/* Render an arc segment starting at (xc + x0, yc + y0) to (xc + x1,
yc + y1), centered at (xc, yc), and with given radius. Both x0^2 +
y0^2 and x1^2 + y1^2 should be equal to radius^2.
A positive value of radius means curve to the left, negative means
curve to the right.
*/
static void
art_svp_vpath_stroke_arc (ArtVpath **p_vpath, int *pn, int *pn_max,
double xc, double yc,
double x0, double y0,
double x1, double y1,
double radius,
double flatness)
{
double theta;
double th_0, th_1;
int n_pts;
int i;
double aradius;
aradius = fabs (radius);
theta = 2 * M_SQRT2 * sqrt (flatness / aradius);
th_0 = atan2 (y0, x0);
th_1 = atan2 (y1, x1);
if (radius > 0)
{
/* curve to the left */
if (th_0 < th_1) th_0 += M_PI * 2;
n_pts = ceil ((th_0 - th_1) / theta);
}
else
{
/* curve to the right */
if (th_1 < th_0) th_1 += M_PI * 2;
n_pts = ceil ((th_1 - th_0) / theta);
}
#ifdef VERBOSE
printf ("start %f %f; th_0 = %f, th_1 = %f, r = %f, theta = %f\n", x0, y0, th_0, th_1, radius, theta);
#endif
art_vpath_add_point (p_vpath, pn, pn_max,
ART_LINETO, xc + x0, yc + y0);
for (i = 1; i < n_pts; i++)
{
theta = th_0 + (th_1 - th_0) * i / n_pts;
art_vpath_add_point (p_vpath, pn, pn_max,
ART_LINETO, xc + cos (theta) * aradius,
yc + sin (theta) * aradius);
#ifdef VERBOSE
printf ("mid %f %f\n", cos (theta) * radius, sin (theta) * radius);
#endif
}
art_vpath_add_point (p_vpath, pn, pn_max,
ART_LINETO, xc + x1, yc + y1);
#ifdef VERBOSE
printf ("end %f %f\n", x1, y1);
#endif
}
/**
* art_vpath_new_vpath_array: Generate a heap-based ArtVpath-array from a vpath iterator
* @src: Source Iterator
* Return value: Newly allocated vpath
**/
ArtVpath *art_vpath_new_vpath_array(ArtVpathIterator *src)
{
ArtVpath *result;
ArtVpath *current;
int n_result, n_result_max;
if (!src->current(src)) return 0;
n_result = 0;
n_result_max = 16;
result = art_new (ArtVpath, n_result_max);
while(1) {
current = src->current(src);
if (!current) break;
art_vpath_add_point (&result, &n_result, &n_result_max,
current->code, current->x, current->y);
if (current->code == ART_END) break;
src->next(src);
}
return result;
}
/**
* art_svp_from_vpath_raw: Stroke a vector path, raw version
* @vpath: #ArtVPath to stroke.
* @join: Join style.
* @cap: Cap style.
* @line_width: Width of stroke.
* @miter_limit: Miter limit.
* @flatness: Flatness.
*
* Exactly the same as art_svp_vpath_stroke(), except that the resulting
* stroke outline may self-intersect and have regions of winding number
* greater than 1.
*
* Return value: Resulting raw stroked outline in svp format.
**/
ArtVpath *
art_svp_vpath_stroke_raw (ArtVpath *vpath,
ArtPathStrokeJoinType join,
ArtPathStrokeCapType cap,
double line_width,
double miter_limit,
double flatness)
{
int begin_idx, end_idx;
int i;
ArtVpath *forw, *rev;
int n_forw, n_rev;
int n_forw_max, n_rev_max;
ArtVpath *result;
int n_result, n_result_max;
double half_lw = 0.5 * line_width;
int closed;
int last, this, next, second;
double dx, dy;
n_forw_max = 16;
forw = art_new (ArtVpath, n_forw_max);
n_rev_max = 16;
rev = art_new (ArtVpath, n_rev_max);
n_result = 0;
n_result_max = 16;
result = art_new (ArtVpath, n_result_max);
for (begin_idx = 0; vpath[begin_idx].code != ART_END; begin_idx = end_idx)
{
n_forw = 0;
n_rev = 0;
closed = (vpath[begin_idx].code == ART_MOVETO);
/* we don't know what the first point joins with until we get to the
last point and see if it's closed. So we start with the second
line in the path.
Note: this is not strictly true (we now know it's closed from
the opening pathcode), but why fix code that isn't broken?
*/
this = begin_idx;
/* skip over identical points at the beginning of the subpath */
for (i = this + 1; vpath[i].code == ART_LINETO; i++)
{
dx = vpath[i].x - vpath[this].x;
dy = vpath[i].y - vpath[this].y;
if (dx * dx + dy * dy > EPSILON_2)
break;
}
next = i;
second = next;
/* invariant: this doesn't coincide with next */
while (vpath[next].code == ART_LINETO)
{
last = this;
this = next;
/* skip over identical points after the beginning of the subpath */
for (i = this + 1; vpath[i].code == ART_LINETO; i++)
{
dx = vpath[i].x - vpath[this].x;
dy = vpath[i].y - vpath[this].y;
if (dx * dx + dy * dy > EPSILON_2)
break;
}
next = i;
if (vpath[next].code != ART_LINETO)
{
/* reached end of path */
/* make "closed" detection conform to PostScript
semantics (i.e. explicit closepath code rather than
just the fact that end of the path is the beginning) */
if (closed &&
vpath[this].x == vpath[begin_idx].x &&
vpath[this].y == vpath[begin_idx].y)
{
int j;
/* path is closed, render join to beginning */
render_seg (&forw, &n_forw, &n_forw_max,
&rev, &n_rev, &n_rev_max,
vpath, last, this, second,
join, half_lw, miter_limit, flatness);
#ifdef VERBOSE
printf ("%% forw %d, rev %d\n", n_forw, n_rev);
#endif
/* do forward path */
art_vpath_add_point (&result, &n_result, &n_result_max,
ART_MOVETO, forw[n_forw - 1].x,
forw[n_forw - 1].y);
for (j = 0; j < n_forw; j++)
art_vpath_add_point (&result, &n_result, &n_result_max,
ART_LINETO, forw[j].x,
forw[j].y);
/* do reverse path, reversed */
art_vpath_add_point (&result, &n_result, &n_result_max,
ART_MOVETO, rev[0].x,
rev[0].y);
for (j = n_rev - 1; j >= 0; j--)
art_vpath_add_point (&result, &n_result, &n_result_max,
ART_LINETO, rev[j].x,
rev[j].y);
}
else
{
/* path is open */
int j;
/* add to forw rather than result to ensure that
forw has at least one point. */
render_cap (&forw, &n_forw, &n_forw_max,
vpath, last, this,
cap, half_lw, flatness);
art_vpath_add_point (&result, &n_result, &n_result_max,
ART_MOVETO, forw[0].x,
forw[0].y);
for (j = 1; j < n_forw; j++)
art_vpath_add_point (&result, &n_result, &n_result_max,
ART_LINETO, forw[j].x,
forw[j].y);
for (j = n_rev - 1; j >= 0; j--)
art_vpath_add_point (&result, &n_result, &n_result_max,
ART_LINETO, rev[j].x,
rev[j].y);
render_cap (&result, &n_result, &n_result_max,
vpath, second, begin_idx,
cap, half_lw, flatness);
art_vpath_add_point (&result, &n_result, &n_result_max,
ART_LINETO, forw[0].x,
forw[0].y);
}
}
else
render_seg (&forw, &n_forw, &n_forw_max,
&rev, &n_rev, &n_rev_max,
vpath, last, this, next,
join, half_lw, miter_limit, flatness);
}
end_idx = next;
}
art_free (forw);
art_free (rev);
#ifdef VERBOSE
printf ("%% n_result = %d\n", n_result);
#endif
art_vpath_add_point (&result, &n_result, &n_result_max, ART_END, 0, 0);
return result;
}
/* caps i1, under the assumption of a vector from i0 */
static void
render_cap (ArtVpath **p_result, int *pn_result, int *pn_result_max,
ArtVpath *vpath, int i0, int i1,
ArtPathStrokeCapType cap, double line_width, double flatness)
{
double dx0, dy0;
double dlx0, dly0;
double scale;
int n_pts;
int i;
dx0 = vpath[i1].x - vpath[i0].x;
dy0 = vpath[i1].y - vpath[i0].y;
/* Set dl[xy]0 to the vector from i0 to i1, rotated counterclockwise
90 degrees, and scaled to the length of line_width. */
scale = line_width / sqrt (dx0 * dx0 + dy0 * dy0);
dlx0 = dy0 * scale;
dly0 = -dx0 * scale;
#ifdef VERBOSE
printf ("cap style = %d\n", cap);
#endif
switch (cap)
{
case ART_PATH_STROKE_CAP_BUTT:
art_vpath_add_point (p_result, pn_result, pn_result_max,
ART_LINETO, vpath[i1].x - dlx0, vpath[i1].y - dly0);
art_vpath_add_point (p_result, pn_result, pn_result_max,
ART_LINETO, vpath[i1].x + dlx0, vpath[i1].y + dly0);
break;
case ART_PATH_STROKE_CAP_ROUND:
n_pts = ceil (M_PI / (2.0 * M_SQRT2 * sqrt (flatness / line_width)));
art_vpath_add_point (p_result, pn_result, pn_result_max,
ART_LINETO, vpath[i1].x - dlx0, vpath[i1].y - dly0);
for (i = 1; i < n_pts; i++)
{
double theta, c_th, s_th;
theta = M_PI * i / n_pts;
c_th = cos (theta);
s_th = sin (theta);
art_vpath_add_point (p_result, pn_result, pn_result_max,
ART_LINETO,
vpath[i1].x - dlx0 * c_th - dly0 * s_th,
vpath[i1].y - dly0 * c_th + dlx0 * s_th);
}
art_vpath_add_point (p_result, pn_result, pn_result_max,
ART_LINETO, vpath[i1].x + dlx0, vpath[i1].y + dly0);
break;
case ART_PATH_STROKE_CAP_SQUARE:
art_vpath_add_point (p_result, pn_result, pn_result_max,
ART_LINETO,
vpath[i1].x - dlx0 - dly0,
vpath[i1].y - dly0 + dlx0);
art_vpath_add_point (p_result, pn_result, pn_result_max,
ART_LINETO,
vpath[i1].x + dlx0 - dly0,
vpath[i1].y + dly0 + dlx0);
break;
}
}
/* Assume that forw and rev are at point i0. Bring them to i1,
joining with the vector i1 - i2.
This used to be true, but isn't now that the stroke_raw code is
filtering out (near)zero length vectors: {It so happens that all
invocations of this function maintain the precondition i1 = i0 + 1,
so we could decrease the number of arguments by one. We haven't
done that here, though.}
forw is to the line's right and rev is to its left.
Precondition: no zero-length vectors, otherwise a divide by
zero will happen. */
static void
render_seg (ArtVpath **p_forw, int *pn_forw, int *pn_forw_max,
ArtVpath **p_rev, int *pn_rev, int *pn_rev_max,
ArtVpath *vpath, int i0, int i1, int i2,
ArtPathStrokeJoinType join,
double line_width, double miter_limit, double flatness)
{
double dx0, dy0;
double dx1, dy1;
double dlx0, dly0;
double dlx1, dly1;
double dmx, dmy;
double dmr2;
double scale;
double cross;
#ifdef VERBOSE
printf ("join style = %d\n", join);
#endif
/* The vectors of the lines from i0 to i1 and i1 to i2. */
dx0 = vpath[i1].x - vpath[i0].x;
dy0 = vpath[i1].y - vpath[i0].y;
dx1 = vpath[i2].x - vpath[i1].x;
dy1 = vpath[i2].y - vpath[i1].y;
/* Set dl[xy]0 to the vector from i0 to i1, rotated counterclockwise
90 degrees, and scaled to the length of line_width. */
scale = line_width / sqrt (dx0 * dx0 + dy0 * dy0);
dlx0 = dy0 * scale;
dly0 = -dx0 * scale;
/* Set dl[xy]1 to the vector from i1 to i2, rotated counterclockwise
90 degrees, and scaled to the length of line_width. */
scale = line_width / sqrt (dx1 * dx1 + dy1 * dy1);
dlx1 = dy1 * scale;
dly1 = -dx1 * scale;
#ifdef VERBOSE
printf ("%% render_seg: (%g, %g) - (%g, %g) - (%g, %g)\n",
vpath[i0].x, vpath[i0].y,
vpath[i1].x, vpath[i1].y,
vpath[i2].x, vpath[i2].y);
printf ("%% render_seg: d[xy]0 = (%g, %g), dl[xy]0 = (%g, %g)\n",
dx0, dy0, dlx0, dly0);
printf ("%% render_seg: d[xy]1 = (%g, %g), dl[xy]1 = (%g, %g)\n",
dx1, dy1, dlx1, dly1);
#endif
/* now, forw's last point is expected to be colinear along d[xy]0
to point i0 - dl[xy]0, and rev with i0 + dl[xy]0. */
/* positive for positive area (i.e. left turn) */
cross = dx1 * dy0 - dx0 * dy1;
dmx = (dlx0 + dlx1) * 0.5;
dmy = (dly0 + dly1) * 0.5;
dmr2 = dmx * dmx + dmy * dmy;
if (join == ART_PATH_STROKE_JOIN_MITER &&
dmr2 * miter_limit * miter_limit < line_width * line_width)
join = ART_PATH_STROKE_JOIN_BEVEL;
/* the case when dmr2 is zero or very small bothers me
(i.e. near a 180 degree angle)
ALEX: So, we avoid the optimization when dmr2 is very small. This should
be safe since dmx/y is only used in optimization and in MITER case, and MITER
should be converted to BEVEL when dmr2 is very small. */
if (dmr2 > EPSILON_2)
{
scale = line_width * line_width / dmr2;
dmx *= scale;
dmy *= scale;
}
if (cross * cross < EPSILON_2 && dx0 * dx1 + dy0 * dy1 >= 0)
{
/* going straight */
#ifdef VERBOSE
printf ("%% render_seg: straight\n");
#endif
art_vpath_add_point (p_forw, pn_forw, pn_forw_max,
ART_LINETO, vpath[i1].x - dlx0, vpath[i1].y - dly0);
art_vpath_add_point (p_rev, pn_rev, pn_rev_max,
ART_LINETO, vpath[i1].x + dlx0, vpath[i1].y + dly0);
}
else if (cross > 0)
{
/* left turn, forw is outside and rev is inside */
#ifdef VERBOSE
printf ("%% render_seg: left\n");
#endif
if (
#ifdef NO_OPTIMIZE_INNER
0 &&
#endif
(dmr2 > EPSILON_2) &&
/* check that i1 + dm[xy] is inside i0-i1 rectangle */
(dx0 + dmx) * dx0 + (dy0 + dmy) * dy0 > 0 &&
/* and that i1 + dm[xy] is inside i1-i2 rectangle */
((dx1 - dmx) * dx1 + (dy1 - dmy) * dy1 > 0)
#ifdef PEDANTIC_INNER
&&
/* check that i1 + dl[xy]1 is inside i0-i1 rectangle */
(dx0 + dlx1) * dx0 + (dy0 + dly1) * dy0 > 0 &&
/* and that i1 + dl[xy]0 is inside i1-i2 rectangle */
((dx1 - dlx0) * dx1 + (dy1 - dly0) * dy1 > 0)
#endif
)
{
/* can safely add single intersection point */
art_vpath_add_point (p_rev, pn_rev, pn_rev_max,
ART_LINETO, vpath[i1].x + dmx, vpath[i1].y + dmy);
}
else
{
/* need to loop-de-loop the inside */
art_vpath_add_point (p_rev, pn_rev, pn_rev_max,
ART_LINETO, vpath[i1].x + dlx0, vpath[i1].y + dly0);
art_vpath_add_point (p_rev, pn_rev, pn_rev_max,
ART_LINETO, vpath[i1].x, vpath[i1].y);
art_vpath_add_point (p_rev, pn_rev, pn_rev_max,
ART_LINETO, vpath[i1].x + dlx1, vpath[i1].y + dly1);
}
if (join == ART_PATH_STROKE_JOIN_BEVEL)
{
/* bevel */
art_vpath_add_point (p_forw, pn_forw, pn_forw_max,
ART_LINETO, vpath[i1].x - dlx0, vpath[i1].y - dly0);
art_vpath_add_point (p_forw, pn_forw, pn_forw_max,
ART_LINETO, vpath[i1].x - dlx1, vpath[i1].y - dly1);
}
else if (join == ART_PATH_STROKE_JOIN_MITER)
{
art_vpath_add_point (p_forw, pn_forw, pn_forw_max,
ART_LINETO, vpath[i1].x - dmx, vpath[i1].y - dmy);
}
else if (join == ART_PATH_STROKE_JOIN_ROUND)
art_svp_vpath_stroke_arc (p_forw, pn_forw, pn_forw_max,
vpath[i1].x, vpath[i1].y,
-dlx0, -dly0,
-dlx1, -dly1,
line_width,
flatness);
}
else
{
/* right turn, rev is outside and forw is inside */
#ifdef VERBOSE
printf ("%% render_seg: right\n");
#endif
if (
#ifdef NO_OPTIMIZE_INNER
0 &&
#endif
(dmr2 > EPSILON_2) &&
/* check that i1 - dm[xy] is inside i0-i1 rectangle */
(dx0 - dmx) * dx0 + (dy0 - dmy) * dy0 > 0 &&
/* and that i1 - dm[xy] is inside i1-i2 rectangle */
((dx1 + dmx) * dx1 + (dy1 + dmy) * dy1 > 0)
#ifdef PEDANTIC_INNER
&&
/* check that i1 - dl[xy]1 is inside i0-i1 rectangle */
(dx0 - dlx1) * dx0 + (dy0 - dly1) * dy0 > 0 &&
/* and that i1 - dl[xy]0 is inside i1-i2 rectangle */
((dx1 + dlx0) * dx1 + (dy1 + dly0) * dy1 > 0)
#endif
)
{
/* can safely add single intersection point */
art_vpath_add_point (p_forw, pn_forw, pn_forw_max,
ART_LINETO, vpath[i1].x - dmx, vpath[i1].y - dmy);
}
else
{
/* need to loop-de-loop the inside */
art_vpath_add_point (p_forw, pn_forw, pn_forw_max,
ART_LINETO, vpath[i1].x - dlx0, vpath[i1].y - dly0);
art_vpath_add_point (p_forw, pn_forw, pn_forw_max,
ART_LINETO, vpath[i1].x, vpath[i1].y);
art_vpath_add_point (p_forw, pn_forw, pn_forw_max,
ART_LINETO, vpath[i1].x - dlx1, vpath[i1].y - dly1);
}
if (join == ART_PATH_STROKE_JOIN_BEVEL)
{
/* bevel */
art_vpath_add_point (p_rev, pn_rev, pn_rev_max,
ART_LINETO, vpath[i1].x + dlx0, vpath[i1].y + dly0);
art_vpath_add_point (p_rev, pn_rev, pn_rev_max,
ART_LINETO, vpath[i1].x + dlx1, vpath[i1].y + dly1);
}
else if (join == ART_PATH_STROKE_JOIN_MITER)
{
art_vpath_add_point (p_rev, pn_rev, pn_rev_max,
ART_LINETO, vpath[i1].x + dmx, vpath[i1].y + dmy);
}
else if (join == ART_PATH_STROKE_JOIN_ROUND)
art_svp_vpath_stroke_arc (p_rev, pn_rev, pn_rev_max,
vpath[i1].x, vpath[i1].y,
dlx0, dly0,
dlx1, dly1,
-line_width,
flatness);
}
}
/**
* art_vpath_render_bez: Render a bezier segment into the vpath.
* @p_vpath: Where the pointer to the #ArtVpath structure is stored.
* @pn_points: Pointer to the number of points in *@p_vpath.
* @pn_points_max: Pointer to the number of points allocated.
* @x0: X coordinate of starting bezier point.
* @y0: Y coordinate of starting bezier point.
* @x1: X coordinate of first bezier control point.
* @y1: Y coordinate of first bezier control point.
* @x2: X coordinate of second bezier control point.
* @y2: Y coordinate of second bezier control point.
* @x3: X coordinate of ending bezier point.
* @y3: Y coordinate of ending bezier point.
* @flatness: Flatness control.
*
* Renders a bezier segment into the vector path, reallocating and
* updating *@p_vpath and *@pn_vpath_max as necessary. *@pn_vpath is
* incremented by the number of vector points added.
*
* This step includes (@x0, @y0) but not (@x3, @y3).
*
* The @flatness argument guides the amount of subdivision. The Adobe
* PostScript reference manual defines flatness as the maximum
* deviation between the any point on the vpath approximation and the
* corresponding point on the "true" curve, and we follow this
* definition here. A value of 0.25 should ensure high quality for aa
* rendering.
**/
static void
art_vpath_render_bez (ArtVpath **p_vpath, int *pn, int *pn_max,
double x0, double y0,
double x1, double y1,
double x2, double y2,
double x3, double y3,
double flatness)
{
double x3_0, y3_0;
double z3_0_dot;
double z1_dot, z2_dot;
double z1_perp, z2_perp;
double max_perp_sq;
double x_m, y_m;
double xa1, ya1;
double xa2, ya2;
double xb1, yb1;
double xb2, yb2;
/* It's possible to optimize this routine a fair amount.
First, once the _dot conditions are met, they will also be met in
all further subdivisions. So we might recurse to a different
routine that only checks the _perp conditions.
Second, the distance _should_ decrease according to fairly
predictable rules (a factor of 4 with each subdivision). So it might
be possible to note that the distance is within a factor of 4 of
acceptable, and subdivide once. But proving this might be hard.
Third, at the last subdivision, x_m and y_m can be computed more
expeditiously (as in the routine above).
Finally, if we were able to subdivide by, say 2 or 3, this would
allow considerably finer-grain control, i.e. fewer points for the
same flatness tolerance. This would speed things up downstream.
In any case, this routine is unlikely to be the bottleneck. It's
just that I have this undying quest for more speed...
*/
x3_0 = x3 - x0;
y3_0 = y3 - y0;
/* z3_0_dot is dist z0-z3 squared */
z3_0_dot = x3_0 * x3_0 + y3_0 * y3_0;
/* todo: this test is far from satisfactory. */
if (z3_0_dot < 0.001)
goto nosubdivide;
/* we can avoid subdivision if:
z1 has distance no more than flatness from the z0-z3 line
z1 is no more z0'ward than flatness past z0-z3
z1 is more z0'ward than z3'ward on the line traversing z0-z3
and correspondingly for z2 */
/* perp is distance from line, multiplied by dist z0-z3 */
max_perp_sq = flatness * flatness * z3_0_dot;
z1_perp = (y1 - y0) * x3_0 - (x1 - x0) * y3_0;
if (z1_perp * z1_perp > max_perp_sq)
goto subdivide;
z2_perp = (y3 - y2) * x3_0 - (x3 - x2) * y3_0;
if (z2_perp * z2_perp > max_perp_sq)
goto subdivide;
z1_dot = (x1 - x0) * x3_0 + (y1 - y0) * y3_0;
if (z1_dot < 0 && z1_dot * z1_dot > max_perp_sq)
goto subdivide;
z2_dot = (x3 - x2) * x3_0 + (y3 - y2) * y3_0;
if (z2_dot < 0 && z2_dot * z2_dot > max_perp_sq)
goto subdivide;
if (z1_dot + z1_dot > z3_0_dot)
goto subdivide;
if (z2_dot + z2_dot > z3_0_dot)
goto subdivide;
nosubdivide:
/* don't subdivide */
art_vpath_add_point (p_vpath, pn, pn_max,
ART_LINETO, x3, y3);
return;
subdivide:
xa1 = (x0 + x1) * 0.5;
ya1 = (y0 + y1) * 0.5;
xa2 = (x0 + 2 * x1 + x2) * 0.25;
ya2 = (y0 + 2 * y1 + y2) * 0.25;
xb1 = (x1 + 2 * x2 + x3) * 0.25;
yb1 = (y1 + 2 * y2 + y3) * 0.25;
xb2 = (x2 + x3) * 0.5;
yb2 = (y2 + y3) * 0.5;
x_m = (xa2 + xb1) * 0.5;
y_m = (ya2 + yb1) * 0.5;
#ifdef VERBOSE
printf ("%g,%g %g,%g %g,%g %g,%g\n", xa1, ya1, xa2, ya2,
xb1, yb1, xb2, yb2);
#endif
art_vpath_render_bez (p_vpath, pn, pn_max,
x0, y0, xa1, ya1, xa2, ya2, x_m, y_m, flatness);
art_vpath_render_bez (p_vpath, pn, pn_max,
x_m, y_m, xb1, yb1, xb2, yb2, x3, y3, flatness);
}
