Improve flat corner definition.

* include/internal/ftcalc.h (FT_HYPOT): Macro to approximate Euclidean
distance with the alpha max plus beta min algorithm.
* src/base/ftcalc.c (ft_corner_is_flat): Use it instead of Taxicab metric.

ChangeLog

@@ -1,3 +1,12 @@
+2014-10-25  Alexei Podtelezhnikov  <apodtele@gmail.com>
+
+	Improve flat corner definition.
+
+	* include/internal/ftcalc.h (FT_HYPOT): Macro to approximate Euclidean
+	distance with the alpha max plus beta min algorithm.
+	* src/base/ftcalc.c (ft_corner_is_flat): Use it instead of Taxicab
+	metric.
+
 2014-10-23  David Weiß  <David.Weiss@ptvgroup.com>
 
 	[build] Improve property file for vc2010.

include/internal/ftcalc.h

@@ -311,10 +311,11 @@ FT_BEGIN_HEADER
                          FT_Pos  out_x,
                          FT_Pos  out_y );
 
+
   /*
    *  Return TRUE if a corner is flat or nearly flat.  This is equivalent to
-   *  saying that the angle difference between the `in' and `out' vectors is
-   *  very small.
+   *  saying that the corner point is close to its neighbors, or inside an 
+   *  ellipse defined by the neighbor focal points to be more precise.
    */
   FT_BASE( FT_Int )
   ft_corner_is_flat( FT_Pos  in_x,
@@ -361,6 +362,15 @@ FT_BEGIN_HEADER
             FT_Fixed  y );
 
 
+  /*
+   *  Approximate sqrt(x*x+y*y) using alpha max plus beta min algorithm. 
+   */  
+#define FT_HYPOT( x, y )                      \
+          ( x = FT_ABS( x ), y = FT_ABS( y ), \
+            x > y ? x + ( 3 * y >> 3 )        \
+                  : y + ( 3 * x >> 3 ) )
+
+
 #if 0
 
   /*************************************************************************/

src/base/ftcalc.c

@@ -858,6 +858,8 @@
                      FT_Pos  out_x,
                      FT_Pos  out_y )
   {
+#if 0
+
     FT_Pos  ax = in_x;
     FT_Pos  ay = in_y;
 
@@ -902,6 +904,27 @@
       ay = -ay;
     d_corner = ax + ay;  /* d_corner = || in + out || */
 
+#else
+
+    FT_Pos  ax = in_x + out_x;
+    FT_Pos  ay = in_y + out_y;
+
+    FT_Pos  d_in, d_out, d_corner;
+
+    /* The original implementation always returned TRUE      */
+    /* for vectors from the same quadrant dues to additivity */
+    /* of Taxicab metric there. The alpha max plus beta min  */
+    /* algorithm used here is additive within each octant,   */
+    /* so we now reject some near 90-degree corners within   */
+    /* quadrants, consistently with eliptic definition of    */
+    /* flat corner.                                          */
+
+    d_in     = FT_HYPOT(  in_x,  in_y );
+    d_out    = FT_HYPOT( out_x, out_y );
+    d_corner = FT_HYPOT(    ax,    ay );
+
+#endif
+
     /* now do a simple length comparison: */
     /*                                    */
     /*   d_in + d_out < 17/16 d_corner    */