diff -r f9283dc4860d -r 88f2e05288ba misc/libfreetype/src/base/ftbbox.c --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/misc/libfreetype/src/base/ftbbox.c Mon Apr 25 01:46:54 2011 +0200 @@ -0,0 +1,662 @@ +/***************************************************************************/ +/* */ +/* ftbbox.c */ +/* */ +/* FreeType bbox computation (body). */ +/* */ +/* Copyright 1996-2001, 2002, 2004, 2006, 2010 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 +#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; + + + /*************************************************************************/ + /* */ + /* */ + /* BBox_Move_To */ + /* */ + /* */ + /* 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. */ + /* */ + /* */ + /* to :: A pointer to the destination vector. */ + /* */ + /* */ + /* user :: A pointer to the current walk context. */ + /* */ + /* */ + /* 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 ) + + + /*************************************************************************/ + /* */ + /* */ + /* BBox_Conic_Check */ + /* */ + /* */ + /* 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. */ + /* */ + /* */ + /* y1 :: The start coordinate. */ + /* */ + /* y2 :: The coordinate of the control point. */ + /* */ + /* y3 :: The end coordinate. */ + /* */ + /* */ + /* 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; + } + + + /*************************************************************************/ + /* */ + /* */ + /* BBox_Conic_To */ + /* */ + /* */ + /* 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. */ + /* */ + /* */ + /* control :: A pointer to a control point. */ + /* */ + /* to :: A pointer to the destination vector. */ + /* */ + /* */ + /* user :: The address of the current walk context. */ + /* */ + /* */ + /* Always 0. Needed for the interface only. */ + /* */ + /* */ + /* 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; + } + + + /*************************************************************************/ + /* */ + /* */ + /* BBox_Cubic_Check */ + /* */ + /* */ + /* 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. */ + /* */ + /* */ + /* p1 :: The start coordinate. */ + /* */ + /* p2 :: The coordinate of the first control point. */ + /* */ + /* p3 :: The coordinate of the second control point. */ + /* */ + /* p4 :: The end coordinate. */ + /* */ + /* */ + /* 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 stack[32*3 + 1], *arc; + + + arc = stack; + + arc[0] = p1; + arc[1] = p2; + arc[2] = p3; + arc[3] = p4; + + do + { + FT_Pos y1 = arc[0]; + FT_Pos y2 = arc[1]; + FT_Pos y3 = arc[2]; + FT_Pos y4 = arc[3]; + + + if ( y1 == y4 ) + { + if ( y1 == y2 && y1 == y3 ) /* flat */ + goto Test; + } + else if ( y1 < y4 ) + { + if ( y2 >= y1 && y2 <= y4 && y3 >= y1 && y3 <= y4 ) /* ascending */ + goto Test; + } + else + { + if ( y2 >= y4 && y2 <= y1 && y3 >= y4 && y3 <= y1 ) /* descending */ + { + y2 = y1; + y1 = y4; + y4 = y2; + goto Test; + } + } + + /* unknown direction -- split the arc in two */ + arc[6] = y4; + arc[1] = y1 = ( y1 + y2 ) / 2; + arc[5] = y4 = ( y4 + y3 ) / 2; + y2 = ( y2 + y3 ) / 2; + arc[2] = y1 = ( y1 + y2 ) / 2; + arc[4] = y4 = ( y4 + y2 ) / 2; + arc[3] = ( y1 + y4 ) / 2; + + arc += 3; + goto Suite; + + Test: + if ( y1 < *min ) *min = y1; + if ( y4 > *max ) *max = y4; + arc -= 3; + + Suite: + ; + } while ( arc >= stack ); + } + +#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. */ + { + 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; + + + /* 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 float values to ensure */ + /* that its product is held in a `16.16' value. */ + + { + FT_ULong t1, t2; + int shift = 0; + + + /* The following computation is based on the fact that for */ + /* any value `y', if `n' is the position of the most */ + /* significant bit of `abs(y)' (starting from 0 for the */ + /* least significant bit), then `y' is in the range */ + /* */ + /* -2^n..2^n-1 */ + /* */ + /* We want to shift `a', `b', and `c' concurrently in order */ + /* to ensure that they all fit in 8.16 values, which maps */ + /* to the integer range `-2^23..2^23-1'. */ + /* */ + /* Necessarily, we need to shift `a', `b', and `c' so that */ + /* the most significant bit of its absolute values is at */ + /* _most_ at position 23. */ + /* */ + /* We begin by computing `t1' as the bitwise `OR' of the */ + /* absolute values of `a', `b', `c'. */ + + t1 = (FT_ULong)( ( a >= 0 ) ? a : -a ); + t2 = (FT_ULong)( ( b >= 0 ) ? b : -b ); + t1 |= t2; + t2 = (FT_ULong)( ( c >= 0 ) ? c : -c ); + t1 |= t2; + + /* Now we can be sure that the most significant bit of `t1' */ + /* is the most significant bit of either `a', `b', or `c', */ + /* depending on the greatest integer range of the particular */ + /* variable. */ + /* */ + /* Next, we compute the `shift', by shifting `t1' as many */ + /* times as necessary to move its MSB to position 23. This */ + /* corresponds to a value of `t1' that is in the range */ + /* 0x40_0000..0x7F_FFFF. */ + /* */ + /* Finally, we shift `a', `b', and `c' by the same amount. */ + /* This ensures that all values are now in the range */ + /* -2^23..2^23, i.e., they are now expressed as 8.16 */ + /* fixed-float numbers. This also means that we are using */ + /* 24 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). */ + + if ( t1 == 0 ) /* all coefficients are 0! */ + return; + + if ( t1 > 0x7FFFFFUL ) + { + do + { + shift++; + t1 >>= 1; + + } while ( t1 > 0x7FFFFFUL ); + + /* this loses some bits of precision, but we use 24 of them */ + /* for the computation anyway */ + a >>= shift; + b >>= shift; + c >>= shift; + } + else if ( t1 < 0x400000UL ) + { + do + { + shift++; + t1 <<= 1; + + } while ( t1 < 0x400000UL ); + + 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 + + + /*************************************************************************/ + /* */ + /* */ + /* BBox_Cubic_To */ + /* */ + /* */ + /* 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. */ + /* */ + /* */ + /* control1 :: A pointer to the first control point. */ + /* */ + /* control2 :: A pointer to the second control point. */ + /* */ + /* to :: A pointer to the destination vector. */ + /* */ + /* */ + /* user :: The address of the current walk context. */ + /* */ + /* */ + /* Always 0. Needed for the interface only. */ + /* */ + /* */ + /* 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_Err_Invalid_Argument; + + if ( !outline ) + return FT_Err_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 */