Commit fc32e1c8cc67b0481d3e563e39dd11f120585b7f
2013-08-19T22:57:05
[base] Enable new algorithm for BBox_Cubic_Check. * src/base/ftbbox.c: Enable new BBox_Cubic_Check algorithm, remove the old one. Improve comments.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295
diff --git a/ChangeLog b/ChangeLog
index eb13f32..051ef3b 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,10 @@
+2013-08-19 Alexei Podtelezhnikov <apodtele@gmail.com>
+
+ [base] Enable new algorithm for BBox_Cubic_Check.
+
+ * src/base/ftbbox.c: Enable new BBox_Cubic_Check algorithm, remove the
+ old one. Improve comments.
+
2013-08-18 Werner Lemberg <wl@gnu.org>
* builds/unix/unix-def.in (freetype2.pc): Don't set executable bit.
diff --git a/src/base/ftbbox.c b/src/base/ftbbox.c
index c4bd027..ebbfb1a 100644
--- a/src/base/ftbbox.c
+++ b/src/base/ftbbox.c
@@ -109,9 +109,9 @@
FT_Pos* max )
{
/* This function is only called when a control off-point is outside */
- /* the bbox. This also means there must be a local extremum within */
- /* the segment with the value of (y1*y3 - y2*y2)/(y1 - 2*y2 + y3). */
- /* Offsetting from the closest point to the extermum, y2, we get */
+ /* 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;
@@ -185,8 +185,8 @@
/* */
/* <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. */
+ /* updates a bounding range. This version uses iterative splitting */
+ /* because it is faster than the exact solution with square roots. */
/* */
/* <Input> */
/* p1 :: The start coordinate. */
@@ -203,17 +203,15 @@
/* max :: The address of the current maximum. */
/* */
-#if 0
-
static FT_Pos
- update_max( FT_Pos q1,
- FT_Pos q2,
- FT_Pos q3,
- FT_Pos q4,
- FT_Pos max )
+ update_cubic_max( FT_Pos q1,
+ FT_Pos q2,
+ FT_Pos q3,
+ FT_Pos q4,
+ FT_Pos max )
{
- /* for a conic segment to possibly reach new maximum */
- /* one of its off-points must be above the current value */
+ /* for a cubic segment to possibly reach new maximum, at least */
+ /* one of its off-points must stay above the current value */
while ( q2 > max || q3 > max )
{
/* determine which half contains the maximum and split */
@@ -267,13 +265,15 @@
FT_Pos nmin, nmax;
FT_Int shift;
- /* This implementation relies on iterative bisection of the segment. */
- /* The fixed-point arithmentic 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 bisection. This */
- /* function is only called when a control off-point is outside the */
- /* the bbox and, thus, has the top absolute value among arguments. */
+ /* 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 using iterative bisection of the segment. */
+ /* The fixed-point arithmentic 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 bisection. */
+ /* The control off-point outside the bbox is likely to have the top */
+ /* absolute value among arguments. */
shift = 27 - FT_MSB( FT_ABS( p2 ) | FT_ABS( p3 ) );
@@ -282,7 +282,7 @@
/* upscaling too much just wastes time */
if ( shift > 2 )
shift = 2;
-
+
p1 <<= shift;
p2 <<= shift;
p3 <<= shift;
@@ -290,7 +290,7 @@
nmin = *min << shift;
nmax = *max << shift;
}
- else
+ else
{
p1 >>= -shift;
p2 >>= -shift;
@@ -300,10 +300,10 @@
nmax = *max >> -shift;
}
- nmax = update_max( p1, p2, p3, p4, nmax );
+ nmax = update_cubic_max( p1, p2, p3, p4, nmax );
/* now flip the signs to update the minimum */
- nmin = -update_max( -p1, -p2, -p3, -p4, -nmin );
+ nmin = -update_cubic_max( -p1, -p2, -p3, -p4, -nmin );
if ( shift > 0 )
{
@@ -322,172 +322,6 @@
*max = nmax;
}
-#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
-
/*************************************************************************/
/* */