static void
_compute_face (const cairo_point_t *point,
const cairo_slope_t *dev_slope,
double slope_dx,
double slope_dy,
cairo_stroker_t *stroker,
cairo_stroke_face_t *face)
{
double face_dx, face_dy;
cairo_point_t offset_ccw, offset_cw;
/*
* rotate to get a line_width/2 vector along the face, note that
* the vector must be rotated the right direction in device space,
* but by 90° in user space. So, the rotation depends on
* whether the ctm reflects or not, and that can be determined
* by looking at the determinant of the matrix.
*/
if (stroker->ctm_det_positive)
{
face_dx = - slope_dy * (stroker->style.line_width / 2.0);
face_dy = slope_dx * (stroker->style.line_width / 2.0);
}
else
{
face_dx = slope_dy * (stroker->style.line_width / 2.0);
face_dy = - slope_dx * (stroker->style.line_width / 2.0);
}
/* back to device space */
cairo_matrix_transform_distance (stroker->ctm, &face_dx, &face_dy);
offset_ccw.x = _cairo_fixed_from_double (face_dx);
offset_ccw.y = _cairo_fixed_from_double (face_dy);
offset_cw.x = -offset_ccw.x;
offset_cw.y = -offset_ccw.y;
face->ccw = *point;
_translate_point (&face->ccw, &offset_ccw);
face->point = *point;
face->cw = *point;
_translate_point (&face->cw, &offset_cw);
face->usr_vector.x = slope_dx;
face->usr_vector.y = slope_dy;
face->dev_vector = *dev_slope;
}
/*
* Construct a fan around the midpoint using the vertices from pen between
* inpt and outpt.
*/
static cairo_status_t
_tessellate_fan (cairo_stroker_t *stroker,
const cairo_slope_t *in_vector,
const cairo_slope_t *out_vector,
const cairo_point_t *midpt,
const cairo_point_t *inpt,
const cairo_point_t *outpt,
cairo_bool_t clockwise)
{
cairo_point_t stack_points[64], *points = stack_points;
int start, stop, step, i, npoints;
cairo_status_t status;
if (clockwise) {
step = -1;
start = _cairo_pen_find_active_ccw_vertex_index (&stroker->pen,
in_vector);
if (_cairo_slope_compare (&stroker->pen.vertices[start].slope_ccw,
in_vector) < 0)
start = _range_step (start, -1, stroker->pen.num_vertices);
stop = _cairo_pen_find_active_ccw_vertex_index (&stroker->pen,
out_vector);
if (_cairo_slope_compare (&stroker->pen.vertices[stop].slope_cw,
out_vector) > 0)
{
stop = _range_step (stop, 1, stroker->pen.num_vertices);
if (_cairo_slope_compare (&stroker->pen.vertices[stop].slope_ccw,
in_vector) < 0)
{
goto BEVEL;
}
}
npoints = start - stop;
} else {
step = 1;
start = _cairo_pen_find_active_cw_vertex_index (&stroker->pen,
in_vector);
if (_cairo_slope_compare (&stroker->pen.vertices[start].slope_cw,
in_vector) < 0)
start = _range_step (start, 1, stroker->pen.num_vertices);
stop = _cairo_pen_find_active_cw_vertex_index (&stroker->pen,
out_vector);
if (_cairo_slope_compare (&stroker->pen.vertices[stop].slope_ccw,
out_vector) > 0)
{
stop = _range_step (stop, -1, stroker->pen.num_vertices);
if (_cairo_slope_compare (&stroker->pen.vertices[stop].slope_cw,
in_vector) < 0)
{
goto BEVEL;
}
}
npoints = stop - start;
}
stop = _range_step (stop, step, stroker->pen.num_vertices);
if (npoints < 0)
npoints += stroker->pen.num_vertices;
npoints += 3;
if (npoints <= 1)
goto BEVEL;
if (npoints > ARRAY_LENGTH (stack_points)) {
points = _cairo_malloc_ab (npoints, sizeof (cairo_point_t));
if (unlikely (points == NULL))
return _cairo_error (CAIRO_STATUS_NO_MEMORY);
}
/* Construct the fan. */
npoints = 0;
points[npoints++] = *inpt;
for (i = start;
i != stop;
i = _range_step (i, step, stroker->pen.num_vertices))
{
points[npoints] = *midpt;
_translate_point (&points[npoints], &stroker->pen.vertices[i].point);
npoints++;
}
points[npoints++] = *outpt;
if (stroker->add_external_edge != NULL) {
for (i = 0; i < npoints - 1; i++) {
if (clockwise) {
status = stroker->add_external_edge (stroker->closure,
&points[i], &points[i+1]);
} else {
status = stroker->add_external_edge (stroker->closure,
&points[i+1], &points[i]);
}
if (unlikely (status))
break;
}
} else {
status = stroker->add_triangle_fan (stroker->closure,
midpt, points, npoints);
}
if (points != stack_points)
free (points);
return status;
BEVEL:
/* Ensure a leak free connection... */
if (stroker->add_external_edge != NULL) {
if (clockwise)
return stroker->add_external_edge (stroker->closure, inpt, outpt);
else
return stroker->add_external_edge (stroker->closure, outpt, inpt);
} else {
stack_points[0] = *midpt;
stack_points[1] = *inpt;
stack_points[2] = *outpt;
return stroker->add_triangle (stroker->closure, stack_points);
}
}
static cairo_status_t
_cairo_stroker_add_cap (cairo_stroker_t *stroker, cairo_stroke_face_t *f)
{
cairo_status_t status;
if (stroker->style->line_cap == CAIRO_LINE_CAP_BUTT)
return CAIRO_STATUS_SUCCESS;
switch (stroker->style->line_cap) {
case CAIRO_LINE_CAP_ROUND: {
int i;
int start, stop;
cairo_slope_t slope;
cairo_point_t tri[3];
cairo_pen_t *pen = &stroker->pen;
slope = f->dev_vector;
start = _cairo_pen_find_active_cw_vertex_index (pen, &slope);
slope.dx = -slope.dx;
slope.dy = -slope.dy;
stop = _cairo_pen_find_active_cw_vertex_index (pen, &slope);
tri[0] = f->point;
tri[1] = f->cw;
for (i=start; i != stop; i = (i+1) % pen->num_vertices) {
tri[2] = f->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];
}
tri[2] = f->ccw;
return _cairo_traps_tessellate_triangle (stroker->traps, tri);
}
case CAIRO_LINE_CAP_SQUARE: {
double dx, dy;
cairo_slope_t fvector;
cairo_point_t occw, ocw;
cairo_polygon_t polygon;
dx = f->usr_vector.x;
dy = f->usr_vector.y;
dx *= stroker->style->line_width / 2.0;
dy *= stroker->style->line_width / 2.0;
cairo_matrix_transform_distance (stroker->ctm, &dx, &dy);
fvector.dx = _cairo_fixed_from_double (dx);
fvector.dy = _cairo_fixed_from_double (dy);
occw.x = f->ccw.x + fvector.dx;
occw.y = f->ccw.y + fvector.dy;
ocw.x = f->cw.x + fvector.dx;
ocw.y = f->cw.y + fvector.dy;
_cairo_polygon_init (&polygon);
_cairo_polygon_move_to (&polygon, &f->cw);
_cairo_polygon_line_to (&polygon, &ocw);
_cairo_polygon_line_to (&polygon, &occw);
_cairo_polygon_line_to (&polygon, &f->ccw);
_cairo_polygon_close (&polygon);
status = _cairo_polygon_status (&polygon);
if (status == CAIRO_STATUS_SUCCESS) {
status = _cairo_bentley_ottmann_tessellate_polygon (stroker->traps,
&polygon,
CAIRO_FILL_RULE_WINDING);
}
_cairo_polygon_fini (&polygon);
return status;
}
case CAIRO_LINE_CAP_BUTT:
default:
return CAIRO_STATUS_SUCCESS;
}
}
/*
* Construct a fan around the midpoint using the vertices from pen between
* inpt and outpt.
*/
static cairo_status_t
_tessellate_fan (cairo_stroker_t *stroker,
const cairo_slope_t *in_vector,
const cairo_slope_t *out_vector,
const cairo_point_t *midpt,
const cairo_point_t *inpt,
const cairo_point_t *outpt,
cairo_bool_t clockwise)
{
cairo_point_t stack_points[64], *points = stack_points;
cairo_pen_t *pen = &stroker->pen;
int start, stop, num_points = 0;
cairo_status_t status;
if (stroker->has_bounds &&
! _cairo_box_contains_point (&stroker->bounds, midpt))
goto BEVEL;
assert (stroker->pen.num_vertices);
if (clockwise) {
_cairo_pen_find_active_ccw_vertices (pen,
in_vector, out_vector,
&start, &stop);
if (stroker->add_external_edge) {
cairo_point_t last;
last = *inpt;
while (start != stop) {
cairo_point_t p = *midpt;
_translate_point (&p, &pen->vertices[start].point);
status = stroker->add_external_edge (stroker->closure,
&last, &p);
if (unlikely (status))
return status;
last = p;
if (start-- == 0)
start += pen->num_vertices;
}
status = stroker->add_external_edge (stroker->closure,
&last, outpt);
} else {
if (start == stop)
goto BEVEL;
num_points = stop - start;
if (num_points < 0)
num_points += pen->num_vertices;
num_points += 2;
if (num_points > ARRAY_LENGTH(stack_points)) {
points = _cairo_malloc_ab (num_points, sizeof (cairo_point_t));
if (unlikely (points == NULL))
return _cairo_error (CAIRO_STATUS_NO_MEMORY);
}
points[0] = *inpt;
num_points = 1;
while (start != stop) {
points[num_points] = *midpt;
_translate_point (&points[num_points], &pen->vertices[start].point);
num_points++;
if (start-- == 0)
start += pen->num_vertices;
}
points[num_points++] = *outpt;
}
} else {
_cairo_pen_find_active_cw_vertices (pen,
in_vector, out_vector,
&start, &stop);
if (stroker->add_external_edge) {
cairo_point_t last;
last = *inpt;
while (start != stop) {
cairo_point_t p = *midpt;
_translate_point (&p, &pen->vertices[start].point);
status = stroker->add_external_edge (stroker->closure,
&p, &last);
if (unlikely (status))
return status;
last = p;
if (++start == pen->num_vertices)
start = 0;
}
status = stroker->add_external_edge (stroker->closure,
outpt, &last);
} else {
if (start == stop)
goto BEVEL;
num_points = stop - start;
if (num_points < 0)
num_points += pen->num_vertices;
num_points += 2;
if (num_points > ARRAY_LENGTH(stack_points)) {
points = _cairo_malloc_ab (num_points, sizeof (cairo_point_t));
if (unlikely (points == NULL))
return _cairo_error (CAIRO_STATUS_NO_MEMORY);
}
points[0] = *inpt;
num_points = 1;
while (start != stop) {
points[num_points] = *midpt;
_translate_point (&points[num_points], &pen->vertices[start].point);
num_points++;
if (++start == pen->num_vertices)
start = 0;
}
points[num_points++] = *outpt;
}
}
if (num_points) {
status = stroker->add_triangle_fan (stroker->closure,
midpt, points, num_points);
}
if (points != stack_points)
free (points);
return status;
BEVEL:
/* Ensure a leak free connection... */
if (stroker->add_external_edge != NULL) {
if (clockwise)
return stroker->add_external_edge (stroker->closure, inpt, outpt);
else
return stroker->add_external_edge (stroker->closure, outpt, inpt);
} else {
stack_points[0] = *midpt;
stack_points[1] = *inpt;
stack_points[2] = *outpt;
return stroker->add_triangle (stroker->closure, stack_points);
}
}
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);
}
}
}
