Graham,
Here's a final revision.
It produces exactly the same results as the previous one but the code is a bit
faster (and also easier to understand - the previous code was trying to be a
bit too clever).
David %^>
static void
gray_render_cubic( RAS_ARG_ const FT_Vector* control1,
const FT_Vector* control2,
const FT_Vector* to )
{
FT_Vector* arc;
arc = ras.bez_stack;
arc[0].x = UPSCALE( to->x );
arc[0].y = UPSCALE( to->y );
arc[1].x = UPSCALE( control2->x );
arc[1].y = UPSCALE( control2->y );
arc[2].x = UPSCALE( control1->x );
arc[2].y = UPSCALE( control1->y );
arc[3].x = ras.x;
arc[3].y = ras.y;
for (;;)
{
/* Check that the arc crosses the current band. */
TPos min, max, y;
min = max = arc[0].y;
y = arc[1].y;
if ( y< min ) min = y;
if ( y> max ) max = y;
y = arc[2].y;
if ( y< min ) min = y;
if ( y> max ) max = y;
y = arc[3].y;
if ( y< min ) min = y;
if ( y> max ) max = y;
if ( TRUNC( min )>= ras.max_ey || TRUNC( max )< 0 )
goto Draw;
/* Decide whether to split or draw */
/* See Hain's paper at http://tinyurl.com/HainBez for more info */
{
TPos dx, dy, L, dx1, dy1, dx2, dy2, s, s_limit;
/* dx and dy are x- and y- components of the P0-P3 chord vector */
dx = arc[3].x - arc[0].x;
dy = arc[3].y - arc[0].y;
/* L is an (under)estimate of the Euclidean distance P0-P3 */
L = ( 236 * FT_MAX(labs(dx), labs(dy))
+ 97 * FT_MIN(labs(dx), labs(dy)))>> 8;
/* avoid possible arithmetic overflow below by splitting */
if (L> 32767)
goto Split;
/* s is L * the perpendicular distance from P1 to the line P0-P3 */
s = labs( dy * (dx1 = arc[1].x - arc[0].x)
- dx * (dy1 = arc[1].y - arc[0].y));
/* max deviation may be as much as (s/L) * 3/4 (if Hain's v = 1) */
if (s> (s_limit = L * (TPos)(FT_MAX_CURVE_DEVIATION / 0.75)))
goto Split;
/* s is L * the perpendicular distance from P2 to the line P0-P3 */
s = labs( dy * (dx2 = arc[2].x - arc[0].x)
- dx * (dy2 = arc[2].y - arc[0].y));
/* max deviation may be as much as (s/L) * 3/4 (if Hain's v = 1) */
if (s> s_limit)
goto Split;
/* if P1 or P2 is outside P0-P3, split */
if ( dy * dy1 + dx * dx1< 0
|| dy * dy2 + dx * dx2< 0
|| dy * (arc[3].y - arc[1].y) + dx * (arc[3].x - arc[1].x)< 0
|| dy * (arc[3].y - arc[2].y) + dx * (arc[3].x - arc[2].x)< 0
)
goto Split;
/* no reason to split */
goto Draw;
}
Split:
gray_split_cubic( arc );
arc += 3;
continue;
Draw:
gray_render_line( RAS_VAR_ arc[0].x, arc[0].y );
if (arc == ras.bez_stack)
return;
arc -= 3;
}
}