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+/***************************************************************************/
+/* */
+/* ftbbox.c */
+/* */
+/* FreeType bbox computation (body). */
+/* */
+/* Copyright 1996-2002, 2004, 2006, 2010, 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. */
+/* */
+/***************************************************************************/
+
+
+ /*************************************************************************/
+ /* */
+ /* This component has a _single_ role: to compute exact outline bounding */
+ /* boxes. */
+ /* */
+ /*************************************************************************/
+
+
+#include <ft2build.h>
+#include FT_INTERNAL_DEBUG_H
+
+#include FT_BBOX_H
+#include FT_IMAGE_H
+#include FT_OUTLINE_H
+#include FT_INTERNAL_CALC_H
+#include FT_INTERNAL_OBJECTS_H
+
+
+ typedef struct TBBox_Rec_
+ {
+ FT_Vector last;
+ FT_BBox bbox;
+
+ } TBBox_Rec;
+
+
+#define FT_UPDATE_BBOX(p, bbox) \
+ FT_BEGIN_STMNT \
+ if ( p->x < bbox.xMin ) \
+ bbox.xMin = p->x; \
+ if ( p->x > bbox.xMax ) \
+ bbox.xMax = p->x; \
+ if ( p->y < bbox.yMin ) \
+ bbox.yMin = p->y; \
+ if ( p->y > bbox.yMax ) \
+ bbox.yMax = p->y; \
+ FT_END_STMNT
+
+#define CHECK_X( p, bbox ) \
+ ( p->x < bbox.xMin || p->x > bbox.xMax )
+
+#define CHECK_Y( p, bbox ) \
+ ( p->y < bbox.yMin || p->y > bbox.yMax )
+
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* BBox_Move_To */
+ /* */
+ /* <Description> */
+ /* This function is used as a `move_to' emitter during */
+ /* FT_Outline_Decompose(). It simply records the destination point */
+ /* in `user->last'. We also update bbox in case contour starts with */
+ /* an implicit `on' point. */
+ /* */
+ /* <Input> */
+ /* to :: A pointer to the destination vector. */
+ /* */
+ /* <InOut> */
+ /* user :: A pointer to the current walk context. */
+ /* */
+ /* <Return> */
+ /* Always 0. Needed for the interface only. */
+ /* */
+ static int
+ BBox_Move_To( FT_Vector* to,
+ TBBox_Rec* user )
+ {
+ FT_UPDATE_BBOX( to, user->bbox );
+
+ user->last = *to;
+
+ return 0;
+ }
+
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* BBox_Line_To */
+ /* */
+ /* <Description> */
+ /* This function is used as a `line_to' emitter during */
+ /* FT_Outline_Decompose(). It simply records the destination point */
+ /* in `user->last'; no further computations are necessary because */
+ /* bbox already contains both explicit ends of the line segment. */
+ /* */
+ /* <Input> */
+ /* to :: A pointer to the destination vector. */
+ /* */
+ /* <InOut> */
+ /* user :: A pointer to the current walk context. */
+ /* */
+ /* <Return> */
+ /* Always 0. Needed for the interface only. */
+ /* */
+ static int
+ BBox_Line_To( FT_Vector* to,
+ TBBox_Rec* user )
+ {
+ user->last = *to;
+
+ return 0;
+ }
+
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* BBox_Conic_Check */
+ /* */
+ /* <Description> */
+ /* Find the extrema of a 1-dimensional conic Bezier curve and update */
+ /* a bounding range. This version uses direct computation, as it */
+ /* doesn't need square roots. */
+ /* */
+ /* <Input> */
+ /* y1 :: The start coordinate. */
+ /* */
+ /* y2 :: The coordinate of the control point. */
+ /* */
+ /* y3 :: The end coordinate. */
+ /* */
+ /* <InOut> */
+ /* min :: The address of the current minimum. */
+ /* */
+ /* max :: The address of the current maximum. */
+ /* */
+ static void
+ BBox_Conic_Check( FT_Pos y1,
+ FT_Pos y2,
+ FT_Pos y3,
+ FT_Pos* min,
+ FT_Pos* max )
+ {
+ /* This function is only called when a control off-point is outside */
+ /* the bbox that contains all on-points. It finds a local extremum */
+ /* within the segment, equal to (y1*y3 - y2*y2)/(y1 - 2*y2 + y3). */
+ /* Or, offsetting from y2, we get */
+
+ y1 -= y2;
+ y3 -= y2;
+ y2 += FT_MulDiv( y1, y3, y1 + y3 );
+
+ if ( y2 < *min )
+ *min = y2;
+ if ( y2 > *max )
+ *max = y2;
+ }
+
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* BBox_Conic_To */
+ /* */
+ /* <Description> */
+ /* This function is used as a `conic_to' emitter during */
+ /* FT_Outline_Decompose(). It checks a conic Bezier curve with the */
+ /* current bounding box, and computes its extrema if necessary to */
+ /* update it. */
+ /* */
+ /* <Input> */
+ /* control :: A pointer to a control point. */
+ /* */
+ /* to :: A pointer to the destination vector. */
+ /* */
+ /* <InOut> */
+ /* user :: The address of the current walk context. */
+ /* */
+ /* <Return> */
+ /* Always 0. Needed for the interface only. */
+ /* */
+ /* <Note> */
+ /* In the case of a non-monotonous arc, we compute directly the */
+ /* extremum coordinates, as it is sufficiently fast. */
+ /* */
+ static int
+ BBox_Conic_To( FT_Vector* control,
+ FT_Vector* to,
+ TBBox_Rec* user )
+ {
+ /* in case `to' is implicit and not included in bbox yet */
+ FT_UPDATE_BBOX( to, user->bbox );
+
+ if ( CHECK_X( control, user->bbox ) )
+ BBox_Conic_Check( user->last.x,
+ control->x,
+ to->x,
+ &user->bbox.xMin,
+ &user->bbox.xMax );
+
+ if ( CHECK_Y( control, user->bbox ) )
+ BBox_Conic_Check( user->last.y,
+ control->y,
+ to->y,
+ &user->bbox.yMin,
+ &user->bbox.yMax );
+
+ user->last = *to;
+
+ return 0;
+ }
+
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* BBox_Cubic_Check */
+ /* */
+ /* <Description> */
+ /* Find the extrema of a 1-dimensional cubic Bezier curve and */
+ /* update a bounding range. This version uses iterative splitting */
+ /* because it is faster than the exact solution with square roots. */
+ /* */
+ /* <Input> */
+ /* p1 :: The start coordinate. */
+ /* */
+ /* p2 :: The coordinate of the first control point. */
+ /* */
+ /* p3 :: The coordinate of the second control point. */
+ /* */
+ /* p4 :: The end coordinate. */
+ /* */
+ /* <InOut> */
+ /* min :: The address of the current minimum. */
+ /* */
+ /* max :: The address of the current maximum. */
+ /* */
+ static FT_Pos
+ cubic_peak( FT_Pos q1,
+ FT_Pos q2,
+ FT_Pos q3,
+ FT_Pos q4 )
+ {
+ FT_Pos peak = 0;
+ FT_Int shift;
+
+ /* This function finds a peak of a cubic segment if it is above 0 */
+ /* using iterative bisection of the segment, or returns 0. */
+ /* The fixed-point arithmetic of bisection is inherently stable */
+ /* but may loose accuracy in the two lowest bits. To compensate, */
+ /* we upscale the segment if there is room. Large values may need */
+ /* to be downscaled to avoid overflows during bisection. */
+ /* It is called with either q2 or q3 positive, which is necessary */
+ /* for the peak to exist and avoids undefined FT_MSB. */
+
+ shift = 27 -
+ FT_MSB( FT_ABS( q1 ) | FT_ABS( q2 ) | FT_ABS( q3 ) | FT_ABS( q4 ) );
+
+ if ( shift > 0 )
+ {
+ /* upscaling too much just wastes time */
+ if ( shift > 2 )
+ shift = 2;
+
+ q1 <<= shift;
+ q2 <<= shift;
+ q3 <<= shift;
+ q4 <<= shift;
+ }
+ else
+ {
+ q1 >>= -shift;
+ q2 >>= -shift;
+ q3 >>= -shift;
+ q4 >>= -shift;
+ }
+
+ /* for a peak to exist above 0, the cubic segment must have */
+ /* at least one of its control off-points above 0. */
+ while ( q2 > 0 || q3 > 0 )
+ {
+ /* determine which half contains the maximum and split */
+ if ( q1 + q2 > q3 + q4 ) /* first half */
+ {
+ q4 = q4 + q3;
+ q3 = q3 + q2;
+ q2 = q2 + q1;
+ q4 = q4 + q3;
+ q3 = q3 + q2;
+ q4 = ( q4 + q3 ) / 8;
+ q3 = q3 / 4;
+ q2 = q2 / 2;
+ }
+ else /* second half */
+ {
+ q1 = q1 + q2;
+ q2 = q2 + q3;
+ q3 = q3 + q4;
+ q1 = q1 + q2;
+ q2 = q2 + q3;
+ q1 = ( q1 + q2 ) / 8;
+ q2 = q2 / 4;
+ q3 = q3 / 2;
+ }
+
+ /* check whether either end reached the maximum */
+ if ( q1 == q2 && q1 >= q3 )
+ {
+ peak = q1;
+ break;
+ }
+ if ( q3 == q4 && q2 <= q4 )
+ {
+ peak = q4;
+ break;
+ }
+ }
+
+ if ( shift > 0 )
+ peak >>= shift;
+ else
+ peak <<= -shift;
+
+ return peak;
+ }
+
+
+ static void
+ BBox_Cubic_Check( FT_Pos p1,
+ FT_Pos p2,
+ FT_Pos p3,
+ FT_Pos p4,
+ FT_Pos* min,
+ FT_Pos* max )
+ {
+ /* This function is only called when a control off-point is outside */
+ /* the bbox that contains all on-points. So at least one of the */
+ /* conditions below holds and cubic_peak is called with at least one */
+ /* non-zero argument. */
+
+ if ( p2 > *max || p3 > *max )
+ *max += cubic_peak( p1 - *max, p2 - *max, p3 - *max, p4 - *max );
+
+ /* now flip the signs to update the minimum */
+ if ( p2 < *min || p3 < *min )
+ *min -= cubic_peak( *min - p1, *min - p2, *min - p3, *min - p4 );
+ }
+
+
+ /*************************************************************************/
+ /* */
+ /* <Function> */
+ /* BBox_Cubic_To */
+ /* */
+ /* <Description> */
+ /* This function is used as a `cubic_to' emitter during */
+ /* FT_Outline_Decompose(). It checks a cubic Bezier curve with the */
+ /* current bounding box, and computes its extrema if necessary to */
+ /* update it. */
+ /* */
+ /* <Input> */
+ /* control1 :: A pointer to the first control point. */
+ /* */
+ /* control2 :: A pointer to the second control point. */
+ /* */
+ /* to :: A pointer to the destination vector. */
+ /* */
+ /* <InOut> */
+ /* user :: The address of the current walk context. */
+ /* */
+ /* <Return> */
+ /* Always 0. Needed for the interface only. */
+ /* */
+ /* <Note> */
+ /* In the case of a non-monotonous arc, we don't compute directly */
+ /* extremum coordinates, we subdivide instead. */
+ /* */
+ static int
+ BBox_Cubic_To( FT_Vector* control1,
+ FT_Vector* control2,
+ FT_Vector* to,
+ TBBox_Rec* user )
+ {
+ /* We don't need to check `to' since it is always an on-point, */
+ /* thus within the bbox. Only segments with an off-point outside */
+ /* the bbox can possibly reach new extreme values. */
+
+ if ( CHECK_X( control1, user->bbox ) ||
+ CHECK_X( control2, user->bbox ) )
+ BBox_Cubic_Check( user->last.x,
+ control1->x,
+ control2->x,
+ to->x,
+ &user->bbox.xMin,
+ &user->bbox.xMax );
+
+ if ( CHECK_Y( control1, user->bbox ) ||
+ CHECK_Y( control2, user->bbox ) )
+ BBox_Cubic_Check( user->last.y,
+ control1->y,
+ control2->y,
+ to->y,
+ &user->bbox.yMin,
+ &user->bbox.yMax );
+
+ user->last = *to;
+
+ return 0;
+ }
+
+FT_DEFINE_OUTLINE_FUNCS(bbox_interface,
+ (FT_Outline_MoveTo_Func) BBox_Move_To,
+ (FT_Outline_LineTo_Func) BBox_Line_To,
+ (FT_Outline_ConicTo_Func)BBox_Conic_To,
+ (FT_Outline_CubicTo_Func)BBox_Cubic_To,
+ 0, 0
+ )
+
+ /* documentation is in ftbbox.h */
+
+ FT_EXPORT_DEF( FT_Error )
+ FT_Outline_Get_BBox( FT_Outline* outline,
+ FT_BBox *abbox )
+ {
+ FT_BBox cbox = { 0x7FFFFFFF, 0x7FFFFFFF, -0x7FFFFFFF, -0x7FFFFFFF };
+ FT_BBox bbox = { 0x7FFFFFFF, 0x7FFFFFFF, -0x7FFFFFFF, -0x7FFFFFFF };
+ FT_Vector* vec;
+ FT_UShort n;
+
+
+ if ( !abbox )
+ return FT_THROW( Invalid_Argument );
+
+ if ( !outline )
+ return FT_THROW( Invalid_Outline );
+
+ /* if outline is empty, return (0,0,0,0) */
+ if ( outline->n_points == 0 || outline->n_contours <= 0 )
+ {
+ abbox->xMin = abbox->xMax = 0;
+ abbox->yMin = abbox->yMax = 0;
+ return 0;
+ }
+
+ /* We compute the control box as well as the bounding box of */
+ /* all `on' points in the outline. Then, if the two boxes */
+ /* coincide, we exit immediately. */
+
+ vec = outline->points;
+
+ for ( n = 0; n < outline->n_points; n++ )
+ {
+ FT_UPDATE_BBOX( vec, cbox);
+
+ if ( FT_CURVE_TAG( outline->tags[n] ) == FT_CURVE_TAG_ON )
+ FT_UPDATE_BBOX( vec, bbox);
+
+ vec++;
+ }
+
+ /* test two boxes for equality */
+ if ( cbox.xMin < bbox.xMin || cbox.xMax > bbox.xMax ||
+ cbox.yMin < bbox.yMin || cbox.yMax > bbox.yMax )
+ {
+ /* the two boxes are different, now walk over the outline to */
+ /* get the Bezier arc extrema. */
+
+ FT_Error error;
+ TBBox_Rec user;
+
+#ifdef FT_CONFIG_OPTION_PIC
+ FT_Outline_Funcs bbox_interface;
+ Init_Class_bbox_interface(&bbox_interface);
+#endif
+
+ user.bbox = bbox;
+
+ error = FT_Outline_Decompose( outline, &bbox_interface, &user );
+ if ( error )
+ return error;
+
+ *abbox = user.bbox;
+ }
+ else
+ *abbox = bbox;
+
+ return FT_Err_Ok;
+ }
+
+
+/* END */
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