/****************************************************************************
*
* ftbbox.c
*
* FreeType bbox computation (body).
*
* Copyright 1996-2019 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_UInt32)( 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, /* move_to */
(FT_Outline_LineTo_Func) BBox_Line_To, /* line_to */
(FT_Outline_ConicTo_Func)BBox_Conic_To, /* conic_to */
(FT_Outline_CubicTo_Func)BBox_Cubic_To, /* cubic_to */
0, /* shift */
0 /* delta */
)
/* documentation is in ftbbox.h */
FT_EXPORT_DEF( FT_Error )
FT_Outline_Get_BBox( FT_Outline* outline,
FT_BBox *abbox )
{
FT_BBox cbox = { 0x7FFFFFFFL, 0x7FFFFFFFL,
-0x7FFFFFFFL, -0x7FFFFFFFL };
FT_BBox bbox = { 0x7FFFFFFFL, 0x7FFFFFFFL,
-0x7FFFFFFFL, -0x7FFFFFFFL };
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;
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 */
