Commit 2600ef637ef29bcfceb533e554463b4a1ee96f49
2022-03-04T16:53:27
[sdf] Implement deviation-based splitting for Bezier curves. * src/sdf/ftsdf.c (split_sdf_cubic, split_sdf_shape): Add checks to figure out the deviation of Bezier curves and stop splitting if the curve is flat enough. * src/sdf/ftsdfcommon.h (ONE_PIXEL): New macro.
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diff --git a/src/sdf/ftsdf.c b/src/sdf/ftsdf.c
index f5e5551..fa551ea 100644
--- a/src/sdf/ftsdf.c
+++ b/src/sdf/ftsdf.c
@@ -764,9 +764,9 @@
const FT_26D6_Vec* to,
void* user )
{
- SDF_Shape* shape = ( SDF_Shape* )user;
- SDF_Edge* edge = NULL;
- SDF_Contour* contour = NULL;
+ SDF_Shape* shape = ( SDF_Shape* )user;
+ SDF_Edge* edge = NULL;
+ SDF_Contour* contour = NULL;
FT_Error error = FT_Err_Ok;
FT_Memory memory = shape->memory;
@@ -1137,23 +1137,38 @@
FT_Int max_splits,
SDF_Edge** out )
{
- FT_Error error = FT_Err_Ok;
- FT_26D6_Vec cpos[7];
- SDF_Edge* left,* right;
+ FT_Error error = FT_Err_Ok;
+ FT_26D6_Vec cpos[7];
+ SDF_Edge* left, *right;
+ const FT_26D6 threshold = ONE_PIXEL / 4;
- if ( !memory || !out )
+ if ( !memory || !out )
{
error = FT_THROW( Invalid_Argument );
goto Exit;
}
- /* split the conic */
+ /* split the cubic */
cpos[0] = control_points[0];
cpos[1] = control_points[1];
cpos[2] = control_points[2];
cpos[3] = control_points[3];
+ /* If the segment is flat enough we won't get any benefit by */
+ /* splitting it further, so we can just stop splitting. */
+ /* */
+ /* Check the deviation of the Bezier curve and stop if it is */
+ /* smaller than the pre-defined `threshold` value. */
+ if ( FT_ABS( 2 * cpos[0].x - 3 * cpos[1].x + cpos[3].x ) < threshold &&
+ FT_ABS( 2 * cpos[0].y - 3 * cpos[1].y + cpos[3].y ) < threshold &&
+ FT_ABS( cpos[0].x - 3 * cpos[2].x + 2 * cpos[3].x ) < threshold &&
+ FT_ABS( cpos[0].y - 3 * cpos[2].y + 2 * cpos[3].y ) < threshold )
+ {
+ split_cubic( cpos );
+ goto Append;
+ }
+
split_cubic( cpos );
/* If max number of splits is done */
@@ -1250,13 +1265,32 @@
/* Subdivide the curve and add it to the list. */
{
FT_26D6_Vec ctrls[3];
+ FT_26D6 dx, dy;
+ FT_UInt num_splits;
ctrls[0] = edge->start_pos;
ctrls[1] = edge->control_a;
ctrls[2] = edge->end_pos;
- error = split_sdf_conic( memory, ctrls, 32, &new_edges );
+ dx = FT_ABS( ctrls[2].x + ctrls[0].x - 2 * ctrls[1].x );
+ dy = FT_ABS( ctrls[2].y + ctrls[0].y - 2 * ctrls[1].y );
+ if ( dx < dy )
+ dx = dy;
+
+ /* Calculate the number of necessary bisections. Each */
+ /* bisection causes a four-fold reduction of the deviation, */
+ /* hence we bisect the Bezier curve until the deviation */
+ /* becomes less than 1/8th of a pixel. For more details */
+ /* check file `ftgrays.c`. */
+ num_splits = 1;
+ while ( dx > ONE_PIXEL / 8 )
+ {
+ dx >>= 2;
+ num_splits <<= 1;
+ }
+
+ error = split_sdf_conic( memory, ctrls, num_splits, &new_edges );
}
break;
diff --git a/src/sdf/ftsdfcommon.h b/src/sdf/ftsdfcommon.h
index c8ea380..af4490b 100644
--- a/src/sdf/ftsdfcommon.h
+++ b/src/sdf/ftsdfcommon.h
@@ -48,6 +48,8 @@ FT_BEGIN_HEADER
#define MIN_SPREAD 2
/* maximum spread supported by the renderer */
#define MAX_SPREAD 32
+ /* pixel size in 26.6 */
+#define ONE_PIXEL ( 1 << 6 )
/**************************************************************************