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* src/base/ftbbox.c (BBox_Conic_Check): Fix boundary cases.

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Reported by Mikey Anbary <manbary@vizrt.com>.
This commit is contained in:
Werner Lemberg 2004-05-19 09:22:26 +00:00
parent b6420e84ed
commit b6370384ae
2 changed files with 111 additions and 100 deletions
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5
ChangeLog
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@ -1,3 +1,8 @@
2004-05-17 Werner Lemberg <wl@gnu.org>
* src/base/ftbbox.c (BBox_Conic_Check): Fix boundary cases.
Reported by Mikey Anbary <manbary@vizrt.com>.
2004-05-15 Werner Lemberg <wl@gnu.org>
* src/sfnt/sfobjs.c (sfnt_done_face): Free face->postscript_name.

206
src/base/ftbbox.c
View File

@ -4,7 +4,7 @@
/* */
/* FreeType bbox computation (body). */
/* */
/* Copyright 1996-2001, 2002 by */
/* Copyright 1996-2001, 2002, 2004 by */
/* David Turner, Robert Wilhelm, and Werner Lemberg. */
/* */
/* This file is part of the FreeType project, and may only be used */
@ -48,7 +48,7 @@
/* 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 */
/* the cbox as the starting bbox which must be refined. */
/* use the cbox as the starting bbox which must be refined. */
/* */
/* <Input> */
/* to :: A pointer to the destination vector. */
@ -88,11 +88,14 @@
/* */
/* <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
@ -102,19 +105,17 @@
FT_Pos* min,
FT_Pos* max )
{
if ( y1 <= y3 )
if ( y1 <= y3 && y2 == y1 ) /* flat arc */
goto Suite;
if ( y1 < y3 )
{
if ( y2 == y1 ) /* Flat arc */
goto Suite;
}
else if ( y1 < y3 )
{
if ( y2 >= y1 && y2 <= y3 ) /* Ascending arc */
if ( y2 >= y1 && y2 <= y3 ) /* ascending arc */
goto Suite;
}
else
{
if ( y2 >= y3 && y2 <= y1 ) /* Descending arc */
if ( y2 >= y3 && y2 <= y1 ) /* descending arc */
{
y2 = y1;
y1 = y3;
@ -144,6 +145,7 @@
/* */
/* <Input> */
/* control :: A pointer to a control point. */
/* */
/* to :: A pointer to the destination vector. */
/* */
/* <InOut> */
@ -165,7 +167,6 @@
/* within the bbox */
if ( CHECK_X( control, user->bbox ) )
BBox_Conic_Check( user->last.x,
control->x,
to->x,
@ -173,7 +174,6 @@
&user->bbox.xMax );
if ( CHECK_Y( control, user->bbox ) )
BBox_Conic_Check( user->last.y,
control->y,
to->y,
@ -194,19 +194,25 @@
/* <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 accuracies. */
/* 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,
@ -235,17 +241,17 @@
if ( y1 == y4 )
{
if ( y1 == y2 && y1 == y3 ) /* Flat */
if ( y1 == y2 && y1 == y3 ) /* flat */
goto Test;
}
else if ( y1 < y4 )
{
if ( y2 >= y1 && y2 <= y4 && y3 >= y1 && y3 <= y4 ) /* Ascending */
if ( y2 >= y1 && y2 <= y4 && y3 >= y1 && y3 <= y4 ) /* ascending */
goto Test;
}
else
{
if ( y2 >= y4 && y2 <= y1 && y3 >= y4 && y3 <= y1 ) /* Descending */
if ( y2 >= y4 && y2 <= y1 && y3 >= y4 && y3 <= y1 ) /* descending */
{
y2 = y1;
y1 = y4;
@ -254,7 +260,7 @@
}
}
/* Unknown direction -- split the arc in two */
/* unknown direction -- split the arc in two */
arc[6] = y4;
arc[1] = y1 = ( y1 + y2 ) / 2;
arc[5] = y4 = ( y4 + y3 ) / 2;
@ -275,6 +281,7 @@
;
} while ( arc >= stack );
}
#else
static void
@ -296,17 +303,19 @@
FT_UNUSED ( y4 );
/* The polynom is */
/* */
/* a*x^3 + 3b*x^2 + 3c*x + d . */
/* */
/* However, we also have */
/* */
/* dP/dx(u) = 0 , */
/* */
/* which implies that */
/* */
/* P(u) = b*u^2 + 2c*u + d */
/* The polynom 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 )
{
@ -357,72 +366,67 @@
FT_Fixed t;
/* We need to solve "ax^2+2bx+c" here, without floating points! */
/* 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 the */
/* the 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 their product is held in a "16.16" value. */
/* 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;
/* Technical explanation of what's happening there. */
/* */
/* 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 their 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 );
/* 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 );
t2 = (FT_ULong)( ( c >= 0 ) ? c : -c );
t1 |= t2;
/* Now, the most significant bit of "t1" is sure to be the */
/* msb of one of "a", "b", "c", depending on which one is */
/* expressed in the greatest integer range. */
/* */
/* We now 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. that 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 polynom coefficients. */
/* */
/* This should ensure reasonably accurate values for the */
/* zeros. Note that the latter 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). */
/* */
/* 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;
@ -432,10 +436,11 @@
{
shift++;
t1 >>= 1;
} while ( t1 > 0x7FFFFFUL );
/* losing some bits of precision, but we use 24 of them */
/* for the computation anyway. */
/* this loses some bits of precision, but we use 24 of them */
/* for the computation anyway */
a >>= shift;
b >>= shift;
c >>= shift;
@ -446,6 +451,7 @@
{
shift++;
t1 <<= 1;
} while ( t1 < 0x400000UL );
a <<= shift;
@ -478,7 +484,7 @@
}
else
{
/* there are two solutions; we need to filter them though */
/* 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 );
@ -506,7 +512,9 @@
/* */
/* <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> */
@ -517,7 +525,7 @@
/* */
/* <Note> */
/* In the case of a non-monotonous arc, we don't compute directly */
/* extremum coordinates, we subdivise instead. */
/* extremum coordinates, we subdivide instead. */
/* */
static int
BBox_Cubic_To( FT_Vector* control1,
@ -530,23 +538,21 @@
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 );
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 );
BBox_Cubic_Check( user->last.y,
control1->y,
control2->y,
to->y,
&user->bbox.yMin,
&user->bbox.yMax );
user->last = *to;