static cairo_status_t
_cairo_stroker_add_sub_edge (cairo_stroker_t *stroker,
const cairo_point_t *p1,
const cairo_point_t *p2,
cairo_slope_t *dev_slope,
double slope_dx, double slope_dy,
cairo_stroke_face_t *start,
cairo_stroke_face_t *end)
{
cairo_point_t rectangle[4];
_compute_face (p1, dev_slope, slope_dx, slope_dy, stroker, start);
/* XXX: This could be optimized slightly by not calling
_compute_face again but rather translating the relevant
fields from start. */
_compute_face (p2, dev_slope, slope_dx, slope_dy, stroker, end);
if (p1->x == p2->x && p1->y == p2->y)
return CAIRO_STATUS_SUCCESS;
rectangle[0] = start->cw;
rectangle[1] = start->ccw;
rectangle[2] = end->ccw;
rectangle[3] = end->cw;
return _cairo_traps_tessellate_convex_quad (stroker->traps, rectangle);
}
/* A triangle is simply a degenerate case of a convex
* quadrilateral. We would not benefit from having any distinct
* implementation of triangle vs. quadrilateral tessellation here. */
cairo_status_t
_cairo_traps_tessellate_triangle (cairo_traps_t *traps, cairo_point_t t[3])
{
cairo_point_t quad[4];
quad[0] = t[0];
quad[1] = t[0];
quad[2] = t[1];
quad[3] = t[2];
return _cairo_traps_tessellate_convex_quad (traps, quad);
}
static cairo_status_t
_cairo_stroker_join (cairo_stroker_t *stroker, cairo_stroke_face_t *in, cairo_stroke_face_t *out)
{
int clockwise = _cairo_stroker_face_clockwise (out, in);
cairo_point_t *inpt, *outpt;
cairo_status_t status;
if (in->cw.x == out->cw.x
&& in->cw.y == out->cw.y
&& in->ccw.x == out->ccw.x
&& in->ccw.y == out->ccw.y)
{
return CAIRO_STATUS_SUCCESS;
}
if (clockwise) {
inpt = &in->ccw;
outpt = &out->ccw;
} else {
inpt = &in->cw;
outpt = &out->cw;
}
switch (stroker->style->line_join) {
case CAIRO_LINE_JOIN_ROUND: {
int i;
int start, step, stop;
cairo_point_t tri[3];
cairo_pen_t *pen = &stroker->pen;
tri[0] = in->point;
if (clockwise) {
start =
_cairo_pen_find_active_ccw_vertex_index (pen, &in->dev_vector);
stop =
_cairo_pen_find_active_ccw_vertex_index (pen, &out->dev_vector);
step = -1;
} else {
start =
_cairo_pen_find_active_cw_vertex_index (pen, &in->dev_vector);
stop =
_cairo_pen_find_active_cw_vertex_index (pen, &out->dev_vector);
step = +1;
}
i = start;
tri[1] = *inpt;
while (i != stop) {
tri[2] = in->point;
_translate_point (&tri[2], &pen->vertices[i].point);
status = _cairo_traps_tessellate_triangle (stroker->traps, tri);
if (unlikely (status))
return status;
tri[1] = tri[2];
i += step;
if (i < 0)
i = pen->num_vertices - 1;
if (i >= pen->num_vertices)
i = 0;
}
tri[2] = *outpt;
return _cairo_traps_tessellate_triangle (stroker->traps, tri);
}
case CAIRO_LINE_JOIN_MITER:
default: {
/* dot product of incoming slope vector with outgoing slope vector */
double in_dot_out = ((-in->usr_vector.x * out->usr_vector.x)+
(-in->usr_vector.y * out->usr_vector.y));
double ml = stroker->style->miter_limit;
/* Check the miter limit -- lines meeting at an acute angle
* can generate long miters, the limit converts them to bevel
*
* Consider the miter join formed when two line segments
* meet at an angle psi:
*
* /.\
* /. .\
* /./ \.\
* /./psi\.\
*
* We can zoom in on the right half of that to see:
*
* |\
* | \ psi/2
* | \
* | \
* | \
* | \
* miter \
* length \
* | \
* | .\
* | . \
* |. line \
* \ width \
* \ \
*
*
* The right triangle in that figure, (the line-width side is
* shown faintly with three '.' characters), gives us the
* following expression relating miter length, angle and line
* width:
*
* 1 /sin (psi/2) = miter_length / line_width
*
* The right-hand side of this relationship is the same ratio
* in which the miter limit (ml) is expressed. We want to know
* when the miter length is within the miter limit. That is
* when the following condition holds:
*
* 1/sin(psi/2) <= ml
* 1 <= ml sin(psi/2)
* 1 <= ml² sin²(psi/2)
* 2 <= ml² 2 sin²(psi/2)
* 2·sin²(psi/2) = 1-cos(psi)
* 2 <= ml² (1-cos(psi))
*
* in · out = |in| |out| cos (psi)
*
* in and out are both unit vectors, so:
*
* in · out = cos (psi)
*
* 2 <= ml² (1 - in · out)
*
*/
if (2 <= ml * ml * (1 - in_dot_out))
{
double x1, y1, x2, y2;
double mx, my;
double dx1, dx2, dy1, dy2;
cairo_point_t outer;
cairo_point_t quad[4];
double ix, iy;
double fdx1, fdy1, fdx2, fdy2;
double mdx, mdy;
/*
* we've got the points already transformed to device
* space, but need to do some computation with them and
* also need to transform the slope from user space to
* device space
*/
/* outer point of incoming line face */
x1 = _cairo_fixed_to_double (inpt->x);
y1 = _cairo_fixed_to_double (inpt->y);
dx1 = in->usr_vector.x;
dy1 = in->usr_vector.y;
cairo_matrix_transform_distance (stroker->ctm, &dx1, &dy1);
/* outer point of outgoing line face */
x2 = _cairo_fixed_to_double (outpt->x);
y2 = _cairo_fixed_to_double (outpt->y);
dx2 = out->usr_vector.x;
dy2 = out->usr_vector.y;
cairo_matrix_transform_distance (stroker->ctm, &dx2, &dy2);
/*
* Compute the location of the outer corner of the miter.
* That's pretty easy -- just the intersection of the two
* outer edges. We've got slopes and points on each
* of those edges. Compute my directly, then compute
* mx by using the edge with the larger dy; that avoids
* dividing by values close to zero.
*/
my = (((x2 - x1) * dy1 * dy2 - y2 * dx2 * dy1 + y1 * dx1 * dy2) /
(dx1 * dy2 - dx2 * dy1));
if (fabs (dy1) >= fabs (dy2))
mx = (my - y1) * dx1 / dy1 + x1;
else
mx = (my - y2) * dx2 / dy2 + x2;
/*
* When the two outer edges are nearly parallel, slight
* perturbations in the position of the outer points of the lines
* caused by representing them in fixed point form can cause the
* intersection point of the miter to move a large amount. If
* that moves the miter intersection from between the two faces,
* then draw a bevel instead.
*/
ix = _cairo_fixed_to_double (in->point.x);
iy = _cairo_fixed_to_double (in->point.y);
/* slope of one face */
fdx1 = x1 - ix; fdy1 = y1 - iy;
/* slope of the other face */
fdx2 = x2 - ix; fdy2 = y2 - iy;
/* slope from the intersection to the miter point */
mdx = mx - ix; mdy = my - iy;
/*
* Make sure the miter point line lies between the two
* faces by comparing the slopes
*/
if (_cairo_slope_compare_sgn (fdx1, fdy1, mdx, mdy) !=
_cairo_slope_compare_sgn (fdx2, fdy2, mdx, mdy))
{
/*
* Draw the quadrilateral
*/
outer.x = _cairo_fixed_from_double (mx);
outer.y = _cairo_fixed_from_double (my);
quad[0] = in->point;
quad[1] = *inpt;
quad[2] = outer;
quad[3] = *outpt;
return _cairo_traps_tessellate_convex_quad (stroker->traps, quad);
}
}
/* fall through ... */
}
case CAIRO_LINE_JOIN_BEVEL: {
cairo_point_t tri[3];
tri[0] = in->point;
tri[1] = *inpt;
tri[2] = *outpt;
return _cairo_traps_tessellate_triangle (stroker->traps, tri);
}
}
}
