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[truetype] Cheaper way to threshold angles between vectors.

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* src/truetype/ttinterp.c (Ins_ISECT): Thresholding tangent is a lot
cheaper than thresholding sine.
This commit is contained in:
Alexei Podtelezhnikov 2012-10-20 22:23:01 -04:00
parent ad4eecca77
commit 24e897db28
2 changed files with 19 additions and 31 deletions
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7
ChangeLog
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@ -1,3 +1,10 @@
2012-10-20 Alexei Podtelezhnikov <apodtele@gmail.com>
[truetype] Cheaper way to threshold angles between vectors.
* src/truetype/ttinterp.c (Ins_ISECT): Thresholding tangent is a lot
cheaper than thresholding sine.
2012-10-20 Werner Lemberg <wl@gnu.org>
[cff] Improve parsing of invalid real numbers.

43
src/truetype/ttinterp.c
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@ -6835,15 +6835,12 @@
a0, a1,
b0, b1;
FT_F26Dot6 discriminant;
FT_F26Dot6 discriminant, dotproduct;
FT_F26Dot6 dx, dy,
dax, day,
dbx, dby;
FT_F26Dot6 len_a, len_b;
FT_Long sine;
FT_F26Dot6 val;
FT_Vector R;
@ -6882,34 +6879,18 @@
discriminant = TT_MULDIV( dax, -dby, 0x40 ) +
TT_MULDIV( day, dbx, 0x40 );
dotproduct = TT_MULDIV( dax, dbx, 0x40 ) +
TT_MULDIV( day, dby, 0x40 );
/* Let */
/* */
/* a = vector(a0, a1) */
/* b = vector(b0, b1) . */
/* */
/* Then */
/* */
/* dot_product(normal_vector(a), b) */
/* = discriminant */
/* = |a| * |b| * sin(alpha) . */
len_a = TT_VecLen( dax, day );
len_b = TT_VecLen( dbx, dby );
if ( len_a && len_b )
{
/* precision: (F.6 * F.16) / F.6 = F.16 */
sine = FT_DivFix( discriminant, len_a );
/* precision: (F.16 * F.16) / F.6 = F.26 */
sine = FT_DivFix( sine, len_b );
}
else
sine = 0;
/* We reject grazing intersections; heuristic value 2342066 */
/* corresponds to arcsin(2342066/2^26), this is approx 2 degrees. */
if ( FT_ABS( sine ) >= 2342066 )
/* The discriminant above is actually a cross product of vectors */
/* da and db. Together with the dot product, they can be used as */
/* surrogates for sine and cosine of the angle between the vectors. */
/* Indeed, */
/* dotproduct = |da||db|cos(angle) */
/* discriminant = |da||db|sin(angle) . */
/* We use these equations to reject grazing intersections by */
/* thresholding abs(tan(angle)) at 1/19, corresponding to 3 degrees. */
if ( 19 * FT_ABS( discriminant ) > FT_ABS( dotproduct ) )
{
val = TT_MULDIV( dx, -dby, 0x40 ) + TT_MULDIV( dy, dbx, 0x40 );