ref: e0a9a93330d3057ddf532205709ba4e1423b2557
parent: d38ba0c92d7c07e8a187a501c0e923e507c7bda6
author: Graham Asher <[email protected]>
date: Mon Sep 20 05:29:23 EDT 2010
[smooth] Fix and improve spline flattening. This fixes the flattening of cubic, S-shaped curves and speeds up the handling of both the conic and cubic arcs. See the discussions on the freetype-devel mailing list in late August and September 2010 for details. * src/smooth/ftgrays.c (FT_MAX_CURVE_DEVIATION): New macro. (TWorker): Remove `conic_level' and `cubic_level' elements. (gray_render_conic): Simplify algorithm. (gray_render_cubic): New algorithm; details are given in the code comments. (gray_convert_glyph): Remove heuristics.
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,21 @@
+2010-09-20 Graham Asher <[email protected]>
+ David Bevan <[email protected]>
+
+ [smooth] Fix and improve spline flattening.
+
+ This fixes the flattening of cubic, S-shaped curves and speeds up
+ the handling of both the conic and cubic arcs.
+
+ See the discussions on the freetype-devel mailing list in late
+ August and September 2010 for details.
+
+ * src/smooth/ftgrays.c (FT_MAX_CURVE_DEVIATION): New macro.
+ (TWorker): Remove `conic_level' and `cubic_level' elements.
+ (gray_render_conic): Simplify algorithm.
+ (gray_render_cubic): New algorithm; details are given in the code
+ comments.
+ (gray_convert_glyph): Remove heuristics.
+
2010-09-19 Werner Lemberg <[email protected]>
Minor fixes.
--- a/src/smooth/ftgrays.c
+++ b/src/smooth/ftgrays.c
@@ -91,6 +91,11 @@
#define FT_COMPONENT trace_smooth
+ /* The maximum distance of a curve from the chord, in 64ths of a pixel; */
+ /* used when flattening curves. */
+#define FT_MAX_CURVE_DEVIATION 16
+
+
#ifdef _STANDALONE_
@@ -187,7 +192,7 @@
shift_, \
delta_ \
};
-
+
#define FT_DEFINE_RASTER_FUNCS( class_, glyph_format_, \
raster_new_, raster_reset_, \
raster_set_mode_, raster_render_, \
@@ -354,8 +359,6 @@
int band_size;
int band_shoot;
- int conic_level;
- int cubic_level;
ft_jmp_buf jump_buffer;
@@ -888,33 +891,20 @@
if ( dx < dy )
dx = dy;
+ if ( dx <= FT_MAX_CURVE_DEVIATION )
+ {+ gray_render_line( RAS_VAR_ UPSCALE( to->x ), UPSCALE( to->y ) );
+ return;
+ }
+
level = 1;
- dx = dx / ras.conic_level;
- while ( dx > 0 )
+ dx /= FT_MAX_CURVE_DEVIATION;
+ while ( dx > 1 )
{dx >>= 2;
level++;
}
- /* a shortcut to speed things up */
- if ( level <= 1 )
- {- /* we compute the mid-point directly in order to avoid */
- /* calling gray_split_conic() */
- TPos to_x, to_y, mid_x, mid_y;
-
-
- to_x = UPSCALE( to->x );
- to_y = UPSCALE( to->y );
- mid_x = ( ras.x + to_x + 2 * UPSCALE( control->x ) ) / 4;
- mid_y = ( ras.y + to_y + 2 * UPSCALE( control->y ) ) / 4;
-
- gray_render_line( RAS_VAR_ mid_x, mid_y );
- gray_render_line( RAS_VAR_ to_x, to_y );
-
- return;
- }
-
arc = ras.bez_stack;
levels = ras.lev_stack;
top = 0;
@@ -957,21 +947,9 @@
}
Draw:
- {- TPos to_x, to_y, mid_x, mid_y;
-
-
- to_x = arc[0].x;
- to_y = arc[0].y;
- mid_x = ( ras.x + to_x + 2 * arc[1].x ) / 4;
- mid_y = ( ras.y + to_y + 2 * arc[1].y ) / 4;
-
- gray_render_line( RAS_VAR_ mid_x, mid_y );
- gray_render_line( RAS_VAR_ to_x, to_y );
-
- top--;
- arc -= 2;
- }
+ gray_render_line( RAS_VAR_ arc[0].x, arc[0].y );
+ top--;
+ arc -= 2;
}
return;
@@ -1011,56 +989,9 @@
const FT_Vector* control2,
const FT_Vector* to )
{- int top, level;
- int* levels;
FT_Vector* arc;
- int mid_x = ( DOWNSCALE( ras.x ) + to->x +
- 3 * (control1->x + control2->x ) ) / 8;
- int mid_y = ( DOWNSCALE( ras.y ) + to->y +
- 3 * (control1->y + control2->y ) ) / 8;
- TPos dx = DOWNSCALE( ras.x ) + to->x - ( mid_x << 1 );
- TPos dy = DOWNSCALE( ras.y ) + to->y - ( mid_y << 1 );
- if ( dx < 0 )
- dx = -dx;
- if ( dy < 0 )
- dy = -dy;
- if ( dx < dy )
- dx = dy;
-
- level = 1;
- dx /= ras.cubic_level;
- while ( dx > 0 )
- {- dx >>= 2;
- level++;
- }
-
- if ( level <= 1 )
- {- TPos to_x, to_y;
-
-
- to_x = UPSCALE( to->x );
- to_y = UPSCALE( to->y );
-
- /* Recalculation of midpoint is needed only if */
- /* UPSCALE and DOWNSCALE have any effect. */
-
-#if ( PIXEL_BITS != 6 )
- mid_x = ( ras.x + to_x +
- 3 * UPSCALE( control1->x + control2->x ) ) / 8;
- mid_y = ( ras.y + to_y +
- 3 * UPSCALE( control1->y + control2->y ) ) / 8;
-#endif
-
- gray_render_line( RAS_VAR_ mid_x, mid_y );
- gray_render_line( RAS_VAR_ to_x, to_y );
-
- return;
- }
-
arc = ras.bez_stack;
arc[0].x = UPSCALE( to->x );
arc[0].y = UPSCALE( to->y );
@@ -1071,60 +1002,123 @@
arc[3].x = ras.x;
arc[3].y = ras.y;
- levels = ras.lev_stack;
- top = 0;
- levels[0] = level;
-
- while ( top >= 0 )
+ for (;;)
{- level = levels[top];
- if ( level > 1 )
- {- /* check that the arc crosses the current band */
- TPos min, max, y;
+ /* Check that the arc crosses the current band. */
+ TPos min, max, y;
- min = max = arc[0].y;
- y = arc[1].y;
- if ( y < min ) min = y;
- if ( y > max ) max = y;
- y = arc[2].y;
- if ( y < min ) min = y;
- if ( y > max ) max = y;
- y = arc[3].y;
- if ( y < min ) min = y;
- if ( y > max ) max = y;
- if ( TRUNC( min ) >= ras.max_ey || TRUNC( max ) < 0 )
- goto Draw;
- gray_split_cubic( arc );
- arc += 3;
- top ++;
- levels[top] = levels[top - 1] = level - 1;
- continue;
- }
+ min = max = arc[0].y;
- Draw:
+ y = arc[1].y;
+ if ( y < min )
+ min = y;
+ if ( y > max )
+ max = y;
+
+ y = arc[2].y;
+ if ( y < min )
+ min = y;
+ if ( y > max )
+ max = y;
+
+ y = arc[3].y;
+ if ( y < min )
+ min = y;
+ if ( y > max )
+ max = y;
+
+ if ( TRUNC( min ) >= ras.max_ey || TRUNC( max ) < 0 )
+ goto Draw;
+
+ /* Decide whether to split or draw. See `Rapid Termination */
+ /* Evaluation for Recursive Subdivision of Bezier Curves' by Thomas */
+ /* F. Hain, at */
+ /* http://www.cis.southalabama.edu/~hain/general/Publications/Bezier/Camera-ready%20CISST02%202.pdf */
+
{- TPos to_x, to_y;
+ TPos dx, dy, dx_, dy_;
+ TPos dx1, dy1, dx2, dy2;
+ TPos L, s, s_limit;
- to_x = arc[0].x;
- to_y = arc[0].y;
- mid_x = ( ras.x + to_x + 3 * ( arc[1].x + arc[2].x ) ) / 8;
- mid_y = ( ras.y + to_y + 3 * ( arc[1].y + arc[2].y ) ) / 8;
+ /* dx and dy are x and y components of the P0-P3 chord vector. */
+ dx = arc[3].x - arc[0].x;
+ dy = arc[3].y - arc[0].y;
- gray_render_line( RAS_VAR_ mid_x, mid_y );
- gray_render_line( RAS_VAR_ to_x, to_y );
- top --;
- arc -= 3;
+ /* L is an (under)estimate of the Euclidean distance P0-P3. */
+ /* */
+ /* If dx >= dy, then r = sqrt(dx^2 + dy^2) can be overestimated */
+ /* with least maximum error by */
+ /* */
+ /* r_upperbound = dx + (sqrt(2) - 1) * dy , */
+ /* */
+ /* where sqrt(2) - 1 can be (over)estimated by 107/256, giving an */
+ /* error of no more than 8.4%. */
+ /* */
+ /* Similarly, some elementary calculus shows that r can be */
+ /* underestimated with least maximum error by */
+ /* */
+ /* r_lowerbound = sqrt(2 + sqrt(2)) / 2 * dx */
+ /* + sqrt(2 - sqrt(2)) / 2 * dy . */
+ /* */
+ /* 236/256 and 97/256 are (under)estimates of the two algebraic */
+ /* numbers, giving an error of no more than 8.1%. */
+
+ dx_ = FT_ABS( dx );
+ dy_ = FT_ABS( dy );
+ L = ( 236 * FT_MAX( dx_, dy_ ) + 97 * FT_MIN( dx_, dy_ ) ) >> 8;
+
+ /* Avoid possible arithmetic overflow below by splitting. */
+ if ( L > 32767 )
+ goto Split;
+
+ /* Max deviation may be as much as (s/L) * 3/4 (if Hain's v = 1). */
+ s_limit = L * (TPos)( FT_MAX_CURVE_DEVIATION / 0.75 );
+
+ /* s is L * the perpendicular distance from P1 to the line P0-P3. */
+ dx1 = arc[1].x - arc[0].x;
+ dy1 = arc[1].y - arc[0].y;
+ s = FT_ABS( dy * dx1 - dx * dy1 );
+
+ if ( s > s_limit )
+ goto Split;
+
+ /* s is L * the perpendicular distance from P2 to the line P0-P3. */
+ dx2 = arc[2].x - arc[0].x;
+ dy2 = arc[2].y - arc[0].y;
+ s = FT_ABS( dy * dx2 - dx * dy2 );
+
+ if ( s > s_limit )
+ goto Split;
+
+ /* If P1 or P2 is outside P0-P3, split the curve. */
+ if ( dy * dy1 + dx * dx1 < 0 ||
+ dy * dy2 + dx * dx2 < 0 ||
+ dy * (arc[3].y - arc[1].y) + dx * (arc[3].x - arc[1].x) < 0 ||
+ dy * (arc[3].y - arc[2].y) + dx * (arc[3].x - arc[2].x) < 0 )
+ goto Split;
+
+ /* No reason to split. */
+ goto Draw;
}
- }
- return;
- }
+ Split:
+ gray_split_cubic( arc );
+ arc += 3;
+ continue;
+ Draw:
+ gray_render_line( RAS_VAR_ arc[0].x, arc[0].y );
+ if ( arc == ras.bez_stack )
+ return;
+ arc -= 3;
+ }
+ }
+
+
static int
gray_move_to( const FT_Vector* to,
PWorker worker )
@@ -1759,25 +1753,6 @@
ras.count_ex = ras.max_ex - ras.min_ex;
ras.count_ey = ras.max_ey - ras.min_ey;
-
- /* simple heuristic used to speed up the bezier decomposition -- see */
- /* the code in gray_render_conic() and gray_render_cubic() for more */
- /* details */
- ras.conic_level = 32;
- ras.cubic_level = 16;
-
- {- int level = 0;
-
-
- if ( ras.count_ex > 24 || ras.count_ey > 24 )
- level++;
- if ( ras.count_ex > 120 || ras.count_ey > 120 )
- level++;
-
- ras.conic_level <<= level;
- ras.cubic_level <<= level;
- }
/* set up vertical bands */
num_bands = (int)( ( ras.max_ey - ras.min_ey ) / ras.band_size );