ref: d8632a842edecf4d59349e727ba2df44a714abc8
parent: fe15152ce7eb72079276e4406275acbbbd780214
author: Werner Lemberg <[email protected]>
date: Sat Oct 25 02:28:18 EDT 2014
Improve comments, remove dead code.
--- a/include/internal/ftcalc.h
+++ b/include/internal/ftcalc.h
@@ -363,11 +363,14 @@
/*
- * Approximate sqrt(x*x+y*y) using alpha max plus beta min algorithm.
+ * Approximate sqrt(x*x+y*y) using the `alpha max plus beta min'
+ * algorithm. We use alpha = 1, beta = 3/8, giving us results with a
+ * largest error less than 7% compared to the exact value.
*/
-#define FT_HYPOT( x, y ) \
- ( x = FT_ABS( x ), y = FT_ABS( y ), \
- x > y ? x + ( 3 * y >> 3 ) \
+#define FT_HYPOT( x, y ) \
+ ( x = FT_ABS( x ), \
+ y = FT_ABS( y ), \
+ x > y ? x + ( 3 * y >> 3 ) \
: y + ( 3 * x >> 3 ) )
--- a/src/autofit/afangles.c
+++ b/src/autofit/afangles.c
@@ -20,66 +20,6 @@
#include "aftypes.h"
-#if 0
-
- FT_LOCAL_DEF( FT_Int )
- af_corner_is_flat( FT_Pos x_in,
- FT_Pos y_in,
- FT_Pos x_out,
- FT_Pos y_out )
- {- FT_Pos ax = x_in;
- FT_Pos ay = y_in;
-
- FT_Pos d_in, d_out, d_corner;
-
-
- if ( ax < 0 )
- ax = -ax;
- if ( ay < 0 )
- ay = -ay;
- d_in = ax + ay;
-
- ax = x_out;
- if ( ax < 0 )
- ax = -ax;
- ay = y_out;
- if ( ay < 0 )
- ay = -ay;
- d_out = ax + ay;
-
- ax = x_out + x_in;
- if ( ax < 0 )
- ax = -ax;
- ay = y_out + y_in;
- if ( ay < 0 )
- ay = -ay;
- d_corner = ax + ay;
-
- return ( d_in + d_out - d_corner ) < ( d_corner >> 4 );
- }
-
-
- FT_LOCAL_DEF( FT_Int )
- af_corner_orientation( FT_Pos x_in,
- FT_Pos y_in,
- FT_Pos x_out,
- FT_Pos y_out )
- {- FT_Pos delta;
-
-
- delta = x_in * y_out - y_in * x_out;
-
- if ( delta == 0 )
- return 0;
- else
- return 1 - 2 * ( delta < 0 );
- }
-
-#endif /* 0 */
-
-
/*
* We are not using `af_angle_atan' anymore, but we keep the source
* code below just in case...
--- a/src/base/ftcalc.c
+++ b/src/base/ftcalc.c
@@ -858,78 +858,40 @@
FT_Pos out_x,
FT_Pos out_y )
{-#if 0
-
- FT_Pos ax = in_x;
- FT_Pos ay = in_y;
-
- FT_Pos d_in, d_out, d_corner;
-
-
- /* We approximate the Euclidean metric (sqrt(x^2 + y^2)) with */
- /* the Taxicab metric (|x| + |y|), which can be computed much */
- /* faster. If one of the two vectors is much longer than the */
- /* other one, the direction of the shorter vector doesn't */
- /* influence the result any more. */
- /* */
- /* corner */
- /* x---------------------------x */
- /* \ / */
- /* \ / */
- /* in \ / out */
- /* \ / */
- /* o */
- /* Point */
- /* */
-
- if ( ax < 0 )
- ax = -ax;
- if ( ay < 0 )
- ay = -ay;
- d_in = ax + ay; /* d_in = || in || */
-
- ax = out_x;
- if ( ax < 0 )
- ax = -ax;
- ay = out_y;
- if ( ay < 0 )
- ay = -ay;
- d_out = ax + ay; /* d_out = || out || */
-
- ax = out_x + in_x;
- if ( ax < 0 )
- ax = -ax;
- ay = out_y + in_y;
- if ( ay < 0 )
- 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;
+ FT_Pos d_in, d_out, d_hypot;
- /* 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 );
+ /* The idea of this function is to compare the length of the */
+ /* hypotenuse with the `in' and `out' length. The `corner' */
+ /* represented by `in' and `out' is flat if the hypotenuse's */
+ /* length isn't too large. */
+ /* */
+ /* This approach has the advantage that the angle between */
+ /* `in' and `out' is not checked. In case one of the two */
+ /* vectors is `dominant', this is, much larger than the */
+ /* other vector, we thus always have a flat corner. */
+ /* */
+ /* hypotenuse */
+ /* x---------------------------x */
+ /* \ / */
+ /* \ / */
+ /* in \ / out */
+ /* \ / */
+ /* o */
+ /* Point */
-#endif
+ d_in = FT_HYPOT( in_x, in_y );
+ d_out = FT_HYPOT( out_x, out_y );
+ d_hypot = FT_HYPOT( ax, ay );
/* now do a simple length comparison: */
/* */
- /* d_in + d_out < 17/16 d_corner */
+ /* d_in + d_out < 17/16 d_hypot */
- return ( d_in + d_out - d_corner ) < ( d_corner >> 4 );
+ return ( d_in + d_out - d_hypot ) < ( d_hypot >> 4 );
}