT_STROKER_LINEJOIN_MITER_FIXED, has been introduced to support PostScript and PDF miter joins. o FT_STROKER_LINEJOIN_MITER_VARIABLE has been introduced as an alias for FT_STROKER_LINEJOIN_MITER. Additionally, a variety of stroking errors have been fixed. These would cause various artifacts (including points `at infinity'), especially when stroking poor quality fonts. See http://lists.gnu.org/archive/html/freetype-devel/2011-07/msg00001.html for example documents. The FreeType stroker now produces results very similar to that produced by GhostScript and Distiller for these fonts. Other problems -------------- The following problems have been resolved: o Inside corners could be generated incorrectly. Intersecting the inside corner could cause a missing triangular area and other effects. The intersection point can only be used if the join is between two lines and both lines are long enough. The `optimization' condition in `ft_stroker_inside' has been corrected; this requires the line length to be passed into various functions and stored in `FT_StrokerRec'. o Incorrect cubic curves could be generated. The angle calculations in `FT_Stroker_CubicTo' have been corrected to handle the case of the curve crossing the +/-PI direction. o If the border radius was greater than the radius of curvature of a curve, then the negative sector would end up outside (not inside) the border. This situation is now recognized and the negative sector is circumnavigated in the opposite direction. (If round line joins are being used, this code is disabled because the line join will always cover the negative sector.) o When a curve is split, the arcs may not join smoothly (especially if the curve turns sharply back on itself). Changes in direction between adjacent arcs were not handled. A round corner is now added if the deviation from one arc to the next is greater than a suitable threshold. o The current direction wasn't retained if a the outline contained a zero length lineto or a curve that was determined to be `basically a point'. This could cause a spurious join to be added. o Cubics with close control points could be mishandled. All eight cases are now distinguished correctly. Other improvements ------------------ o Borders for cubic curves could be too `flat'. FT_SMALL_CUBIC_THRESHOLD has been reduced a little to prevent this. o The handling and use of movable points has been simplified a little. o Various values are now computed only if the results are actually needed. o The directions of the outer and inner borders have been swapped, as recommended by Graham Asher. * src/base/ftstroke.c: Revised. * include/freetype/ftstroke.h: Updated.

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diff --git a/ChangeLog b/ChangeLog
index aec2939..a7025bc 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,102 @@
+2011-07-02  David Bevan  <david.bevan@pb.com>
+
+	[ftstroke] Major revision.
+
+	The main problems
+	-----------------
+
+	  o If FT_STROKER_LINEJOIN_BEVEL was specified, unlimited miter
+	    joins (not bevel joins) were generated.  Indeed, the meanings of
+	    `miter' and `bevel' were incorrectly reversed (consistently) in
+	    both the code and comments.
+
+	  o The way bevel joins were constructed (whether specified
+	    explicitly, or created as a result of exceeding the miter limit)
+	    did not match what is required for stroked text in PostScript or
+	    PDF.
+
+	The main fixes
+	--------------
+
+	  o The behaviour of FT_STROKER_LINEJOIN_BEVEL has been corrected.
+
+	  o A new line join style, FT_STROKER_LINEJOIN_MITER_FIXED, has been
+	    introduced to support PostScript and PDF miter joins.
+
+	  o FT_STROKER_LINEJOIN_MITER_VARIABLE has been introduced as an
+	    alias for FT_STROKER_LINEJOIN_MITER.
+
+	Additionally, a variety of stroking errors have been fixed.  These
+	would cause various artifacts (including points `at infinity'),
+	especially when stroking poor quality fonts.
+
+	See
+
+	  http://lists.gnu.org/archive/html/freetype-devel/2011-07/msg00001.html
+
+	for example documents.  The FreeType stroker now produces results
+	very similar to that produced by GhostScript and Distiller for these
+	fonts.
+
+	Other problems
+	--------------
+
+	The following problems have been resolved:
+
+	  o Inside corners could be generated incorrectly.  Intersecting the
+	    inside corner could cause a missing triangular area and other
+	    effects.
+
+	    The intersection point can only be used if the join is between
+	    two lines and both lines are long enough.  The `optimization'
+	    condition in `ft_stroker_inside' has been corrected; this
+	    requires the line length to be passed into various functions and
+	    stored in `FT_StrokerRec'.
+
+	  o Incorrect cubic curves could be generated.  The angle
+	    calculations in `FT_Stroker_CubicTo' have been corrected to
+	    handle the case of the curve crossing the +/-PI direction.
+
+	  o If the border radius was greater than the radius of curvature of
+	    a curve, then the negative sector would end up outside (not
+	    inside) the border.  This situation is now recognized and the
+	    negative sector is circumnavigated in the opposite direction.
+	    (If round line joins are being used, this code is disabled
+	    because the line join will always cover the negative sector.)
+
+	  o When a curve is split, the arcs may not join smoothly (especially
+	    if the curve turns sharply back on itself).  Changes in
+	    direction between adjacent arcs were not handled.  A round
+	    corner is now added if the deviation from one arc to the next is
+	    greater than a suitable threshold.
+
+	  o The current direction wasn't retained if a the outline contained
+	    a zero length lineto or a curve that was determined to be
+	    `basically a point'.  This could cause a spurious join to be
+	    added.
+
+	  o Cubics with close control points could be mishandled.  All eight
+	    cases are now distinguished correctly.
+
+	Other improvements
+	------------------
+
+	o Borders for cubic curves could be too `flat'.
+	  FT_SMALL_CUBIC_THRESHOLD has been reduced a little to prevent
+	  this.
+
+	o The handling and use of movable points has been simplified a
+	  little.
+
+	o Various values are now computed only if the results are actually
+	  needed.
+
+	o The directions of the outer and inner borders have been swapped,
+	  as recommended by Graham Asher.
+
+	* src/base/ftstroke.c: Revised.
+	* include/freetype/ftstroke.h: Updated.
+
 2011-06-30  İsmail Dönmez <ismail@namtrac.org>
 
 	* builds/toplevel.mk: We use git, not CVS, thus skip `.gitignore'.
@@ -299,7 +398,7 @@
 
 	[autofit] Remove unused structure member.
 
-	* src/autofit/afhints.h (AF_SegmentRec): Remove `contour'. 
+	* src/autofit/afhints.h (AF_SegmentRec): Remove `contour'.
 	* src/autofit/aflatin.c (af_latin_hints_compute_segments),
 	src/autofit/aflatin2.c (af_latin2_hints_compute_segments): Updated.
 
@@ -325,7 +424,7 @@
 
 	[mac] Conditionalize the inclusion of `AvailabilityMacros.h'.
 
-	The native SDK on earliest Mac OS X (10.0-10.1) did not have 
+	The native SDK on earliest Mac OS X (10.0-10.1) did not have
 	`AvailabilityMacros.h'.  To prevent the inclusion of missing
 	header file, ECANCELED (introduced in 10.2) in POSIX header
 	file <errno.h> is checked to detect the system version.
@@ -401,7 +500,7 @@
 	(af_cjk_metrics_init_widths): Duplicate af_latin_metrics_init_widths.
 	(af_cjk_metrics_check_digits): Duplicate af_latin_metrics_check_digits.
 	(af_cjk_metrics_init): Call CJK bluezone initializer.
-	(af_cjk_metrics_scale_dim): Add code to scale bluezones.  
+	(af_cjk_metrics_scale_dim): Add code to scale bluezones.
 	(af_cjk_hints_compute_blue_edges): New function, CJK version of
 	af_latin_hints_compute_blue_edges.
 	(af_cjk_metrics_init_blues): New function, CJK version of
@@ -439,7 +538,7 @@
 
 	Add new option `--disable-mmap' to configure script.
 
-	* builds/unix/configure.raw: New option `--disable-mmap' 
+	* builds/unix/configure.raw: New option `--disable-mmap'
 	is added.  It is for the developers to simulate the systems
 	without mmap() (like 4.3BSD, minix etc) on POSIX systems.
 
diff --git a/include/freetype/ftstroke.h b/include/freetype/ftstroke.h
index 3afb87d..dbda6d2 100644
--- a/include/freetype/ftstroke.h
+++ b/include/freetype/ftstroke.h
@@ -4,7 +4,7 @@
 /*                                                                         */
 /*    FreeType path stroker (specification).                               */
 /*                                                                         */
-/*  Copyright 2002, 2003, 2004, 2005, 2006, 2008, 2009 by                  */
+/*  Copyright 2002-2006, 2008, 2009, 2011 by                               */
 /*  David Turner, Robert Wilhelm, and Werner Lemberg.                      */
 /*                                                                         */
 /*  This file is part of the FreeType project, and may only be used,       */
@@ -75,20 +75,44 @@ FT_BEGIN_HEADER
    *     to join two lines smoothly.
    *
    *   FT_STROKER_LINEJOIN_BEVEL ::
-   *     Used to render beveled line joins; i.e., the two joining lines
-   *     are extended until they intersect.
-   *
+   *     Used to render beveled line joins.  The outer corner of
+   *     the joined lines is filled by enclosing the triangular
+   *     region of the corner with a straight line between the
+   *     outer corners of each stroke.
+   *
+   *   FT_STROKER_LINEJOIN_MITER_FIXED ::
+   *     Used to render mitered line joins, with fixed bevels if the
+   *     miter limit is exceeded.  The outer edges of the strokes
+   *     for the two segments are extended until they meet at an
+   *     angle.  If the segments meet at too sharp an angle (such
+   *     that the miter would extend from the intersection of the 
+   *     segments a distance greater than the product of the miter 
+   *     limit value and the border radius), then a bevel join (see 
+   *     above) is used instead.  This prevents long spikes being 
+   *     created.  FT_STROKER_LINEJOIN_MITER_FIXED generates a miter 
+   *     line join as used in PostScript and PDF.
+   *
+   *   FT_STROKER_LINEJOIN_MITER_VARIABLE ::
    *   FT_STROKER_LINEJOIN_MITER ::
-   *     Same as beveled rendering, except that an additional line
-   *     break is added if the angle between the two joining lines
-   *     is too closed (this is useful to avoid unpleasant spikes
-   *     in beveled rendering).
+   *     Used to render mitered line joins, with variable bevels if
+   *     the miter limit is exceeded.  The intersection of the 
+   *     strokes is clipped at a line perpendicular to the bisector 
+   *     of the angle between the strokes, at the distance from the 
+   *     intersection of the segments equal to the product of the 
+   *     miter limit value and the border radius.  This prevents 
+   *     long spikes being created.  
+   *     FT_STROKER_LINEJOIN_MITER_VARIABLE generates a mitered line 
+   *     join as used in XPS.  FT_STROKER_LINEJOIN_MITER is an alias 
+   *     for FT_STROKER_LINEJOIN_MITER_VARIABLE, retained for 
+   *     backwards compatibility.
    */
   typedef enum  FT_Stroker_LineJoin_
   {
-    FT_STROKER_LINEJOIN_ROUND = 0,
-    FT_STROKER_LINEJOIN_BEVEL,
-    FT_STROKER_LINEJOIN_MITER
+    FT_STROKER_LINEJOIN_ROUND          = 0,
+    FT_STROKER_LINEJOIN_BEVEL          = 1,
+    FT_STROKER_LINEJOIN_MITER_VARIABLE = 2,
+    FT_STROKER_LINEJOIN_MITER          = FT_STROKER_LINEJOIN_MITER_VARIABLE,
+    FT_STROKER_LINEJOIN_MITER_FIXED    = 3
 
   } FT_Stroker_LineJoin;
 
@@ -245,7 +269,8 @@ FT_BEGIN_HEADER
    *     The line join style.
    *
    *   miter_limit ::
-   *     The miter limit for the FT_STROKER_LINEJOIN_MITER style,
+   *     The miter limit for the FT_STROKER_LINEJOIN_MITER_FIXED and
+   *     FT_STROKER_LINEJOIN_MITER_VARIABLE line join styles,
    *     expressed as 16.16 fixed point value.
    *
    * @note:
diff --git a/src/base/ftstroke.c b/src/base/ftstroke.c
index cd4bf04..3f24f9e 100644
--- a/src/base/ftstroke.c
+++ b/src/base/ftstroke.c
@@ -34,7 +34,7 @@
 
 
     return o == FT_ORIENTATION_TRUETYPE ? FT_STROKER_BORDER_RIGHT
-                                        : FT_STROKER_BORDER_LEFT ;
+                                        : FT_STROKER_BORDER_LEFT;
   }
 
 
@@ -47,20 +47,21 @@
 
 
     return o == FT_ORIENTATION_TRUETYPE ? FT_STROKER_BORDER_LEFT
-                                        : FT_STROKER_BORDER_RIGHT ;
+                                        : FT_STROKER_BORDER_RIGHT;
   }
 
 
- /***************************************************************************/
- /***************************************************************************/
- /*****                                                                 *****/
- /*****                       BEZIER COMPUTATIONS                       *****/
- /*****                                                                 *****/
- /***************************************************************************/
- /***************************************************************************/
+  /*************************************************************************/
+  /*************************************************************************/
+  /*****                                                               *****/
+  /*****                      BEZIER COMPUTATIONS                      *****/
+  /*****                                                               *****/
+  /*************************************************************************/
+  /*************************************************************************/
 
 #define FT_SMALL_CONIC_THRESHOLD  ( FT_ANGLE_PI / 6 )
-#define FT_SMALL_CUBIC_THRESHOLD  ( FT_ANGLE_PI / 6 )
+#define FT_SMALL_CUBIC_THRESHOLD  ( FT_ANGLE_PI / 8 )
+
 #define FT_EPSILON  2
 
 #define FT_IS_SMALL( x )  ( (x) > -FT_EPSILON && (x) < FT_EPSILON )
@@ -69,7 +70,7 @@
   static FT_Pos
   ft_pos_abs( FT_Pos  x )
   {
-    return x >= 0 ? x : -x ;
+    return x >= 0 ? x : -x;
   }
 
 
@@ -114,18 +115,28 @@
     if ( close1 )
     {
       if ( close2 )
-        *angle_in = *angle_out = 0;
+      {
+        /* basically a point;                      */
+        /* do nothing to retain original direction */
+      }
       else
-        *angle_in = *angle_out = FT_Atan2( d2.x, d2.y );
-    }
-    else if ( close2 )
-    {
-      *angle_in = *angle_out = FT_Atan2( d1.x, d1.y );
+      {
+        *angle_in  =
+        *angle_out = FT_Atan2( d2.x, d2.y );
+      }
     }
-    else
+    else /* !close1 */
     {
-      *angle_in  = FT_Atan2( d1.x, d1.y );
-      *angle_out = FT_Atan2( d2.x, d2.y );
+      if ( close2 )
+      {
+        *angle_in  =
+        *angle_out = FT_Atan2( d1.x, d1.y );
+      }
+      else
+      {
+        *angle_in  = FT_Atan2( d1.x, d1.y );
+        *angle_out = FT_Atan2( d2.x, d2.y );
+      }
     }
 
     theta = ft_pos_abs( FT_Angle_Diff( *angle_in, *angle_out ) );
@@ -162,6 +173,17 @@
   }
 
 
+  /* Return the average of `angle1' and `angle2'.            */
+  /* This gives correct result even if `angle1' and `angle2' */
+  /* have opposite signs.                                    */
+  static FT_Angle
+  ft_angle_mean( FT_Angle  angle1,
+                 FT_Angle  angle2 )
+  {
+    return angle1 + FT_Angle_Diff( angle1, angle2 ) / 2;
+  }
+
+
   static FT_Bool
   ft_cubic_is_small_enough( FT_Vector*  base,
                             FT_Angle   *angle_in,
@@ -184,34 +206,70 @@
     close2 = FT_IS_SMALL( d2.x ) && FT_IS_SMALL( d2.y );
     close3 = FT_IS_SMALL( d3.x ) && FT_IS_SMALL( d3.y );
 
-    if ( close1 || close3 )
+    if ( close1 )
     {
       if ( close2 )
       {
-        /* basically a point */
-        *angle_in = *angle_out = *angle_mid = 0;
-      }
-      else if ( close1 )
-      {
-        *angle_in  = *angle_mid = FT_Atan2( d2.x, d2.y );
-        *angle_out = FT_Atan2( d3.x, d3.y );
+        if ( close3 )
+        {
+          /* basically a point;                      */
+          /* do nothing to retain original direction */
+        }
+        else /* !close3 */
+        {
+          *angle_in  =
+          *angle_mid =
+          *angle_out = FT_Atan2( d3.x, d3.y );
+        }
       }
-      else  /* close2 */
+      else /* !close2 */
       {
-        *angle_in  = FT_Atan2( d1.x, d1.y );
-        *angle_mid = *angle_out = FT_Atan2( d2.x, d2.y );
+        if ( close3 )
+        {
+          *angle_in  =
+          *angle_mid =
+          *angle_out = FT_Atan2( d2.x, d2.y );
+        }
+        else /* !close3 */
+        {
+          *angle_in  =
+          *angle_mid = FT_Atan2( d2.x, d2.y );
+          *angle_out = FT_Atan2( d3.x, d3.y );
+        }
       }
     }
-    else if ( close2 )
-    {
-      *angle_in  = *angle_mid = FT_Atan2( d1.x, d1.y );
-      *angle_out = FT_Atan2( d3.x, d3.y );
-    }
-    else
+    else /* !close1 */
     {
-      *angle_in  = FT_Atan2( d1.x, d1.y );
-      *angle_mid = FT_Atan2( d2.x, d2.y );
-      *angle_out = FT_Atan2( d3.x, d3.y );
+      if ( close2 )
+      {
+        if ( close3 )
+        {
+          *angle_in  =
+          *angle_mid =
+          *angle_out = FT_Atan2( d1.x, d1.y );
+        }
+        else /* !close3 */
+        {
+          *angle_in  = FT_Atan2( d1.x, d1.y );
+          *angle_out = FT_Atan2( d3.x, d3.y );
+          *angle_mid = ft_angle_mean( *angle_in, *angle_out );
+        }
+      }
+      else /* !close2 */
+      {
+        if ( close3 )
+        {
+          *angle_in  = FT_Atan2( d1.x, d1.y );
+          *angle_mid =
+          *angle_out = FT_Atan2( d2.x, d2.y );
+        }
+        else /* !close3 */
+        {
+          *angle_in  = FT_Atan2( d1.x, d1.y );
+          *angle_mid = FT_Atan2( d2.x, d2.y );
+          *angle_out = FT_Atan2( d3.x, d3.y );
+        }
+      }
     }
 
     theta1 = ft_pos_abs( FT_Angle_Diff( *angle_in,  *angle_mid ) );
@@ -222,13 +280,13 @@
   }
 
 
- /***************************************************************************/
- /***************************************************************************/
- /*****                                                                 *****/
- /*****                       STROKE BORDERS                            *****/
- /*****                                                                 *****/
- /***************************************************************************/
- /***************************************************************************/
+  /*************************************************************************/
+  /*************************************************************************/
+  /*****                                                               *****/
+  /*****                       STROKE BORDERS                          *****/
+  /*****                                                               *****/
+  /*************************************************************************/
+  /*************************************************************************/
 
   typedef enum  FT_StrokeTags_
   {
@@ -239,7 +297,7 @@
 
   } FT_StrokeTags;
 
-#define  FT_STROKE_TAG_BEGIN_END  (FT_STROKE_TAG_BEGIN|FT_STROKE_TAG_END)
+#define  FT_STROKE_TAG_BEGIN_END  ( FT_STROKE_TAG_BEGIN | FT_STROKE_TAG_END )
 
   typedef struct  FT_StrokeBorderRec_
   {
@@ -247,7 +305,7 @@
     FT_UInt     max_points;
     FT_Vector*  points;
     FT_Byte*    tags;
-    FT_Bool     movable;
+    FT_Bool     movable;  /* TRUE for ends of lineto borders */
     FT_Int      start;    /* index of current sub-path start point */
     FT_Memory   memory;
     FT_Bool     valid;
@@ -368,6 +426,12 @@
     }
     else
     {
+      /* don't add zero-length lineto */
+      if ( border->num_points > 0                                          &&
+           FT_IS_SMALL( border->points[border->num_points - 1].x - to->x ) &&
+           FT_IS_SMALL( border->points[border->num_points - 1].y - to->y ) )
+        return error;
+
       /* add one point */
       error = ft_stroke_border_grow( border, 1 );
       if ( !error )
@@ -403,6 +467,7 @@
       FT_Vector*  vec = border->points + border->num_points;
       FT_Byte*    tag = border->tags   + border->num_points;
 
+
       vec[0] = *control;
       vec[1] = *to;
 
@@ -411,7 +476,9 @@
 
       border->num_points += 2;
     }
+
     border->movable = FALSE;
+
     return error;
   }
 
@@ -444,7 +511,9 @@
 
       border->num_points += 3;
     }
+
     border->movable = FALSE;
+
     return error;
   }
 
@@ -530,7 +599,7 @@
     if ( border->start >= 0 )
       ft_stroke_border_close( border, FALSE );
 
-    border->start   = border->num_points;
+    border->start = border->num_points;
     border->movable = FALSE;
 
     return ft_stroke_border_lineto( border, to, FALSE );
@@ -673,34 +742,38 @@
       }
     }
 
-    outline->n_points  = (short)( outline->n_points + border->num_points );
+    outline->n_points = (short)( outline->n_points + border->num_points );
 
     FT_ASSERT( FT_Outline_Check( outline ) == 0 );
   }
 
 
- /***************************************************************************/
- /***************************************************************************/
- /*****                                                                 *****/
- /*****                           STROKER                               *****/
- /*****                                                                 *****/
- /***************************************************************************/
- /***************************************************************************/
+  /*************************************************************************/
+  /*************************************************************************/
+  /*****                                                               *****/
+  /*****                           STROKER                             *****/
+  /*****                                                               *****/
+  /*************************************************************************/
+  /*************************************************************************/
 
 #define FT_SIDE_TO_ROTATE( s )   ( FT_ANGLE_PI2 - (s) * FT_ANGLE_PI )
 
   typedef struct  FT_StrokerRec_
   {
-    FT_Angle             angle_in;
-    FT_Angle             angle_out;
-    FT_Vector            center;
-    FT_Bool              first_point;
-    FT_Bool              subpath_open;
-    FT_Angle             subpath_angle;
-    FT_Vector            subpath_start;
+    FT_Angle             angle_in;             /* direction into curr join */
+    FT_Angle             angle_out;            /* direction out of join  */
+    FT_Vector            center;               /* current position */
+    FT_Fixed             line_length;          /* length of last lineto */
+    FT_Bool              first_point;          /* is this the start? */
+    FT_Bool              subpath_open;         /* is the subpath open? */
+    FT_Angle             subpath_angle;        /* subpath start direction */
+    FT_Vector            subpath_start;        /* subpath start position */
+    FT_Fixed             subpath_line_length;  /* subpath start lineto len */
+    FT_Bool              handle_wide_strokes;  /* use wide strokes logic? */
 
     FT_Stroker_LineCap   line_cap;
     FT_Stroker_LineJoin  line_join;
+    FT_Stroker_LineJoin  line_join_saved;
     FT_Fixed             miter_limit;
     FT_Fixed             radius;
 
@@ -733,7 +806,9 @@
       ft_stroke_border_init( &stroker->borders[0], memory );
       ft_stroke_border_init( &stroker->borders[1], memory );
     }
+
     *astroker = stroker;
+
     return error;
   }
 
@@ -752,6 +827,14 @@
     stroker->line_join   = line_join;
     stroker->miter_limit = miter_limit;
 
+    /* ensure miter limit has sensible value */
+    if ( stroker->miter_limit < 0x10000 )
+      stroker->miter_limit = 0x10000;
+
+    /* save line join style:                                           */
+    /* line join style can be temporarily changed when stroking curves */
+    stroker->line_join_saved = line_join;
+
     FT_Stroker_Rewind( stroker );
   }
 
@@ -788,7 +871,7 @@
   }
 
 
-  /* creates a circular arc at a corner or cap */
+  /* create a circular arc at a corner or cap */
   static FT_Error
   ft_stroker_arcto( FT_Stroker  stroker,
                     FT_Int      side )
@@ -815,7 +898,7 @@
   }
 
 
-  /* adds a cap at the end of an opened path */
+  /* add a cap at the end of an opened path */
   static FT_Error
   ft_stroker_cap( FT_Stroker  stroker,
                   FT_Angle    angle,
@@ -829,6 +912,7 @@
       /* add a round cap */
       stroker->angle_in  = angle;
       stroker->angle_out = angle + FT_ANGLE_PI;
+
       error = ft_stroker_arcto( stroker, side );
     }
     else if ( stroker->line_cap == FT_STROKER_LINECAP_SQUARE )
@@ -881,7 +965,7 @@
       delta.x += stroker->center.x;
       delta.y += stroker->center.y;
 
-      error = ft_stroke_border_lineto( border, &delta, FALSE );   
+      error = ft_stroke_border_lineto( border, &delta, FALSE );
     }
 
   Exit:
@@ -892,40 +976,52 @@
   /* process an inside corner, i.e. compute intersection */
   static FT_Error
   ft_stroker_inside( FT_Stroker  stroker,
-                     FT_Int      side)
+                     FT_Int      side,
+                     FT_Fixed    line_length )
   {
     FT_StrokeBorder  border = stroker->borders + side;
     FT_Angle         phi, theta, rotate;
-    FT_Fixed         length, thcos, sigma;
+    FT_Fixed         length, thcos;
     FT_Vector        delta;
     FT_Error         error = FT_Err_Ok;
+    FT_Bool          intersect;          /* use intersection of lines? */
 
 
     rotate = FT_SIDE_TO_ROTATE( side );
 
-    /* compute median angle */
-    theta = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
-    if ( theta == FT_ANGLE_PI )
-      theta = rotate;
+    theta = FT_Angle_Diff( stroker->angle_in, stroker->angle_out ) / 2;
+
+    /* Only intersect borders if between two lineto's and both */
+    /* lines are long enough (line_length is zero for curves). */
+    if ( !border->movable || line_length == 0 )
+      intersect = FALSE;
     else
-      theta = theta / 2;
+    {
+      /* compute minimum required length of lines */
+      FT_Fixed  min_length = ft_pos_abs( FT_MulFix( stroker->radius,
+                                                    FT_Tan( theta ) ) );
 
-    phi = stroker->angle_in + theta;
 
-    thcos = FT_Cos( theta );
-    sigma = FT_MulFix( stroker->miter_limit, thcos );
+      intersect = FT_BOOL( stroker->line_length >= min_length &&
+                           line_length          >= min_length );
+    }
 
-    /* TODO: find better criterion to switch off the optimization */
-    if ( sigma < 0x10000L )
+    if ( !intersect )
     {
       FT_Vector_From_Polar( &delta, stroker->radius,
                             stroker->angle_out + rotate );
       delta.x += stroker->center.x;
       delta.y += stroker->center.y;
+
       border->movable = FALSE;
     }
     else
     {
+      /* compute median angle */
+      phi = stroker->angle_in + theta;
+
+      thcos = FT_Cos( theta );
+
       length = FT_DivFix( stroker->radius, thcos );
 
       FT_Vector_From_Polar( &delta, length, phi + rotate );
@@ -942,7 +1038,8 @@
   /* process an outside corner, i.e. compute bevel/miter/round */
   static FT_Error
   ft_stroker_outside( FT_Stroker  stroker,
-                      FT_Int      side )
+                      FT_Int      side,
+                      FT_Fixed    line_length )
   {
     FT_StrokeBorder  border = stroker->borders + side;
     FT_Error         error;
@@ -953,79 +1050,119 @@
       error = ft_stroker_arcto( stroker, side );
     else
     {
-      /* this is a mitered or beveled corner */
-      FT_Fixed  sigma, radius = stroker->radius;
-      FT_Angle  theta, phi;
-      FT_Fixed  thcos;
-      FT_Bool   miter;
+      /* this is a mitered (pointed) or beveled (truncated) corner */
+      FT_Fixed  sigma = 0, radius = stroker->radius;
+      FT_Angle  theta = 0, phi = 0;
+      FT_Fixed  thcos = 0;
+      FT_Bool   bevel, fixed_bevel;
 
 
       rotate = FT_SIDE_TO_ROTATE( side );
-      miter  = FT_BOOL( stroker->line_join == FT_STROKER_LINEJOIN_MITER );
 
-      theta = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
-      if ( theta == FT_ANGLE_PI )
+      bevel =
+        FT_BOOL( stroker->line_join == FT_STROKER_LINEJOIN_BEVEL );
+
+      fixed_bevel =
+        FT_BOOL( stroker->line_join != FT_STROKER_LINEJOIN_MITER_VARIABLE );
+
+      if ( !bevel )
       {
-        theta = rotate;
-        phi   = stroker->angle_in;
+        theta = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
+
+        if ( theta == FT_ANGLE_PI )
+        {
+          theta = rotate;
+          phi   = stroker->angle_in;
+        }
+        else
+        {
+          theta /= 2;
+          phi    = stroker->angle_in + theta + rotate;
+        }
+
+        thcos = FT_Cos( theta );
+        sigma = FT_MulFix( stroker->miter_limit, thcos );
+
+        /* is miter limit exceeded? */
+        if ( sigma < 0x10000L )
+        {
+          /* don't create variable bevels for very small deviations; */
+          /* FT_Sin(x) = 0 for x <= 57                               */
+          if ( fixed_bevel || ft_pos_abs( theta ) > 57 )
+            bevel = TRUE;
+        }
       }
-      else
+
+      if ( bevel )  /* this is a bevel (broken angle) */
       {
-        theta = theta / 2;
-        phi   = stroker->angle_in + theta + rotate;
-      }
+        if ( fixed_bevel )
+        {
+          /* the outer corners are simply joined together */
+          FT_Vector  delta;
 
-      thcos = FT_Cos( theta );
-      sigma = FT_MulFix( stroker->miter_limit, thcos );
 
-      /* FT_Sin(x) = 0 for x <= 57 */
-      if ( sigma >= 0x10000L || ft_pos_abs( theta ) <= 57 )
-        miter = FALSE;
+          /* add bevel */
+          FT_Vector_From_Polar( &delta,
+                                radius,
+                                stroker->angle_out + rotate );
+          delta.x += stroker->center.x;
+          delta.y += stroker->center.y;
 
-      if ( miter )  /* this is a miter (broken angle) */
-      {
-        FT_Vector  middle, delta;
-        FT_Fixed   length;
+          border->movable = FALSE;
+          error = ft_stroke_border_lineto( border, &delta, FALSE );
+        }
+        else /* variable bevel */
+        {
+          /* the miter is truncated */
+          FT_Vector  middle, delta;
+          FT_Fixed   length;
 
 
-        /* compute middle point */
-        FT_Vector_From_Polar( &middle,
-                              FT_MulFix( radius, stroker->miter_limit ),
-                              phi );
-        middle.x += stroker->center.x;
-        middle.y += stroker->center.y;
+          /* compute middle point */
+          FT_Vector_From_Polar( &middle,
+                                FT_MulFix( radius, stroker->miter_limit ),
+                                phi );
+          middle.x += stroker->center.x;
+          middle.y += stroker->center.y;
 
-        /* compute first angle point */
-        length = FT_MulFix( radius,
-                            FT_DivFix( 0x10000L - sigma,
-                                       ft_pos_abs( FT_Sin( theta ) ) ) );
+          /* compute first angle point */
+          length = FT_MulFix( radius,
+                              FT_DivFix( 0x10000L - sigma,
+                                         ft_pos_abs( FT_Sin( theta ) ) ) );
 
-        FT_Vector_From_Polar( &delta, length, phi + rotate );
-        delta.x += middle.x;
-        delta.y += middle.y;
+          FT_Vector_From_Polar( &delta, length, phi + rotate );
+          delta.x += middle.x;
+          delta.y += middle.y;
 
-        error = ft_stroke_border_lineto( border, &delta, FALSE );
-        if ( error )
-          goto Exit;
+          error = ft_stroke_border_lineto( border, &delta, FALSE );
+          if ( error )
+            goto Exit;
 
-        /* compute second angle point */
-        FT_Vector_From_Polar( &delta, length, phi - rotate );
-        delta.x += middle.x;
-        delta.y += middle.y;
+          /* compute second angle point */
+          FT_Vector_From_Polar( &delta, length, phi - rotate );
+          delta.x += middle.x;
+          delta.y += middle.y;
 
-        error = ft_stroke_border_lineto( border, &delta, FALSE );
-        if ( error )
-          goto Exit;
+          error = ft_stroke_border_lineto( border, &delta, FALSE );
+          if ( error )
+            goto Exit;
 
-        /* finally, add a movable end point */
-        FT_Vector_From_Polar( &delta, radius, stroker->angle_out + rotate );
-        delta.x += stroker->center.x;
-        delta.y += stroker->center.y;
+          /* finally, add an end point; only needed if not lineto */
+          /* (line_length is zero for curves)                     */
+          if ( line_length == 0 )
+          {
+            FT_Vector_From_Polar( &delta,
+                                  radius,
+                                  stroker->angle_out + rotate );
 
-        error = ft_stroke_border_lineto( border, &delta, TRUE );
-      }
+            delta.x += stroker->center.x;
+            delta.y += stroker->center.y;
 
-      else /* this is a bevel (intersection) */
+            error = ft_stroke_border_lineto( border, &delta, FALSE );
+          }
+        }
+      }
+      else /* this is a miter (intersection) */
       {
         FT_Fixed   length;
         FT_Vector  delta;
@@ -1041,13 +1178,18 @@
         if ( error )
           goto Exit;
 
-        /* now add end point */
-        FT_Vector_From_Polar( &delta, stroker->radius,
-                              stroker->angle_out + rotate );
-        delta.x += stroker->center.x;
-        delta.y += stroker->center.y;
+        /* now add an end point; only needed if not lineto */
+        /* (line_length is zero for curves)                */
+        if ( line_length == 0 )
+        {
+          FT_Vector_From_Polar( &delta,
+                                stroker->radius,
+                                stroker->angle_out + rotate );
+          delta.x += stroker->center.x;
+          delta.y += stroker->center.y;
 
-        error = ft_stroke_border_lineto( border, &delta, TRUE );
+          error = ft_stroke_border_lineto( border, &delta, FALSE );
+        }
       }
     }
 
@@ -1057,7 +1199,8 @@
 
 
   static FT_Error
-  ft_stroker_process_corner( FT_Stroker  stroker )
+  ft_stroker_process_corner( FT_Stroker  stroker,
+                             FT_Fixed    line_length )
   {
     FT_Error  error = FT_Err_Ok;
     FT_Angle  turn;
@@ -1078,12 +1221,12 @@
       inside_side = 1;
 
     /* process the inside side */
-    error = ft_stroker_inside( stroker, inside_side );
+    error = ft_stroker_inside( stroker, inside_side, line_length );
     if ( error )
       goto Exit;
 
     /* process the outside side */
-    error = ft_stroker_outside( stroker, 1 - inside_side );
+    error = ft_stroker_outside( stroker, 1 - inside_side, line_length );
 
   Exit:
     return error;
@@ -1094,7 +1237,8 @@
   /* start of the subpath                                              */
   static FT_Error
   ft_stroker_subpath_start( FT_Stroker  stroker,
-                            FT_Angle    start_angle )
+                            FT_Angle    start_angle,
+                            FT_Fixed    line_length )
   {
     FT_Vector        delta;
     FT_Vector        point;
@@ -1119,9 +1263,11 @@
     border++;
     error = ft_stroke_border_moveto( border, &point );
 
-    /* save angle for last cap */
-    stroker->subpath_angle = start_angle;
-    stroker->first_point   = FALSE;
+    /* save angle, position, and line length for last join */
+    /* (line_length is zero for curves)                    */
+    stroker->subpath_angle       = start_angle;
+    stroker->first_point         = FALSE;
+    stroker->subpath_line_length = line_length;
 
   Exit:
     return error;
@@ -1139,10 +1285,19 @@
     FT_Vector        delta;
     FT_Angle         angle;
     FT_Int           side;
+    FT_Fixed         line_length;
+
 
     delta.x = to->x - stroker->center.x;
     delta.y = to->y - stroker->center.y;
 
+    /* a zero-length lineto is a no-op; avoid creating a spurious corner */
+    if ( delta.x == 0 && delta.y == 0 )
+       goto Exit;
+
+    /* compute length of line */
+    line_length = FT_Vector_Length( &delta );
+
     angle = FT_Atan2( delta.x, delta.y );
     FT_Vector_From_Polar( &delta, stroker->radius, angle + FT_ANGLE_PI2 );
 
@@ -1152,7 +1307,7 @@
       /* This is the first segment of a subpath.  We need to     */
       /* add a point to each border at their respective starting */
       /* point locations.                                        */
-      error = ft_stroker_subpath_start( stroker, angle );
+      error = ft_stroker_subpath_start( stroker, angle, line_length );
       if ( error )
         goto Exit;
     }
@@ -1160,13 +1315,12 @@
     {
       /* process the current corner */
       stroker->angle_out = angle;
-      error = ft_stroker_process_corner( stroker );
+      error = ft_stroker_process_corner( stroker, line_length );
       if ( error )
         goto Exit;
     }
 
     /* now add a line segment to both the `inside' and `outside' paths */
-
     for ( border = stroker->borders, side = 1; side >= 0; side--, border++ )
     {
       FT_Vector  point;
@@ -1175,6 +1329,7 @@
       point.x = to->x + delta.x;
       point.y = to->y + delta.y;
 
+      /* the ends of lineto borders are movable */
       error = ft_stroke_border_lineto( border, &point, TRUE );
       if ( error )
         goto Exit;
@@ -1183,8 +1338,9 @@
       delta.y = -delta.y;
     }
 
-    stroker->angle_in = angle;
-    stroker->center   = *to;
+    stroker->angle_in    = angle;
+    stroker->center      = *to;
+    stroker->line_length = line_length;
 
   Exit:
     return error;
@@ -1202,10 +1358,20 @@
     FT_Vector   bez_stack[34];
     FT_Vector*  arc;
     FT_Vector*  limit = bez_stack + 30;
-    FT_Angle    start_angle;
     FT_Bool     first_arc = TRUE;
 
 
+    /* if all control points are coincident, this is a no-op; */
+    /* avoid creating a spurious corner                       */
+    if ( FT_IS_SMALL( stroker->center.x - control->x ) &&
+         FT_IS_SMALL( stroker->center.y - control->y ) &&
+         FT_IS_SMALL( control->x        - to->x      ) &&
+         FT_IS_SMALL( control->y        - to->y      ) )
+    {
+       stroker->center = *to;
+       goto Exit;
+    }
+
     arc    = bez_stack;
     arc[0] = *to;
     arc[1] = *control;
@@ -1216,11 +1382,15 @@
       FT_Angle  angle_in, angle_out;
 
 
-      angle_in = angle_out = 0;  /* remove compiler warnings */
+      /* initialize with current direction */
+      angle_in = angle_out = stroker->angle_in;
 
       if ( arc < limit                                             &&
            !ft_conic_is_small_enough( arc, &angle_in, &angle_out ) )
       {
+        if ( stroker->first_point )
+          stroker->angle_in = angle_in;
+
         ft_conic_split( arc );
         arc += 2;
         continue;
@@ -1230,32 +1400,54 @@
       {
         first_arc = FALSE;
 
-        start_angle = angle_in;
-
         /* process corner if necessary */
         if ( stroker->first_point )
-          error = ft_stroker_subpath_start( stroker, start_angle );
+          error = ft_stroker_subpath_start( stroker, angle_in, 0 );
         else
         {
-          stroker->angle_out = start_angle;
-          error = ft_stroker_process_corner( stroker );
+          stroker->angle_out = angle_in;
+          error = ft_stroker_process_corner( stroker, 0 );
         }
       }
+      else if ( ft_pos_abs( FT_Angle_Diff( stroker->angle_in, angle_in ) ) >
+                  FT_SMALL_CONIC_THRESHOLD / 4                             )
+      {
+        /* if the deviation from one arc to the next is too great, */
+        /* add a round corner                                      */
+        stroker->center    = arc[2];
+        stroker->angle_out = angle_in;
+        stroker->line_join = FT_STROKER_LINEJOIN_ROUND;
+
+        error = ft_stroker_process_corner( stroker, 0 );
+
+        /* reinstate line join style */
+        stroker->line_join = stroker->line_join_saved;
+      }
+
+      if ( error )
+        goto Exit;
 
       /* the arc's angle is small enough; we can add it directly to each */
       /* border                                                          */
       {
-        FT_Vector  ctrl, end;
-        FT_Angle   theta, phi, rotate;
-        FT_Fixed   length;
-        FT_Int     side;
+        FT_Vector        ctrl, end;
+        FT_Angle         theta, phi, rotate, alpha0 = 0;
+        FT_Fixed         length;
+        FT_StrokeBorder  border;
+        FT_Int           side;
 
 
         theta  = FT_Angle_Diff( angle_in, angle_out ) / 2;
         phi    = angle_in + theta;
         length = FT_DivFix( stroker->radius, FT_Cos( theta ) );
 
-        for ( side = 0; side <= 1; side++ )
+        /* compute direction of original arc */
+        if ( stroker->handle_wide_strokes )
+          alpha0 = FT_Atan2( arc[0].x - arc[2].x, arc[0].y - arc[2].y );
+
+        for ( border = stroker->borders, side = 0;
+              side <= 1;
+              side++, border++ )
         {
           rotate = FT_SIDE_TO_ROTATE( side );
 
@@ -1269,8 +1461,70 @@
           end.x += arc[0].x;
           end.y += arc[0].y;
 
-          error = ft_stroke_border_conicto( stroker->borders + side,
-                                            &ctrl, &end );
+          if ( stroker->handle_wide_strokes )
+          {
+            FT_Vector  start;
+            FT_Angle   alpha1;
+
+
+            /* determine whether the border radius is greater than the */
+            /* radius of curvature of the original arc                 */
+            start = border->points[border->num_points - 1];
+
+            alpha1 = FT_Atan2( end.x - start.x, end.y - start.y );
+
+            /* is the direction of the border arc opposite to */
+            /* that of the original arc? */
+            if ( ft_pos_abs( FT_Angle_Diff( alpha0, alpha1 ) ) >
+                   FT_ANGLE_PI / 2                             )
+            {
+              FT_Angle   beta, gamma;
+              FT_Vector  bvec, delta;
+              FT_Fixed   blen, sinA, sinB, alen;
+
+
+              /* use the sine rule to find the intersection point */
+              beta  = FT_Atan2( arc[2].x - start.x, arc[2].y - start.y );
+              gamma = FT_Atan2( arc[0].x - end.x,   arc[0].y - end.y );
+
+              bvec.x = end.x - start.x;
+              bvec.y = end.y - start.y;
+
+              blen = FT_Vector_Length( &bvec );
+
+              sinA = ft_pos_abs( FT_Sin( alpha1 - gamma ) );
+              sinB = ft_pos_abs( FT_Sin( beta - gamma ) );
+
+              alen = FT_DivFix( FT_MulFix( blen, sinA ), sinB );
+
+              FT_Vector_From_Polar( &delta, alen, beta );
+              delta.x += start.x;
+              delta.y += start.y;
+
+              /* circumnavigate the negative sector backwards */
+              border->movable = FALSE;
+              error = ft_stroke_border_lineto( border, &delta, FALSE );
+              if ( error )
+                goto Exit;
+              error = ft_stroke_border_lineto( border, &end, FALSE );
+              if ( error )
+                goto Exit;
+              error = ft_stroke_border_conicto( border, &ctrl, &start );
+              if ( error )
+                goto Exit;
+              /* and then move to the endpoint */
+              error = ft_stroke_border_lineto( border, &end, FALSE );
+              if ( error )
+                goto Exit;
+
+              continue;
+            }
+
+            /* else fall through */
+          }
+
+          /* simply add an arc */
+          error = ft_stroke_border_conicto( border, &ctrl, &end );
           if ( error )
             goto Exit;
         }
@@ -1278,8 +1532,7 @@
 
       arc -= 2;
 
-      if ( arc < bez_stack )
-        stroker->angle_in = angle_out;
+      stroker->angle_in = angle_out;
     }
 
     stroker->center = *to;
@@ -1301,10 +1554,22 @@
     FT_Vector   bez_stack[37];
     FT_Vector*  arc;
     FT_Vector*  limit = bez_stack + 32;
-    FT_Angle    start_angle;
     FT_Bool     first_arc = TRUE;
 
 
+    /* if all control points are coincident, this is a no-op; */
+    /* avoid creating a spurious corner */
+    if ( FT_IS_SMALL( stroker->center.x - control1->x ) &&
+         FT_IS_SMALL( stroker->center.y - control1->y ) &&
+         FT_IS_SMALL( control1->x       - control2->x ) &&
+         FT_IS_SMALL( control1->y       - control2->y ) &&
+         FT_IS_SMALL( control2->x       - to->x       ) &&
+         FT_IS_SMALL( control2->y       - to->y       ) )
+    {
+       stroker->center = *to;
+       goto Exit;
+    }
+
     arc    = bez_stack;
     arc[0] = *to;
     arc[1] = *control2;
@@ -1316,13 +1581,16 @@
       FT_Angle  angle_in, angle_mid, angle_out;
 
 
-      /* remove compiler warnings */
-      angle_in = angle_out = angle_mid = 0;
+      /* initialize with current direction */
+      angle_in = angle_out = angle_mid = stroker->angle_in;
 
       if ( arc < limit                                         &&
            !ft_cubic_is_small_enough( arc, &angle_in,
                                       &angle_mid, &angle_out ) )
       {
+        if ( stroker->first_point )
+          stroker->angle_in = angle_in;
+
         ft_cubic_split( arc );
         arc += 3;
         continue;
@@ -1333,36 +1601,56 @@
         first_arc = FALSE;
 
         /* process corner if necessary */
-        start_angle = angle_in;
-
         if ( stroker->first_point )
-          error = ft_stroker_subpath_start( stroker, start_angle );
+          error = ft_stroker_subpath_start( stroker, angle_in, 0 );
         else
         {
-          stroker->angle_out = start_angle;
-          error = ft_stroker_process_corner( stroker );
+          stroker->angle_out = angle_in;
+          error = ft_stroker_process_corner( stroker, 0 );
         }
-        if ( error )
-          goto Exit;
+      }
+      else if ( ft_pos_abs( FT_Angle_Diff( stroker->angle_in, angle_in ) ) >
+                  FT_SMALL_CUBIC_THRESHOLD / 4                             )
+      {
+        /* if the deviation from one arc to the next is too great, */
+        /* add a round corner                                      */
+        stroker->center    = arc[3];
+        stroker->angle_out = angle_in;
+        stroker->line_join = FT_STROKER_LINEJOIN_ROUND;
+
+        error = ft_stroker_process_corner( stroker, 0 );
+
+        /* reinstate line join style */
+        stroker->line_join = stroker->line_join_saved;
       }
 
+      if ( error )
+        goto Exit;
+
       /* the arc's angle is small enough; we can add it directly to each */
       /* border                                                          */
       {
-        FT_Vector  ctrl1, ctrl2, end;
-        FT_Angle   theta1, phi1, theta2, phi2, rotate;
-        FT_Fixed   length1, length2;
-        FT_Int     side;
+        FT_Vector        ctrl1, ctrl2, end;
+        FT_Angle         theta1, phi1, theta2, phi2, rotate, alpha0 = 0;
+        FT_Fixed         length1, length2;
+        FT_StrokeBorder  border;
+        FT_Int           side;
 
 
-        theta1  = ft_pos_abs( angle_mid - angle_in ) / 2;
-        theta2  = ft_pos_abs( angle_out - angle_mid ) / 2;
-        phi1    = (angle_mid + angle_in ) / 2;
-        phi2    = (angle_mid + angle_out ) / 2;
+        theta1  = FT_Angle_Diff( angle_in,  angle_mid ) / 2;
+        theta2  = FT_Angle_Diff( angle_mid, angle_out ) / 2;
+        phi1    = ft_angle_mean( angle_in,  angle_mid );
+        phi2    = ft_angle_mean( angle_mid, angle_out );
         length1 = FT_DivFix( stroker->radius, FT_Cos( theta1 ) );
         length2 = FT_DivFix( stroker->radius, FT_Cos( theta2 ) );
 
-        for ( side = 0; side <= 1; side++ )
+        /* compute direction of original arc */
+        if ( stroker->handle_wide_strokes )
+          alpha0 = FT_Atan2( arc[0].x - arc[3].x, arc[0].y - arc[3].y );
+
+        for ( border = stroker->borders, side = 0;
+              side <= 1;
+              side++, border++ )
         {
           rotate = FT_SIDE_TO_ROTATE( side );
 
@@ -1380,16 +1668,81 @@
           end.x += arc[0].x;
           end.y += arc[0].y;
 
-          error = ft_stroke_border_cubicto( stroker->borders + side,
-                                            &ctrl1, &ctrl2, &end );
+          if ( stroker->handle_wide_strokes )
+          {
+            FT_Vector  start;
+            FT_Angle   alpha1;
+
+
+            /* determine whether the border radius is greater than the */
+            /* radius of curvature of the original arc                 */
+            start = border->points[border->num_points - 1];
+
+            alpha1 = FT_Atan2( end.x - start.x, end.y - start.y );
+
+            /* is the direction of the border arc opposite to */
+            /* that of the original arc? */
+            if ( ft_pos_abs( FT_Angle_Diff( alpha0, alpha1 ) ) >
+                   FT_ANGLE_PI / 2                             )
+            {
+              FT_Angle   beta, gamma;
+              FT_Vector  bvec, delta;
+              FT_Fixed   blen, sinA, sinB, alen;
+
+
+              /* use the sine rule to find the intersection point */
+              beta  = FT_Atan2( arc[3].x - start.x, arc[3].y - start.y );
+              gamma = FT_Atan2( arc[0].x - end.x,   arc[0].y - end.y );
+
+              bvec.x = end.x - start.x;
+              bvec.y = end.y - start.y;
+
+              blen = FT_Vector_Length( &bvec );
+
+              sinA = ft_pos_abs( FT_Sin( alpha1 - gamma ) );
+              sinB = ft_pos_abs( FT_Sin( beta - gamma ) );
+
+              alen = FT_DivFix( FT_MulFix( blen, sinA ), sinB );
+
+              FT_Vector_From_Polar( &delta, alen, beta );
+              delta.x += start.x;
+              delta.y += start.y;
+
+              /* circumnavigate the negative sector backwards */
+              border->movable = FALSE;
+              error = ft_stroke_border_lineto( border, &delta, FALSE );
+              if ( error )
+                goto Exit;
+              error = ft_stroke_border_lineto( border, &end, FALSE );
+              if ( error )
+                goto Exit;
+              error = ft_stroke_border_cubicto( border,
+                                                &ctrl2,
+                                                &ctrl1,
+                                                &start );
+              if ( error )
+                goto Exit;
+              /* and then move to the endpoint */
+              error = ft_stroke_border_lineto( border, &end, FALSE );
+              if ( error )
+                goto Exit;
+
+              continue;
+            }
+
+            /* else fall through */
+          }
+
+          /* simply add an arc */
+          error = ft_stroke_border_cubicto( border, &ctrl1, &ctrl2, &end );
           if ( error )
             goto Exit;
         }
       }
 
       arc -= 3;
-      if ( arc < bez_stack )
-        stroker->angle_in = angle_out;
+
+      stroker->angle_in = angle_out;
     }
 
     stroker->center = *to;
@@ -1414,9 +1767,21 @@
     stroker->center       = *to;
     stroker->subpath_open = open;
 
+    /* Determine if we need to check whether the border radius is greater */
+    /* than the radius of curvature of a curve, to handle this case       */
+    /* specially.  This is only required if bevel joins or butt caps may  */
+    /* be created, because round & miter joins and round & square caps    */
+    /* cover the negative sector created with wide strokes.               */
+    stroker->handle_wide_strokes =
+      FT_BOOL( stroker->line_join != FT_STROKER_LINEJOIN_ROUND  ||
+               ( stroker->subpath_open                        &&
+                 stroker->line_cap == FT_STROKER_LINECAP_BUTT ) );
+
     /* record the subpath start point for each border */
     stroker->subpath_start = *to;
 
+    stroker->angle_in = 0;
+
     return FT_Err_Ok;
   }
 
@@ -1446,6 +1811,7 @@
         FT_Vector*  src_point = left->points  + left->num_points - 1;
         FT_Byte*    src_tag   = left->tags    + left->num_points - 1;
 
+
         while ( src_point >= left->points + left->start )
         {
           *dst_point = *src_point;
@@ -1455,14 +1821,14 @@
             dst_tag[0] &= ~FT_STROKE_TAG_BEGIN_END;
           else
           {
-            FT_Byte  ttag = (FT_Byte)( dst_tag[0] & FT_STROKE_TAG_BEGIN_END );
+            FT_Byte  ttag =
+                       (FT_Byte)( dst_tag[0] & FT_STROKE_TAG_BEGIN_END );
 
 
             /* switch begin/end tags if necessary */
             if ( ttag == FT_STROKE_TAG_BEGIN ||
                  ttag == FT_STROKE_TAG_END   )
               dst_tag[0] ^= FT_STROKE_TAG_BEGIN_END;
-
           }
 
           src_point--;
@@ -1497,6 +1863,7 @@
     {
       FT_StrokeBorder  right = stroker->borders;
 
+
       /* All right, this is an opened path, we need to add a cap between */
       /* right & left, add the reverse of left, then add a final cap     */
       /* between left & right.                                           */
@@ -1525,13 +1892,14 @@
       FT_Angle  turn;
       FT_Int    inside_side;
 
+
       /* close the path if needed */
       if ( stroker->center.x != stroker->subpath_start.x ||
            stroker->center.y != stroker->subpath_start.y )
       {
-        error = FT_Stroker_LineTo( stroker, &stroker->subpath_start );
-        if ( error )
-          goto Exit;
+         error = FT_Stroker_LineTo( stroker, &stroker->subpath_start );
+         if ( error )
+           goto Exit;
       }
 
       /* process the corner */
@@ -1549,19 +1917,23 @@
         if ( turn < 0 )
           inside_side = 1;
 
-        error = ft_stroker_inside( stroker, inside_side );
+        error = ft_stroker_inside( stroker,
+                                   inside_side,
+                                   stroker->subpath_line_length );
         if ( error )
           goto Exit;
 
         /* process the outside side */
-        error = ft_stroker_outside( stroker, 1 - inside_side );
+        error = ft_stroker_outside( stroker,
+                                    1 - inside_side,
+                                    stroker->subpath_line_length );
         if ( error )
           goto Exit;
       }
 
       /* then end our two subpaths */
-      ft_stroke_border_close( stroker->borders + 0, TRUE );
-      ft_stroke_border_close( stroker->borders + 1, FALSE );
+      ft_stroke_border_close( stroker->borders + 0, FALSE );
+      ft_stroke_border_close( stroker->borders + 1, TRUE );
     }
 
   Exit:
@@ -1683,9 +2055,9 @@
 
     FT_Error    error;
 
-    FT_Int   n;         /* index of contour in outline     */
-    FT_UInt  first;     /* index of first point in contour */
-    FT_Int   tag;       /* current point's state           */
+    FT_Int      n;         /* index of contour in outline     */
+    FT_UInt     first;     /* index of first point in contour */
+    FT_Int      tag;       /* current point's state           */
 
 
     if ( !outline || !stroker )
@@ -1866,9 +2238,10 @@
     return FT_Err_Invalid_Outline;
   }
 
-/* declare an extern to access ft_outline_glyph_class global allocated 
-   in ftglyph.c, and use the FT_OUTLINE_GLYPH_CLASS_GET macro to access 
-   it when FT_CONFIG_OPTION_PIC is defined */
+
+  /* declare an extern to access `ft_outline_glyph_class' globally     */
+  /* allocated  in `ftglyph.c', and use the FT_OUTLINE_GLYPH_CLASS_GET */
+  /* macro to access it when FT_CONFIG_OPTION_PIC is defined           */
 #ifndef FT_CONFIG_OPTION_PIC
   extern const FT_Glyph_Class  ft_outline_glyph_class;
 #endif
@@ -1882,10 +2255,12 @@
                    FT_Stroker   stroker,
                    FT_Bool      destroy )
   {
-    FT_Error  error = FT_Err_Invalid_Argument;
-    FT_Glyph  glyph = NULL;
-    FT_Library library = stroker->library;
-    FT_UNUSED(library);
+    FT_Error    error   = FT_Err_Invalid_Argument;
+    FT_Glyph    glyph   = NULL;
+    FT_Library  library = stroker->library;
+
+    FT_UNUSED( library );
+
 
     if ( pglyph == NULL )
       goto Exit;
@@ -1906,7 +2281,7 @@
     }
 
     {
-      FT_OutlineGlyph  oglyph  = (FT_OutlineGlyph) glyph;
+      FT_OutlineGlyph  oglyph  = (FT_OutlineGlyph)glyph;
       FT_Outline*      outline = &oglyph->outline;
       FT_UInt          num_points, num_contours;
 
@@ -1956,10 +2331,12 @@
                          FT_Bool      inside,
                          FT_Bool      destroy )
   {
-    FT_Error  error = FT_Err_Invalid_Argument;
-    FT_Glyph  glyph = NULL;
-    FT_Library library = stroker->library;
-    FT_UNUSED(library);
+    FT_Error    error   = FT_Err_Invalid_Argument;
+    FT_Glyph    glyph   = NULL;
+    FT_Library  library = stroker->library;
+
+    FT_UNUSED( library );
+
 
     if ( pglyph == NULL )
       goto Exit;
@@ -1980,7 +2357,7 @@
     }
 
     {
-      FT_OutlineGlyph   oglyph  = (FT_OutlineGlyph) glyph;
+      FT_OutlineGlyph   oglyph  = (FT_OutlineGlyph)glyph;
       FT_StrokerBorder  border;
       FT_Outline*       outline = &oglyph->outline;
       FT_UInt           num_points, num_contours;