static inline cairo_bo_intersect_ordinate_t
round_to_nearest (cairo_quorem64_t d,
cairo_int64_t den)
{
cairo_bo_intersect_ordinate_t ordinate;
int32_t quo = d.quo;
cairo_int64_t drem_2 = _cairo_int64_mul (d.rem, _cairo_int32_to_int64 (2));
/* assert (! _cairo_int64_negative (den));*/
if (_cairo_int64_lt (drem_2, _cairo_int64_negate (den))) {
quo -= 1;
drem_2 = _cairo_int64_negate (drem_2);
} else if (_cairo_int64_le (den, drem_2)) {
quo += 1;
drem_2 = _cairo_int64_negate (drem_2);
}
ordinate.ordinate = quo;
ordinate.approx = _cairo_int64_is_zero (drem_2) ? EXACT : _cairo_int64_negative (drem_2) ? EXCESS : DEFAULT;
return ordinate;
}
static cairo_int64_t
distance_from_face (const cairo_stroke_face_t *face,
const cairo_point_t *p,
cairo_bool_t negate)
{
int32_t dx = (p->x - face->point.x);
int32_t dy = (p->y - face->point.y);
cairo_int64_t d;
d = _cairo_int64_sub (_cairo_int32x32_64_mul (dx, face->dev_vector.dy),
_cairo_int32x32_64_mul (dy, face->dev_vector.dx));
if (negate)
d = _cairo_int64_negate (d);
return d;
}
/* Compute the intersection of two lines as defined by two edges. The
* result is provided as a coordinate pair of 128-bit integers.
*
* Returns %CAIRO_BO_STATUS_INTERSECTION if there is an intersection or
* %CAIRO_BO_STATUS_PARALLEL if the two lines are exactly parallel.
*/
static cairo_bool_t
intersect_lines (cairo_bo_edge_t *a,
cairo_bo_edge_t *b,
cairo_bo_intersect_point_t *intersection)
{
cairo_int64_t a_det, b_det;
/* XXX: We're assuming here that dx and dy will still fit in 32
* bits. That's not true in general as there could be overflow. We
* should prevent that before the tessellation algorithm begins.
* What we're doing to mitigate this is to perform clamping in
* cairo_bo_tessellate_polygon().
*/
int32_t dx1 = a->edge.line.p1.x - a->edge.line.p2.x;
int32_t dy1 = a->edge.line.p1.y - a->edge.line.p2.y;
int32_t dx2 = b->edge.line.p1.x - b->edge.line.p2.x;
int32_t dy2 = b->edge.line.p1.y - b->edge.line.p2.y;
cairo_int64_t den_det;
cairo_int64_t R;
cairo_quorem64_t qr;
den_det = det32_64 (dx1, dy1, dx2, dy2);
/* Q: Can we determine that the lines do not intersect (within range)
* much more cheaply than computing the intersection point i.e. by
* avoiding the division?
*
* X = ax + t * adx = bx + s * bdx;
* Y = ay + t * ady = by + s * bdy;
* ∴ t * (ady*bdx - bdy*adx) = bdx * (by - ay) + bdy * (ax - bx)
* => t * L = R
*
* Therefore we can reject any intersection (under the criteria for
* valid intersection events) if:
* L^R < 0 => t < 0, or
* L<R => t > 1
*
* (where top/bottom must at least extend to the line endpoints).
*
* A similar substitution can be performed for s, yielding:
* s * (ady*bdx - bdy*adx) = ady * (ax - bx) - adx * (ay - by)
*/
R = det32_64 (dx2, dy2,
b->edge.line.p1.x - a->edge.line.p1.x,
b->edge.line.p1.y - a->edge.line.p1.y);
if (_cairo_int64_negative (den_det)) {
if (_cairo_int64_ge (den_det, R))
return FALSE;
} else {
if (_cairo_int64_le (den_det, R))
return FALSE;
}
R = det32_64 (dy1, dx1,
a->edge.line.p1.y - b->edge.line.p1.y,
a->edge.line.p1.x - b->edge.line.p1.x);
if (_cairo_int64_negative (den_det)) {
if (_cairo_int64_ge (den_det, R))
return FALSE;
} else {
if (_cairo_int64_le (den_det, R))
return FALSE;
}
/* We now know that the two lines should intersect within range. */
a_det = det32_64 (a->edge.line.p1.x, a->edge.line.p1.y,
a->edge.line.p2.x, a->edge.line.p2.y);
b_det = det32_64 (b->edge.line.p1.x, b->edge.line.p1.y,
b->edge.line.p2.x, b->edge.line.p2.y);
/* x = det (a_det, dx1, b_det, dx2) / den_det */
qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dx1,
b_det, dx2),
den_det);
if (_cairo_int64_eq (qr.rem, den_det))
return FALSE;
#if 0
intersection->x.exactness = _cairo_int64_is_zero (qr.rem) ? EXACT : INEXACT;
#else
intersection->x.exactness = EXACT;
if (! _cairo_int64_is_zero (qr.rem)) {
if (_cairo_int64_negative (den_det) ^ _cairo_int64_negative (qr.rem))
qr.rem = _cairo_int64_negate (qr.rem);
qr.rem = _cairo_int64_mul (qr.rem, _cairo_int32_to_int64 (2));
if (_cairo_int64_ge (qr.rem, den_det)) {
qr.quo = _cairo_int64_add (qr.quo,
_cairo_int32_to_int64 (_cairo_int64_negative (qr.quo) ? -1 : 1));
} else
intersection->x.exactness = INEXACT;
}
#endif
intersection->x.ordinate = _cairo_int64_to_int32 (qr.quo);
/* y = det (a_det, dy1, b_det, dy2) / den_det */
qr = _cairo_int_96by64_32x64_divrem (det64x32_128 (a_det, dy1,
b_det, dy2),
den_det);
if (_cairo_int64_eq (qr.rem, den_det))
return FALSE;
#if 0
intersection->y.exactness = _cairo_int64_is_zero (qr.rem) ? EXACT : INEXACT;
#else
intersection->y.exactness = EXACT;
if (! _cairo_int64_is_zero (qr.rem)) {
if (_cairo_int64_negative (den_det) ^ _cairo_int64_negative (qr.rem))
qr.rem = _cairo_int64_negate (qr.rem);
qr.rem = _cairo_int64_mul (qr.rem, _cairo_int32_to_int64 (2));
if (_cairo_int64_ge (qr.rem, den_det)) {
qr.quo = _cairo_int64_add (qr.quo,
_cairo_int32_to_int64 (_cairo_int64_negative (qr.quo) ? -1 : 1));
} else
intersection->y.exactness = INEXACT;
}
#endif
intersection->y.ordinate = _cairo_int64_to_int32 (qr.quo);
return TRUE;
}