/***************************************************************************/
/* */
/* ftbbox.c */
/* */
/* FreeType bbox computation (body). */
/* */
/* Copyright 1996-2002, 2004, 2006, 2010, 2013 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;
/*************************************************************************/
/* */
/* <Function> */
/* BBox_Move_To */
/* */
/* <Description> */
/* This function is used as a `move_to' and `line_to' emitter during */
/* FT_Outline_Decompose(). It simply records the destination point */
/* in `user->last'; no further computations are necessary since we */
/* use the cbox as the starting bbox which must be refined. */
/* */
/* <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 )
{
user->last = *to;
return 0;
}
#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_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 )
{
/* we don't need to check `to' since it is always an `on' point, thus */
/* within the 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_Move_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;
FT_BBox bbox;
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;
bbox.xMin = bbox.xMax = cbox.xMin = cbox.xMax = vec->x;
bbox.yMin = bbox.yMax = cbox.yMin = cbox.yMax = vec->y;
vec++;
for ( n = 1; n < outline->n_points; n++ )
{
FT_Pos x = vec->x;
FT_Pos y = vec->y;
/* update control box */
if ( x < cbox.xMin ) cbox.xMin = x;
if ( x > cbox.xMax ) cbox.xMax = x;
if ( y < cbox.yMin ) cbox.yMin = y;
if ( y > cbox.yMax ) cbox.yMax = y;
if ( FT_CURVE_TAG( outline->tags[n] ) == FT_CURVE_TAG_ON )
{
/* update bbox for `on' points only */
if ( x < bbox.xMin ) bbox.xMin = x;
if ( x > bbox.xMax ) bbox.xMax = x;
if ( y < bbox.yMin ) bbox.yMin = y;
if ( y > bbox.yMax ) bbox.yMax = y;
}
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 */
