/***************************************************************************/
/* */
/* 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> */
/* Finds 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 )
{
if ( y1 <= y3 && y2 == y1 ) /* flat arc */
goto Suite;
if ( y1 < y3 )
{
if ( y2 >= y1 && y2 <= y3 ) /* ascending arc */
goto Suite;
}
else
{
if ( y2 >= y3 && y2 <= y1 ) /* descending arc */
{
y2 = y1;
y1 = y3;
y3 = y2;
goto Suite;
}
}
y1 = y3 = y1 - FT_MulDiv( y2 - y1, y2 - y1, y1 - 2*y2 + y3 );
Suite:
if ( y1 < *min ) *min = y1;
if ( y3 > *max ) *max = y3;
}
/*************************************************************************/
/* */
/* <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> */
/* Finds the extrema of a 1-dimensional cubic Bezier curve and */
/* updates a bounding range. This version uses splitting because we */
/* don't want to use square roots and extra accuracy. */
/* */
/* <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. */
/* */
#if 0
static void
BBox_Cubic_Check( FT_Pos p1,
FT_Pos p2,
FT_Pos p3,
FT_Pos p4,
FT_Pos* min,
FT_Pos* max )
{
FT_Pos q1, q2, q3, q4;
q1 = p1;
q2 = p2;
q3 = p3;
q4 = p4;
/* for a conic segment to possibly reach new maximum */
/* one of its off-points must be above the current value */
while ( q2 > *max || q3 > *max )
{
/* 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 if either end reached the maximum */
if ( q1 == q2 && q1 >= q3 )
{
*max = q1;
break;
}
if ( q3 == q4 && q2 <= q4 )
{
*max = q4;
break;
}
}
q1 = p1;
q2 = p2;
q3 = p3;
q4 = p4;
/* for a conic segment to possibly reach new minimum */
/* one of its off-points must be below the current value */
while ( q2 < *min || q3 < *min )
{
/* determine which half contains the minimum 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 if either end reached the minimum */
if ( q1 == q2 && q1 <= q3 )
{
*min = q1;
break;
}
if ( q3 == q4 && q2 >= q4 )
{
*min = q4;
break;
}
}
}
#else
static void
test_cubic_extrema( FT_Pos y1,
FT_Pos y2,
FT_Pos y3,
FT_Pos y4,
FT_Fixed u,
FT_Pos* min,
FT_Pos* max )
{
/* FT_Pos a = y4 - 3*y3 + 3*y2 - y1; */
FT_Pos b = y3 - 2*y2 + y1;
FT_Pos c = y2 - y1;
FT_Pos d = y1;
FT_Pos y;
FT_Fixed uu;
FT_UNUSED ( y4 );
/* The polynomial is */
/* */
/* P(x) = a*x^3 + 3b*x^2 + 3c*x + d , */
/* */
/* dP/dx = 3a*x^2 + 6b*x + 3c . */
/* */
/* However, we also have */
/* */
/* dP/dx(u) = 0 , */
/* */
/* which implies by subtraction that */
/* */
/* P(u) = b*u^2 + 2c*u + d . */
if ( u > 0 && u < 0x10000L )
{
uu = FT_MulFix( u, u );
y = d + FT_MulFix( c, 2*u ) + FT_MulFix( b, uu );
if ( y < *min ) *min = y;
if ( y > *max ) *max = y;
}
}
static void
BBox_Cubic_Check( FT_Pos y1,
FT_Pos y2,
FT_Pos y3,
FT_Pos y4,
FT_Pos* min,
FT_Pos* max )
{
/* always compare first and last points */
if ( y1 < *min ) *min = y1;
else if ( y1 > *max ) *max = y1;
if ( y4 < *min ) *min = y4;
else if ( y4 > *max ) *max = y4;
/* now, try to see if there are split points here */
if ( y1 <= y4 )
{
/* flat or ascending arc test */
if ( y1 <= y2 && y2 <= y4 && y1 <= y3 && y3 <= y4 )
return;
}
else /* y1 > y4 */
{
/* descending arc test */
if ( y1 >= y2 && y2 >= y4 && y1 >= y3 && y3 >= y4 )
return;
}
/* There are some split points. Find them. */
/* We already made sure that a, b, and c below cannot be all zero. */
{
FT_Pos a = y4 - 3*y3 + 3*y2 - y1;
FT_Pos b = y3 - 2*y2 + y1;
FT_Pos c = y2 - y1;
FT_Pos d;
FT_Fixed t;
FT_Int shift;
/* We need to solve `ax^2+2bx+c' here, without floating points! */
/* The trick is to normalize to a different representation in order */
/* to use our 16.16 fixed-point routines. */
/* */
/* We compute FT_MulFix(b,b) and FT_MulFix(a,c) after normalization. */
/* These values must fit into a single 16.16 value. */
/* */
/* We normalize a, b, and c to `8.16' fixed-point values to ensure */
/* that their product is held in a `16.16' value including the sign. */
/* Necessarily, we need to shift `a', `b', and `c' so that the most */
/* significant bit of their absolute values is at position 22. */
/* */
/* This also means that we are using 23 bits of precision to compute */
/* the zeros, independently of the range of the original polynomial */
/* coefficients. */
/* */
/* This algorithm should ensure reasonably accurate values for the */
/* zeros. Note that they are only expressed with 16 bits when */
/* computing the extrema (the zeros need to be in 0..1 exclusive */
/* to be considered part of the arc). */
shift = FT_MSB( FT_ABS( a ) | FT_ABS( b ) | FT_ABS( c ) );
if ( shift > 22 )
{
shift -= 22;
/* this loses some bits of precision, but we use 23 of them */
/* for the computation anyway */
a >>= shift;
b >>= shift;
c >>= shift;
}
else
{
shift = 22 - shift;
a <<= shift;
b <<= shift;
c <<= shift;
}
/* handle a == 0 */
if ( a == 0 )
{
if ( b != 0 )
{
t = - FT_DivFix( c, b ) / 2;
test_cubic_extrema( y1, y2, y3, y4, t, min, max );
}
}
else
{
/* solve the equation now */
d = FT_MulFix( b, b ) - FT_MulFix( a, c );
if ( d < 0 )
return;
if ( d == 0 )
{
/* there is a single split point at -b/a */
t = - FT_DivFix( b, a );
test_cubic_extrema( y1, y2, y3, y4, t, min, max );
}
else
{
/* there are two solutions; we need to filter them */
d = FT_SqrtFixed( (FT_Int32)d );
t = - FT_DivFix( b - d, a );
test_cubic_extrema( y1, y2, y3, y4, t, min, max );
t = - FT_DivFix( b + d, a );
test_cubic_extrema( y1, y2, y3, y4, t, min, max );
}
}
}
}
#endif
/*************************************************************************/
/* */
/* <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 */
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 */