summaryrefslogtreecommitdiff
path: root/third_party/freetype/src/base/ftstroke.c
diff options
context:
space:
mode:
authorBo Xu <bo_xu@foxitsoftware.com>2014-12-19 14:29:17 -0800
committerBo Xu <bo_xu@foxitsoftware.com>2014-12-19 14:29:17 -0800
commite4fc5ced45c8fcfbe2487ec64eab036bc7d57602 (patch)
tree1889eac2d57ff76d5f0fef689a3cbdfa37a0b3f4 /third_party/freetype/src/base/ftstroke.c
parent5a35129bce7ca777e155e5498e8d4792fa6a4819 (diff)
downloadpdfium-e4fc5ced45c8fcfbe2487ec64eab036bc7d57602.tar.xz
Update freetype to 2.5.4.
Put freetype into third_party directory, cleaning up header files. Previously freetype header files are in core/src/fxge/freetype and core/include/thirdparties. There were also multiple fx_freetype.h. This patch removes the additional Foxit wrapper to make further update easier. Notice, for original freetype source code, the following files are modified and need to be updated accordingly in future update: third_party/freetype/include/config/ftmodule.h third_party/freetype/include/config/ftoption.h BUG=407341 R=thestig@chromium.org Review URL: https://codereview.chromium.org/815103002
Diffstat (limited to 'third_party/freetype/src/base/ftstroke.c')
-rw-r--r--third_party/freetype/src/base/ftstroke.c2469
1 files changed, 2469 insertions, 0 deletions
diff --git a/third_party/freetype/src/base/ftstroke.c b/third_party/freetype/src/base/ftstroke.c
new file mode 100644
index 0000000000..d123e0274c
--- /dev/null
+++ b/third_party/freetype/src/base/ftstroke.c
@@ -0,0 +1,2469 @@
+/***************************************************************************/
+/* */
+/* ftstroke.c */
+/* */
+/* FreeType path stroker (body). */
+/* */
+/* Copyright 2002-2006, 2008-2011, 2013, 2014 by */
+/* David Turner, Robert Wilhelm, and Werner Lemberg. */
+/* */
+/* This file is part of the FreeType project, and may only be used, */
+/* modified, and distributed under the terms of the FreeType project */
+/* license, LICENSE.TXT. By continuing to use, modify, or distribute */
+/* this file you indicate that you have read the license and */
+/* understand and accept it fully. */
+/* */
+/***************************************************************************/
+
+
+#include <ft2build.h>
+#include FT_STROKER_H
+#include FT_TRIGONOMETRY_H
+#include FT_OUTLINE_H
+#include FT_INTERNAL_MEMORY_H
+#include FT_INTERNAL_DEBUG_H
+#include FT_INTERNAL_OBJECTS_H
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( FT_StrokerBorder )
+ FT_Outline_GetInsideBorder( FT_Outline* outline )
+ {
+ FT_Orientation o = FT_Outline_Get_Orientation( outline );
+
+
+ return o == FT_ORIENTATION_TRUETYPE ? FT_STROKER_BORDER_RIGHT
+ : FT_STROKER_BORDER_LEFT;
+ }
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( FT_StrokerBorder )
+ FT_Outline_GetOutsideBorder( FT_Outline* outline )
+ {
+ FT_Orientation o = FT_Outline_Get_Orientation( outline );
+
+
+ return o == FT_ORIENTATION_TRUETYPE ? FT_STROKER_BORDER_LEFT
+ : FT_STROKER_BORDER_RIGHT;
+ }
+
+
+ /*************************************************************************/
+ /*************************************************************************/
+ /***** *****/
+ /***** BEZIER COMPUTATIONS *****/
+ /***** *****/
+ /*************************************************************************/
+ /*************************************************************************/
+
+#define FT_SMALL_CONIC_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 )
+
+
+ static FT_Pos
+ ft_pos_abs( FT_Pos x )
+ {
+ return x >= 0 ? x : -x;
+ }
+
+
+ static void
+ ft_conic_split( FT_Vector* base )
+ {
+ FT_Pos a, b;
+
+
+ base[4].x = base[2].x;
+ b = base[1].x;
+ a = base[3].x = ( base[2].x + b ) / 2;
+ b = base[1].x = ( base[0].x + b ) / 2;
+ base[2].x = ( a + b ) / 2;
+
+ base[4].y = base[2].y;
+ b = base[1].y;
+ a = base[3].y = ( base[2].y + b ) / 2;
+ b = base[1].y = ( base[0].y + b ) / 2;
+ base[2].y = ( a + b ) / 2;
+ }
+
+
+ static FT_Bool
+ ft_conic_is_small_enough( FT_Vector* base,
+ FT_Angle *angle_in,
+ FT_Angle *angle_out )
+ {
+ FT_Vector d1, d2;
+ FT_Angle theta;
+ FT_Int close1, close2;
+
+
+ d1.x = base[1].x - base[2].x;
+ d1.y = base[1].y - base[2].y;
+ d2.x = base[0].x - base[1].x;
+ d2.y = base[0].y - base[1].y;
+
+ close1 = FT_IS_SMALL( d1.x ) && FT_IS_SMALL( d1.y );
+ close2 = FT_IS_SMALL( d2.x ) && FT_IS_SMALL( d2.y );
+
+ if ( close1 )
+ {
+ if ( close2 )
+ {
+ /* basically a point; */
+ /* do nothing to retain original direction */
+ }
+ else
+ {
+ *angle_in =
+ *angle_out = FT_Atan2( d2.x, d2.y );
+ }
+ }
+ else /* !close1 */
+ {
+ 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 ) );
+
+ return FT_BOOL( theta < FT_SMALL_CONIC_THRESHOLD );
+ }
+
+
+ static void
+ ft_cubic_split( FT_Vector* base )
+ {
+ FT_Pos a, b, c, d;
+
+
+ base[6].x = base[3].x;
+ c = base[1].x;
+ d = base[2].x;
+ base[1].x = a = ( base[0].x + c ) / 2;
+ base[5].x = b = ( base[3].x + d ) / 2;
+ c = ( c + d ) / 2;
+ base[2].x = a = ( a + c ) / 2;
+ base[4].x = b = ( b + c ) / 2;
+ base[3].x = ( a + b ) / 2;
+
+ base[6].y = base[3].y;
+ c = base[1].y;
+ d = base[2].y;
+ base[1].y = a = ( base[0].y + c ) / 2;
+ base[5].y = b = ( base[3].y + d ) / 2;
+ c = ( c + d ) / 2;
+ base[2].y = a = ( a + c ) / 2;
+ base[4].y = b = ( b + c ) / 2;
+ base[3].y = ( a + b ) / 2;
+ }
+
+
+ /* 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,
+ FT_Angle *angle_mid,
+ FT_Angle *angle_out )
+ {
+ FT_Vector d1, d2, d3;
+ FT_Angle theta1, theta2;
+ FT_Int close1, close2, close3;
+
+
+ d1.x = base[2].x - base[3].x;
+ d1.y = base[2].y - base[3].y;
+ d2.x = base[1].x - base[2].x;
+ d2.y = base[1].y - base[2].y;
+ d3.x = base[0].x - base[1].x;
+ d3.y = base[0].y - base[1].y;
+
+ close1 = FT_IS_SMALL( d1.x ) && FT_IS_SMALL( d1.y );
+ close2 = FT_IS_SMALL( d2.x ) && FT_IS_SMALL( d2.y );
+ close3 = FT_IS_SMALL( d3.x ) && FT_IS_SMALL( d3.y );
+
+ if ( close1 )
+ {
+ if ( close2 )
+ {
+ 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 */
+ {
+ 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 /* !close1 */
+ {
+ 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 ) );
+ theta2 = ft_pos_abs( FT_Angle_Diff( *angle_mid, *angle_out ) );
+
+ return FT_BOOL( theta1 < FT_SMALL_CUBIC_THRESHOLD &&
+ theta2 < FT_SMALL_CUBIC_THRESHOLD );
+ }
+
+
+ /*************************************************************************/
+ /*************************************************************************/
+ /***** *****/
+ /***** STROKE BORDERS *****/
+ /***** *****/
+ /*************************************************************************/
+ /*************************************************************************/
+
+ typedef enum FT_StrokeTags_
+ {
+ FT_STROKE_TAG_ON = 1, /* on-curve point */
+ FT_STROKE_TAG_CUBIC = 2, /* cubic off-point */
+ FT_STROKE_TAG_BEGIN = 4, /* sub-path start */
+ FT_STROKE_TAG_END = 8 /* sub-path end */
+
+ } FT_StrokeTags;
+
+#define FT_STROKE_TAG_BEGIN_END ( FT_STROKE_TAG_BEGIN | FT_STROKE_TAG_END )
+
+ typedef struct FT_StrokeBorderRec_
+ {
+ FT_UInt num_points;
+ FT_UInt max_points;
+ FT_Vector* points;
+ FT_Byte* tags;
+ 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;
+
+ } FT_StrokeBorderRec, *FT_StrokeBorder;
+
+
+ static FT_Error
+ ft_stroke_border_grow( FT_StrokeBorder border,
+ FT_UInt new_points )
+ {
+ FT_UInt old_max = border->max_points;
+ FT_UInt new_max = border->num_points + new_points;
+ FT_Error error = FT_Err_Ok;
+
+
+ if ( new_max > old_max )
+ {
+ FT_UInt cur_max = old_max;
+ FT_Memory memory = border->memory;
+
+
+ while ( cur_max < new_max )
+ cur_max += ( cur_max >> 1 ) + 16;
+
+ if ( FT_RENEW_ARRAY( border->points, old_max, cur_max ) ||
+ FT_RENEW_ARRAY( border->tags, old_max, cur_max ) )
+ goto Exit;
+
+ border->max_points = cur_max;
+ }
+
+ Exit:
+ return error;
+ }
+
+
+ static void
+ ft_stroke_border_close( FT_StrokeBorder border,
+ FT_Bool reverse )
+ {
+ FT_UInt start = border->start;
+ FT_UInt count = border->num_points;
+
+
+ FT_ASSERT( border->start >= 0 );
+
+ /* don't record empty paths! */
+ if ( count <= start + 1U )
+ border->num_points = start;
+ else
+ {
+ /* copy the last point to the start of this sub-path, since */
+ /* it contains the `adjusted' starting coordinates */
+ border->num_points = --count;
+ border->points[start] = border->points[count];
+
+ if ( reverse )
+ {
+ /* reverse the points */
+ {
+ FT_Vector* vec1 = border->points + start + 1;
+ FT_Vector* vec2 = border->points + count - 1;
+
+
+ for ( ; vec1 < vec2; vec1++, vec2-- )
+ {
+ FT_Vector tmp;
+
+
+ tmp = *vec1;
+ *vec1 = *vec2;
+ *vec2 = tmp;
+ }
+ }
+
+ /* then the tags */
+ {
+ FT_Byte* tag1 = border->tags + start + 1;
+ FT_Byte* tag2 = border->tags + count - 1;
+
+
+ for ( ; tag1 < tag2; tag1++, tag2-- )
+ {
+ FT_Byte tmp;
+
+
+ tmp = *tag1;
+ *tag1 = *tag2;
+ *tag2 = tmp;
+ }
+ }
+ }
+
+ border->tags[start ] |= FT_STROKE_TAG_BEGIN;
+ border->tags[count - 1] |= FT_STROKE_TAG_END;
+ }
+
+ border->start = -1;
+ border->movable = FALSE;
+ }
+
+
+ static FT_Error
+ ft_stroke_border_lineto( FT_StrokeBorder border,
+ FT_Vector* to,
+ FT_Bool movable )
+ {
+ FT_Error error = FT_Err_Ok;
+
+
+ FT_ASSERT( border->start >= 0 );
+
+ if ( border->movable )
+ {
+ /* move last point */
+ border->points[border->num_points - 1] = *to;
+ }
+ 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 )
+ {
+ FT_Vector* vec = border->points + border->num_points;
+ FT_Byte* tag = border->tags + border->num_points;
+
+
+ vec[0] = *to;
+ tag[0] = FT_STROKE_TAG_ON;
+
+ border->num_points += 1;
+ }
+ }
+ border->movable = movable;
+ return error;
+ }
+
+
+ static FT_Error
+ ft_stroke_border_conicto( FT_StrokeBorder border,
+ FT_Vector* control,
+ FT_Vector* to )
+ {
+ FT_Error error;
+
+
+ FT_ASSERT( border->start >= 0 );
+
+ error = ft_stroke_border_grow( border, 2 );
+ if ( !error )
+ {
+ FT_Vector* vec = border->points + border->num_points;
+ FT_Byte* tag = border->tags + border->num_points;
+
+
+ vec[0] = *control;
+ vec[1] = *to;
+
+ tag[0] = 0;
+ tag[1] = FT_STROKE_TAG_ON;
+
+ border->num_points += 2;
+ }
+
+ border->movable = FALSE;
+
+ return error;
+ }
+
+
+ static FT_Error
+ ft_stroke_border_cubicto( FT_StrokeBorder border,
+ FT_Vector* control1,
+ FT_Vector* control2,
+ FT_Vector* to )
+ {
+ FT_Error error;
+
+
+ FT_ASSERT( border->start >= 0 );
+
+ error = ft_stroke_border_grow( border, 3 );
+ if ( !error )
+ {
+ FT_Vector* vec = border->points + border->num_points;
+ FT_Byte* tag = border->tags + border->num_points;
+
+
+ vec[0] = *control1;
+ vec[1] = *control2;
+ vec[2] = *to;
+
+ tag[0] = FT_STROKE_TAG_CUBIC;
+ tag[1] = FT_STROKE_TAG_CUBIC;
+ tag[2] = FT_STROKE_TAG_ON;
+
+ border->num_points += 3;
+ }
+
+ border->movable = FALSE;
+
+ return error;
+ }
+
+
+#define FT_ARC_CUBIC_ANGLE ( FT_ANGLE_PI / 2 )
+
+
+ static FT_Error
+ ft_stroke_border_arcto( FT_StrokeBorder border,
+ FT_Vector* center,
+ FT_Fixed radius,
+ FT_Angle angle_start,
+ FT_Angle angle_diff )
+ {
+ FT_Angle total, angle, step, rotate, next, theta;
+ FT_Vector a, b, a2, b2;
+ FT_Fixed length;
+ FT_Error error = FT_Err_Ok;
+
+
+ /* compute start point */
+ FT_Vector_From_Polar( &a, radius, angle_start );
+ a.x += center->x;
+ a.y += center->y;
+
+ total = angle_diff;
+ angle = angle_start;
+ rotate = ( angle_diff >= 0 ) ? FT_ANGLE_PI2 : -FT_ANGLE_PI2;
+
+ while ( total != 0 )
+ {
+ step = total;
+ if ( step > FT_ARC_CUBIC_ANGLE )
+ step = FT_ARC_CUBIC_ANGLE;
+
+ else if ( step < -FT_ARC_CUBIC_ANGLE )
+ step = -FT_ARC_CUBIC_ANGLE;
+
+ next = angle + step;
+ theta = step;
+ if ( theta < 0 )
+ theta = -theta;
+
+ theta >>= 1;
+
+ /* compute end point */
+ FT_Vector_From_Polar( &b, radius, next );
+ b.x += center->x;
+ b.y += center->y;
+
+ /* compute first and second control points */
+ length = FT_MulDiv( radius, FT_Sin( theta ) * 4,
+ ( 0x10000L + FT_Cos( theta ) ) * 3 );
+
+ FT_Vector_From_Polar( &a2, length, angle + rotate );
+ a2.x += a.x;
+ a2.y += a.y;
+
+ FT_Vector_From_Polar( &b2, length, next - rotate );
+ b2.x += b.x;
+ b2.y += b.y;
+
+ /* add cubic arc */
+ error = ft_stroke_border_cubicto( border, &a2, &b2, &b );
+ if ( error )
+ break;
+
+ /* process the rest of the arc ?? */
+ a = b;
+ total -= step;
+ angle = next;
+ }
+
+ return error;
+ }
+
+
+ static FT_Error
+ ft_stroke_border_moveto( FT_StrokeBorder border,
+ FT_Vector* to )
+ {
+ /* close current open path if any ? */
+ if ( border->start >= 0 )
+ ft_stroke_border_close( border, FALSE );
+
+ border->start = border->num_points;
+ border->movable = FALSE;
+
+ return ft_stroke_border_lineto( border, to, FALSE );
+ }
+
+
+ static void
+ ft_stroke_border_init( FT_StrokeBorder border,
+ FT_Memory memory )
+ {
+ border->memory = memory;
+ border->points = NULL;
+ border->tags = NULL;
+
+ border->num_points = 0;
+ border->max_points = 0;
+ border->start = -1;
+ border->valid = FALSE;
+ }
+
+
+ static void
+ ft_stroke_border_reset( FT_StrokeBorder border )
+ {
+ border->num_points = 0;
+ border->start = -1;
+ border->valid = FALSE;
+ }
+
+
+ static void
+ ft_stroke_border_done( FT_StrokeBorder border )
+ {
+ FT_Memory memory = border->memory;
+
+
+ FT_FREE( border->points );
+ FT_FREE( border->tags );
+
+ border->num_points = 0;
+ border->max_points = 0;
+ border->start = -1;
+ border->valid = FALSE;
+ }
+
+
+ static FT_Error
+ ft_stroke_border_get_counts( FT_StrokeBorder border,
+ FT_UInt *anum_points,
+ FT_UInt *anum_contours )
+ {
+ FT_Error error = FT_Err_Ok;
+ FT_UInt num_points = 0;
+ FT_UInt num_contours = 0;
+
+ FT_UInt count = border->num_points;
+ FT_Vector* point = border->points;
+ FT_Byte* tags = border->tags;
+ FT_Int in_contour = 0;
+
+
+ for ( ; count > 0; count--, num_points++, point++, tags++ )
+ {
+ if ( tags[0] & FT_STROKE_TAG_BEGIN )
+ {
+ if ( in_contour != 0 )
+ goto Fail;
+
+ in_contour = 1;
+ }
+ else if ( in_contour == 0 )
+ goto Fail;
+
+ if ( tags[0] & FT_STROKE_TAG_END )
+ {
+ in_contour = 0;
+ num_contours++;
+ }
+ }
+
+ if ( in_contour != 0 )
+ goto Fail;
+
+ border->valid = TRUE;
+
+ Exit:
+ *anum_points = num_points;
+ *anum_contours = num_contours;
+ return error;
+
+ Fail:
+ num_points = 0;
+ num_contours = 0;
+ goto Exit;
+ }
+
+
+ static void
+ ft_stroke_border_export( FT_StrokeBorder border,
+ FT_Outline* outline )
+ {
+ /* copy point locations */
+ FT_ARRAY_COPY( outline->points + outline->n_points,
+ border->points,
+ border->num_points );
+
+ /* copy tags */
+ {
+ FT_UInt count = border->num_points;
+ FT_Byte* read = border->tags;
+ FT_Byte* write = (FT_Byte*)outline->tags + outline->n_points;
+
+
+ for ( ; count > 0; count--, read++, write++ )
+ {
+ if ( *read & FT_STROKE_TAG_ON )
+ *write = FT_CURVE_TAG_ON;
+ else if ( *read & FT_STROKE_TAG_CUBIC )
+ *write = FT_CURVE_TAG_CUBIC;
+ else
+ *write = FT_CURVE_TAG_CONIC;
+ }
+ }
+
+ /* copy contours */
+ {
+ FT_UInt count = border->num_points;
+ FT_Byte* tags = border->tags;
+ FT_Short* write = outline->contours + outline->n_contours;
+ FT_Short idx = (FT_Short)outline->n_points;
+
+
+ for ( ; count > 0; count--, tags++, idx++ )
+ {
+ if ( *tags & FT_STROKE_TAG_END )
+ {
+ *write++ = idx;
+ outline->n_contours++;
+ }
+ }
+ }
+
+ outline->n_points = (short)( outline->n_points + border->num_points );
+
+ FT_ASSERT( FT_Outline_Check( outline ) == 0 );
+ }
+
+
+ /*************************************************************************/
+ /*************************************************************************/
+ /***** *****/
+ /***** STROKER *****/
+ /***** *****/
+ /*************************************************************************/
+ /*************************************************************************/
+
+#define FT_SIDE_TO_ROTATE( s ) ( FT_ANGLE_PI2 - (s) * FT_ANGLE_PI )
+
+ typedef struct FT_StrokerRec_
+ {
+ 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;
+
+ FT_StrokeBorderRec borders[2];
+ FT_Library library;
+
+ } FT_StrokerRec;
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( FT_Error )
+ FT_Stroker_New( FT_Library library,
+ FT_Stroker *astroker )
+ {
+ FT_Error error; /* assigned in FT_NEW */
+ FT_Memory memory;
+ FT_Stroker stroker = NULL;
+
+
+ if ( !library )
+ return FT_THROW( Invalid_Library_Handle );
+
+ if ( !astroker )
+ return FT_THROW( Invalid_Argument );
+
+ memory = library->memory;
+
+ if ( !FT_NEW( stroker ) )
+ {
+ stroker->library = library;
+
+ ft_stroke_border_init( &stroker->borders[0], memory );
+ ft_stroke_border_init( &stroker->borders[1], memory );
+ }
+
+ *astroker = stroker;
+
+ return error;
+ }
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( void )
+ FT_Stroker_Set( FT_Stroker stroker,
+ FT_Fixed radius,
+ FT_Stroker_LineCap line_cap,
+ FT_Stroker_LineJoin line_join,
+ FT_Fixed miter_limit )
+ {
+ if ( !stroker )
+ return;
+
+ stroker->radius = radius;
+ stroker->line_cap = line_cap;
+ 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 );
+ }
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( void )
+ FT_Stroker_Rewind( FT_Stroker stroker )
+ {
+ if ( stroker )
+ {
+ ft_stroke_border_reset( &stroker->borders[0] );
+ ft_stroke_border_reset( &stroker->borders[1] );
+ }
+ }
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( void )
+ FT_Stroker_Done( FT_Stroker stroker )
+ {
+ if ( stroker )
+ {
+ FT_Memory memory = stroker->library->memory;
+
+
+ ft_stroke_border_done( &stroker->borders[0] );
+ ft_stroke_border_done( &stroker->borders[1] );
+
+ stroker->library = NULL;
+ FT_FREE( stroker );
+ }
+ }
+
+
+ /* create a circular arc at a corner or cap */
+ static FT_Error
+ ft_stroker_arcto( FT_Stroker stroker,
+ FT_Int side )
+ {
+ FT_Angle total, rotate;
+ FT_Fixed radius = stroker->radius;
+ FT_Error error = FT_Err_Ok;
+ FT_StrokeBorder border = stroker->borders + side;
+
+
+ rotate = FT_SIDE_TO_ROTATE( side );
+
+ total = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
+ if ( total == FT_ANGLE_PI )
+ total = -rotate * 2;
+
+ error = ft_stroke_border_arcto( border,
+ &stroker->center,
+ radius,
+ stroker->angle_in + rotate,
+ total );
+ border->movable = FALSE;
+ return error;
+ }
+
+
+ /* add a cap at the end of an opened path */
+ static FT_Error
+ ft_stroker_cap( FT_Stroker stroker,
+ FT_Angle angle,
+ FT_Int side )
+ {
+ FT_Error error = FT_Err_Ok;
+
+
+ if ( stroker->line_cap == FT_STROKER_LINECAP_ROUND )
+ {
+ /* 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 )
+ {
+ /* add a square cap */
+ FT_Vector delta, delta2;
+ FT_Angle rotate = FT_SIDE_TO_ROTATE( side );
+ FT_Fixed radius = stroker->radius;
+ FT_StrokeBorder border = stroker->borders + side;
+
+
+ FT_Vector_From_Polar( &delta2, radius, angle + rotate );
+ FT_Vector_From_Polar( &delta, radius, angle );
+
+ delta.x += stroker->center.x + delta2.x;
+ delta.y += stroker->center.y + delta2.y;
+
+ error = ft_stroke_border_lineto( border, &delta, FALSE );
+ if ( error )
+ goto Exit;
+
+ FT_Vector_From_Polar( &delta2, radius, angle - rotate );
+ FT_Vector_From_Polar( &delta, radius, angle );
+
+ delta.x += delta2.x + stroker->center.x;
+ delta.y += delta2.y + stroker->center.y;
+
+ error = ft_stroke_border_lineto( border, &delta, FALSE );
+ }
+ else if ( stroker->line_cap == FT_STROKER_LINECAP_BUTT )
+ {
+ /* add a butt ending */
+ FT_Vector delta;
+ FT_Angle rotate = FT_SIDE_TO_ROTATE( side );
+ FT_Fixed radius = stroker->radius;
+ FT_StrokeBorder border = stroker->borders + side;
+
+
+ FT_Vector_From_Polar( &delta, radius, angle + rotate );
+
+ delta.x += stroker->center.x;
+ delta.y += stroker->center.y;
+
+ error = ft_stroke_border_lineto( border, &delta, FALSE );
+ if ( error )
+ goto Exit;
+
+ FT_Vector_From_Polar( &delta, radius, angle - rotate );
+
+ delta.x += stroker->center.x;
+ delta.y += stroker->center.y;
+
+ error = ft_stroke_border_lineto( border, &delta, FALSE );
+ }
+
+ Exit:
+ return error;
+ }
+
+
+ /* process an inside corner, i.e. compute intersection */
+ static FT_Error
+ ft_stroker_inside( FT_Stroker stroker,
+ FT_Int side,
+ FT_Fixed line_length )
+ {
+ FT_StrokeBorder border = stroker->borders + side;
+ FT_Angle phi, theta, rotate;
+ 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 );
+
+ 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
+ {
+ /* compute minimum required length of lines */
+ FT_Fixed min_length = ft_pos_abs( FT_MulFix( stroker->radius,
+ FT_Tan( theta ) ) );
+
+
+ intersect = FT_BOOL( min_length &&
+ stroker->line_length >= min_length &&
+ line_length >= min_length );
+ }
+
+ 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 );
+ delta.x += stroker->center.x;
+ delta.y += stroker->center.y;
+ }
+
+ error = ft_stroke_border_lineto( border, &delta, FALSE );
+
+ return error;
+ }
+
+
+ /* process an outside corner, i.e. compute bevel/miter/round */
+ static FT_Error
+ ft_stroker_outside( FT_Stroker stroker,
+ FT_Int side,
+ FT_Fixed line_length )
+ {
+ FT_StrokeBorder border = stroker->borders + side;
+ FT_Error error;
+ FT_Angle rotate;
+
+
+ if ( stroker->line_join == FT_STROKER_LINEJOIN_ROUND )
+ error = ft_stroker_arcto( stroker, side );
+ else
+ {
+ /* 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 );
+
+ 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 = 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;
+ }
+ }
+
+ if ( bevel ) /* this is a bevel (broken angle) */
+ {
+ if ( fixed_bevel )
+ {
+ /* the outer corners are simply joined together */
+ FT_Vector delta;
+
+
+ /* add bevel */
+ FT_Vector_From_Polar( &delta,
+ radius,
+ stroker->angle_out + rotate );
+ delta.x += stroker->center.x;
+ delta.y += stroker->center.y;
+
+ 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 first angle point */
+ length = FT_MulDiv( radius, 0x10000L - sigma,
+ ft_pos_abs( FT_Sin( theta ) ) );
+
+ 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;
+
+ /* 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;
+
+ /* 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 );
+
+ delta.x += stroker->center.x;
+ delta.y += stroker->center.y;
+
+ error = ft_stroke_border_lineto( border, &delta, FALSE );
+ }
+ }
+ }
+ else /* this is a miter (intersection) */
+ {
+ FT_Fixed length;
+ FT_Vector delta;
+
+
+ length = FT_DivFix( stroker->radius, thcos );
+
+ FT_Vector_From_Polar( &delta, length, phi );
+ delta.x += stroker->center.x;
+ delta.y += stroker->center.y;
+
+ error = ft_stroke_border_lineto( border, &delta, FALSE );
+ if ( error )
+ goto Exit;
+
+ /* 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, FALSE );
+ }
+ }
+ }
+
+ Exit:
+ return error;
+ }
+
+
+ static FT_Error
+ ft_stroker_process_corner( FT_Stroker stroker,
+ FT_Fixed line_length )
+ {
+ FT_Error error = FT_Err_Ok;
+ FT_Angle turn;
+ FT_Int inside_side;
+
+
+ turn = FT_Angle_Diff( stroker->angle_in, stroker->angle_out );
+
+ /* no specific corner processing is required if the turn is 0 */
+ if ( turn == 0 )
+ goto Exit;
+
+ /* when we turn to the right, the inside side is 0 */
+ inside_side = 0;
+
+ /* otherwise, the inside side is 1 */
+ if ( turn < 0 )
+ inside_side = 1;
+
+ /* process the 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, line_length );
+
+ Exit:
+ return error;
+ }
+
+
+ /* add two points to the left and right borders corresponding to the */
+ /* start of the subpath */
+ static FT_Error
+ ft_stroker_subpath_start( FT_Stroker stroker,
+ FT_Angle start_angle,
+ FT_Fixed line_length )
+ {
+ FT_Vector delta;
+ FT_Vector point;
+ FT_Error error;
+ FT_StrokeBorder border;
+
+
+ FT_Vector_From_Polar( &delta, stroker->radius,
+ start_angle + FT_ANGLE_PI2 );
+
+ point.x = stroker->center.x + delta.x;
+ point.y = stroker->center.y + delta.y;
+
+ border = stroker->borders;
+ error = ft_stroke_border_moveto( border, &point );
+ if ( error )
+ goto Exit;
+
+ point.x = stroker->center.x - delta.x;
+ point.y = stroker->center.y - delta.y;
+
+ border++;
+ error = ft_stroke_border_moveto( border, &point );
+
+ /* 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;
+ }
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( FT_Error )
+ FT_Stroker_LineTo( FT_Stroker stroker,
+ FT_Vector* to )
+ {
+ FT_Error error = FT_Err_Ok;
+ FT_StrokeBorder border;
+ FT_Vector delta;
+ FT_Angle angle;
+ FT_Int side;
+ FT_Fixed line_length;
+
+
+ if ( !stroker || !to )
+ return FT_THROW( Invalid_Argument );
+
+ 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 );
+
+ /* process corner if necessary */
+ if ( stroker->first_point )
+ {
+ /* 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, line_length );
+ if ( error )
+ goto Exit;
+ }
+ else
+ {
+ /* process the current corner */
+ stroker->angle_out = angle;
+ 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;
+
+
+ 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;
+
+ delta.x = -delta.x;
+ delta.y = -delta.y;
+ }
+
+ stroker->angle_in = angle;
+ stroker->center = *to;
+ stroker->line_length = line_length;
+
+ Exit:
+ return error;
+ }
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( FT_Error )
+ FT_Stroker_ConicTo( FT_Stroker stroker,
+ FT_Vector* control,
+ FT_Vector* to )
+ {
+ FT_Error error = FT_Err_Ok;
+ FT_Vector bez_stack[34];
+ FT_Vector* arc;
+ FT_Vector* limit = bez_stack + 30;
+ FT_Bool first_arc = TRUE;
+
+
+ if ( !stroker || !control || !to )
+ {
+ error = FT_THROW( Invalid_Argument );
+ goto Exit;
+ }
+
+ /* 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;
+ arc[2] = stroker->center;
+
+ while ( arc >= bez_stack )
+ {
+ FT_Angle angle_in, angle_out;
+
+
+ /* 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;
+ }
+
+ if ( first_arc )
+ {
+ first_arc = FALSE;
+
+ /* process corner if necessary */
+ if ( stroker->first_point )
+ error = ft_stroker_subpath_start( stroker, angle_in, 0 );
+ else
+ {
+ 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, 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 ) );
+
+ /* 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 );
+
+ /* compute control point */
+ FT_Vector_From_Polar( &ctrl, length, phi + rotate );
+ ctrl.x += arc[1].x;
+ ctrl.y += arc[1].y;
+
+ /* compute end point */
+ FT_Vector_From_Polar( &end, stroker->radius, angle_out + rotate );
+ end.x += arc[0].x;
+ end.y += arc[0].y;
+
+ 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_MulDiv( 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;
+ }
+ }
+
+ arc -= 2;
+
+ stroker->angle_in = angle_out;
+ }
+
+ stroker->center = *to;
+
+ Exit:
+ return error;
+ }
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( FT_Error )
+ FT_Stroker_CubicTo( FT_Stroker stroker,
+ FT_Vector* control1,
+ FT_Vector* control2,
+ FT_Vector* to )
+ {
+ FT_Error error = FT_Err_Ok;
+ FT_Vector bez_stack[37];
+ FT_Vector* arc;
+ FT_Vector* limit = bez_stack + 32;
+ FT_Bool first_arc = TRUE;
+
+
+ if ( !stroker || !control1 || !control2 || !to )
+ {
+ error = FT_THROW( Invalid_Argument );
+ goto Exit;
+ }
+
+ /* 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;
+ arc[2] = *control1;
+ arc[3] = stroker->center;
+
+ while ( arc >= bez_stack )
+ {
+ FT_Angle angle_in, angle_mid, angle_out;
+
+
+ /* 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;
+ }
+
+ if ( first_arc )
+ {
+ first_arc = FALSE;
+
+ /* process corner if necessary */
+ if ( stroker->first_point )
+ error = ft_stroker_subpath_start( stroker, angle_in, 0 );
+ else
+ {
+ 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_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, alpha0 = 0;
+ FT_Fixed length1, length2;
+ FT_StrokeBorder border;
+ FT_Int side;
+
+
+ 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 ) );
+
+ /* 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 );
+
+ /* compute control points */
+ FT_Vector_From_Polar( &ctrl1, length1, phi1 + rotate );
+ ctrl1.x += arc[2].x;
+ ctrl1.y += arc[2].y;
+
+ FT_Vector_From_Polar( &ctrl2, length2, phi2 + rotate );
+ ctrl2.x += arc[1].x;
+ ctrl2.y += arc[1].y;
+
+ /* compute end point */
+ FT_Vector_From_Polar( &end, stroker->radius, angle_out + rotate );
+ end.x += arc[0].x;
+ end.y += arc[0].y;
+
+ 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_MulDiv( 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;
+
+ stroker->angle_in = angle_out;
+ }
+
+ stroker->center = *to;
+
+ Exit:
+ return error;
+ }
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( FT_Error )
+ FT_Stroker_BeginSubPath( FT_Stroker stroker,
+ FT_Vector* to,
+ FT_Bool open )
+ {
+ if ( !stroker || !to )
+ return FT_THROW( Invalid_Argument );
+
+ /* We cannot process the first point, because there is not enough */
+ /* information regarding its corner/cap. The latter will be processed */
+ /* in the `FT_Stroker_EndSubPath' routine. */
+ /* */
+ stroker->first_point = TRUE;
+ 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;
+ }
+
+
+ static FT_Error
+ ft_stroker_add_reverse_left( FT_Stroker stroker,
+ FT_Bool open )
+ {
+ FT_StrokeBorder right = stroker->borders + 0;
+ FT_StrokeBorder left = stroker->borders + 1;
+ FT_Int new_points;
+ FT_Error error = FT_Err_Ok;
+
+
+ FT_ASSERT( left->start >= 0 );
+
+ new_points = left->num_points - left->start;
+ if ( new_points > 0 )
+ {
+ error = ft_stroke_border_grow( right, (FT_UInt)new_points );
+ if ( error )
+ goto Exit;
+
+ {
+ FT_Vector* dst_point = right->points + right->num_points;
+ FT_Byte* dst_tag = right->tags + right->num_points;
+ 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;
+ *dst_tag = *src_tag;
+
+ if ( open )
+ dst_tag[0] &= ~FT_STROKE_TAG_BEGIN_END;
+ else
+ {
+ 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--;
+ src_tag--;
+ dst_point++;
+ dst_tag++;
+ }
+ }
+
+ left->num_points = left->start;
+ right->num_points += new_points;
+
+ right->movable = FALSE;
+ left->movable = FALSE;
+ }
+
+ Exit:
+ return error;
+ }
+
+
+ /* documentation is in ftstroke.h */
+
+ /* there's a lot of magic in this function! */
+ FT_EXPORT_DEF( FT_Error )
+ FT_Stroker_EndSubPath( FT_Stroker stroker )
+ {
+ FT_Error error = FT_Err_Ok;
+
+
+ if ( !stroker )
+ {
+ error = FT_THROW( Invalid_Argument );
+ goto Exit;
+ }
+
+ if ( stroker->subpath_open )
+ {
+ 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. */
+ error = ft_stroker_cap( stroker, stroker->angle_in, 0 );
+ if ( error )
+ goto Exit;
+
+ /* add reversed points from `left' to `right' */
+ error = ft_stroker_add_reverse_left( stroker, TRUE );
+ if ( error )
+ goto Exit;
+
+ /* now add the final cap */
+ stroker->center = stroker->subpath_start;
+ error = ft_stroker_cap( stroker,
+ stroker->subpath_angle + FT_ANGLE_PI, 0 );
+ if ( error )
+ goto Exit;
+
+ /* Now end the right subpath accordingly. The left one is */
+ /* rewind and doesn't need further processing. */
+ ft_stroke_border_close( right, FALSE );
+ }
+ else
+ {
+ 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;
+ }
+
+ /* process the corner */
+ stroker->angle_out = stroker->subpath_angle;
+ turn = FT_Angle_Diff( stroker->angle_in,
+ stroker->angle_out );
+
+ /* no specific corner processing is required if the turn is 0 */
+ if ( turn != 0 )
+ {
+ /* when we turn to the right, the inside side is 0 */
+ inside_side = 0;
+
+ /* otherwise, the inside side is 1 */
+ if ( turn < 0 )
+ inside_side = 1;
+
+ 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,
+ stroker->subpath_line_length );
+ if ( error )
+ goto Exit;
+ }
+
+ /* then end our two subpaths */
+ ft_stroke_border_close( stroker->borders + 0, FALSE );
+ ft_stroke_border_close( stroker->borders + 1, TRUE );
+ }
+
+ Exit:
+ return error;
+ }
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( FT_Error )
+ FT_Stroker_GetBorderCounts( FT_Stroker stroker,
+ FT_StrokerBorder border,
+ FT_UInt *anum_points,
+ FT_UInt *anum_contours )
+ {
+ FT_UInt num_points = 0, num_contours = 0;
+ FT_Error error;
+
+
+ if ( !stroker || border > 1 )
+ {
+ error = FT_THROW( Invalid_Argument );
+ goto Exit;
+ }
+
+ error = ft_stroke_border_get_counts( stroker->borders + border,
+ &num_points, &num_contours );
+ Exit:
+ if ( anum_points )
+ *anum_points = num_points;
+
+ if ( anum_contours )
+ *anum_contours = num_contours;
+
+ return error;
+ }
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( FT_Error )
+ FT_Stroker_GetCounts( FT_Stroker stroker,
+ FT_UInt *anum_points,
+ FT_UInt *anum_contours )
+ {
+ FT_UInt count1, count2, num_points = 0;
+ FT_UInt count3, count4, num_contours = 0;
+ FT_Error error;
+
+
+ if ( !stroker )
+ {
+ error = FT_THROW( Invalid_Argument );
+ goto Exit;
+ }
+
+ error = ft_stroke_border_get_counts( stroker->borders + 0,
+ &count1, &count2 );
+ if ( error )
+ goto Exit;
+
+ error = ft_stroke_border_get_counts( stroker->borders + 1,
+ &count3, &count4 );
+ if ( error )
+ goto Exit;
+
+ num_points = count1 + count3;
+ num_contours = count2 + count4;
+
+ Exit:
+ if ( anum_points )
+ *anum_points = num_points;
+
+ if ( anum_contours )
+ *anum_contours = num_contours;
+
+ return error;
+ }
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( void )
+ FT_Stroker_ExportBorder( FT_Stroker stroker,
+ FT_StrokerBorder border,
+ FT_Outline* outline )
+ {
+ if ( !stroker || !outline )
+ return;
+
+ if ( border == FT_STROKER_BORDER_LEFT ||
+ border == FT_STROKER_BORDER_RIGHT )
+ {
+ FT_StrokeBorder sborder = & stroker->borders[border];
+
+
+ if ( sborder->valid )
+ ft_stroke_border_export( sborder, outline );
+ }
+ }
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( void )
+ FT_Stroker_Export( FT_Stroker stroker,
+ FT_Outline* outline )
+ {
+ FT_Stroker_ExportBorder( stroker, FT_STROKER_BORDER_LEFT, outline );
+ FT_Stroker_ExportBorder( stroker, FT_STROKER_BORDER_RIGHT, outline );
+ }
+
+
+ /* documentation is in ftstroke.h */
+
+ /*
+ * The following is very similar to FT_Outline_Decompose, except
+ * that we do support opened paths, and do not scale the outline.
+ */
+ FT_EXPORT_DEF( FT_Error )
+ FT_Stroker_ParseOutline( FT_Stroker stroker,
+ FT_Outline* outline,
+ FT_Bool opened )
+ {
+ FT_Vector v_last;
+ FT_Vector v_control;
+ FT_Vector v_start;
+
+ FT_Vector* point;
+ FT_Vector* limit;
+ char* tags;
+
+ 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 */
+
+
+ if ( !outline )
+ return FT_THROW( Invalid_Outline );
+
+ if ( !stroker )
+ return FT_THROW( Invalid_Argument );
+
+ FT_Stroker_Rewind( stroker );
+
+ first = 0;
+
+ for ( n = 0; n < outline->n_contours; n++ )
+ {
+ FT_UInt last; /* index of last point in contour */
+
+
+ last = outline->contours[n];
+ limit = outline->points + last;
+
+ /* skip empty points; we don't stroke these */
+ if ( last <= first )
+ {
+ first = last + 1;
+ continue;
+ }
+
+ v_start = outline->points[first];
+ v_last = outline->points[last];
+
+ v_control = v_start;
+
+ point = outline->points + first;
+ tags = outline->tags + first;
+ tag = FT_CURVE_TAG( tags[0] );
+
+ /* A contour cannot start with a cubic control point! */
+ if ( tag == FT_CURVE_TAG_CUBIC )
+ goto Invalid_Outline;
+
+ /* check first point to determine origin */
+ if ( tag == FT_CURVE_TAG_CONIC )
+ {
+ /* First point is conic control. Yes, this happens. */
+ if ( FT_CURVE_TAG( outline->tags[last] ) == FT_CURVE_TAG_ON )
+ {
+ /* start at last point if it is on the curve */
+ v_start = v_last;
+ limit--;
+ }
+ else
+ {
+ /* if both first and last points are conic, */
+ /* start at their middle */
+ v_start.x = ( v_start.x + v_last.x ) / 2;
+ v_start.y = ( v_start.y + v_last.y ) / 2;
+ }
+ point--;
+ tags--;
+ }
+
+ error = FT_Stroker_BeginSubPath( stroker, &v_start, opened );
+ if ( error )
+ goto Exit;
+
+ while ( point < limit )
+ {
+ point++;
+ tags++;
+
+ tag = FT_CURVE_TAG( tags[0] );
+ switch ( tag )
+ {
+ case FT_CURVE_TAG_ON: /* emit a single line_to */
+ {
+ FT_Vector vec;
+
+
+ vec.x = point->x;
+ vec.y = point->y;
+
+ error = FT_Stroker_LineTo( stroker, &vec );
+ if ( error )
+ goto Exit;
+ continue;
+ }
+
+ case FT_CURVE_TAG_CONIC: /* consume conic arcs */
+ v_control.x = point->x;
+ v_control.y = point->y;
+
+ Do_Conic:
+ if ( point < limit )
+ {
+ FT_Vector vec;
+ FT_Vector v_middle;
+
+
+ point++;
+ tags++;
+ tag = FT_CURVE_TAG( tags[0] );
+
+ vec = point[0];
+
+ if ( tag == FT_CURVE_TAG_ON )
+ {
+ error = FT_Stroker_ConicTo( stroker, &v_control, &vec );
+ if ( error )
+ goto Exit;
+ continue;
+ }
+
+ if ( tag != FT_CURVE_TAG_CONIC )
+ goto Invalid_Outline;
+
+ v_middle.x = ( v_control.x + vec.x ) / 2;
+ v_middle.y = ( v_control.y + vec.y ) / 2;
+
+ error = FT_Stroker_ConicTo( stroker, &v_control, &v_middle );
+ if ( error )
+ goto Exit;
+
+ v_control = vec;
+ goto Do_Conic;
+ }
+
+ error = FT_Stroker_ConicTo( stroker, &v_control, &v_start );
+ goto Close;
+
+ default: /* FT_CURVE_TAG_CUBIC */
+ {
+ FT_Vector vec1, vec2;
+
+
+ if ( point + 1 > limit ||
+ FT_CURVE_TAG( tags[1] ) != FT_CURVE_TAG_CUBIC )
+ goto Invalid_Outline;
+
+ point += 2;
+ tags += 2;
+
+ vec1 = point[-2];
+ vec2 = point[-1];
+
+ if ( point <= limit )
+ {
+ FT_Vector vec;
+
+
+ vec = point[0];
+
+ error = FT_Stroker_CubicTo( stroker, &vec1, &vec2, &vec );
+ if ( error )
+ goto Exit;
+ continue;
+ }
+
+ error = FT_Stroker_CubicTo( stroker, &vec1, &vec2, &v_start );
+ goto Close;
+ }
+ }
+ }
+
+ Close:
+ if ( error )
+ goto Exit;
+
+ /* don't try to end the path if no segments have been generated */
+ if ( !stroker->first_point )
+ {
+ error = FT_Stroker_EndSubPath( stroker );
+ if ( error )
+ goto Exit;
+ }
+
+ first = last + 1;
+ }
+
+ return FT_Err_Ok;
+
+ Exit:
+ return error;
+
+ Invalid_Outline:
+ return FT_THROW( Invalid_Outline );
+ }
+
+
+ /* 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
+#include "basepic.h"
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( FT_Error )
+ FT_Glyph_Stroke( FT_Glyph *pglyph,
+ FT_Stroker stroker,
+ FT_Bool destroy )
+ {
+ FT_Error error = FT_ERR( Invalid_Argument );
+ FT_Glyph glyph = NULL;
+
+ /* for FT_OUTLINE_GLYPH_CLASS_GET (in PIC mode) */
+ FT_Library library = stroker->library;
+
+ FT_UNUSED( library );
+
+
+ if ( !pglyph )
+ goto Exit;
+
+ glyph = *pglyph;
+ if ( !glyph || glyph->clazz != FT_OUTLINE_GLYPH_CLASS_GET )
+ goto Exit;
+
+ {
+ FT_Glyph copy;
+
+
+ error = FT_Glyph_Copy( glyph, &copy );
+ if ( error )
+ goto Exit;
+
+ glyph = copy;
+ }
+
+ {
+ FT_OutlineGlyph oglyph = (FT_OutlineGlyph)glyph;
+ FT_Outline* outline = &oglyph->outline;
+ FT_UInt num_points, num_contours;
+
+
+ error = FT_Stroker_ParseOutline( stroker, outline, FALSE );
+ if ( error )
+ goto Fail;
+
+ FT_Stroker_GetCounts( stroker, &num_points, &num_contours );
+
+ FT_Outline_Done( glyph->library, outline );
+
+ error = FT_Outline_New( glyph->library,
+ num_points, num_contours, outline );
+ if ( error )
+ goto Fail;
+
+ outline->n_points = 0;
+ outline->n_contours = 0;
+
+ FT_Stroker_Export( stroker, outline );
+ }
+
+ if ( destroy )
+ FT_Done_Glyph( *pglyph );
+
+ *pglyph = glyph;
+ goto Exit;
+
+ Fail:
+ FT_Done_Glyph( glyph );
+ glyph = NULL;
+
+ if ( !destroy )
+ *pglyph = NULL;
+
+ Exit:
+ return error;
+ }
+
+
+ /* documentation is in ftstroke.h */
+
+ FT_EXPORT_DEF( FT_Error )
+ FT_Glyph_StrokeBorder( FT_Glyph *pglyph,
+ FT_Stroker stroker,
+ FT_Bool inside,
+ FT_Bool destroy )
+ {
+ FT_Error error = FT_ERR( Invalid_Argument );
+ FT_Glyph glyph = NULL;
+
+ /* for FT_OUTLINE_GLYPH_CLASS_GET (in PIC mode) */
+ FT_Library library = stroker->library;
+
+ FT_UNUSED( library );
+
+
+ if ( !pglyph )
+ goto Exit;
+
+ glyph = *pglyph;
+ if ( !glyph || glyph->clazz != FT_OUTLINE_GLYPH_CLASS_GET )
+ goto Exit;
+
+ {
+ FT_Glyph copy;
+
+
+ error = FT_Glyph_Copy( glyph, &copy );
+ if ( error )
+ goto Exit;
+
+ glyph = copy;
+ }
+
+ {
+ FT_OutlineGlyph oglyph = (FT_OutlineGlyph)glyph;
+ FT_StrokerBorder border;
+ FT_Outline* outline = &oglyph->outline;
+ FT_UInt num_points, num_contours;
+
+
+ border = FT_Outline_GetOutsideBorder( outline );
+ if ( inside )
+ {
+ if ( border == FT_STROKER_BORDER_LEFT )
+ border = FT_STROKER_BORDER_RIGHT;
+ else
+ border = FT_STROKER_BORDER_LEFT;
+ }
+
+ error = FT_Stroker_ParseOutline( stroker, outline, FALSE );
+ if ( error )
+ goto Fail;
+
+ FT_Stroker_GetBorderCounts( stroker, border,
+ &num_points, &num_contours );
+
+ FT_Outline_Done( glyph->library, outline );
+
+ error = FT_Outline_New( glyph->library,
+ num_points,
+ num_contours,
+ outline );
+ if ( error )
+ goto Fail;
+
+ outline->n_points = 0;
+ outline->n_contours = 0;
+
+ FT_Stroker_ExportBorder( stroker, border, outline );
+ }
+
+ if ( destroy )
+ FT_Done_Glyph( *pglyph );
+
+ *pglyph = glyph;
+ goto Exit;
+
+ Fail:
+ FT_Done_Glyph( glyph );
+ glyph = NULL;
+
+ if ( !destroy )
+ *pglyph = NULL;
+
+ Exit:
+ return error;
+ }
+
+
+/* END */