/** Calculate a bounding box for a set of bezier points.
* @param pts The bezier points
* @param numpoints The number of elements in `pts'
* @param extra Extra spacing information.
* @param closed True if the bezier points form a closed line.
* @param rect Return value: The enclosing rectangle will be stored here.
* @bug This function is way too long (214 lines) and should be split.
*/
void
polybezier_bbox(const BezPoint *pts, int numpoints,
const PolyBBExtras *extra, gboolean closed,
Rectangle *rect)
{
Point vx,vn,vsc,vp;
int i,prev,next;
Rectangle rt;
PolyBBExtras bextra,start_bextra,end_bextra;
LineBBExtras lextra,start_lextra,end_lextra,full_lextra;
gboolean start,end;
vp.x=0;
vp.y=0;
g_assert(pts[0].type == BEZ_MOVE_TO);
rect->left = rect->right = pts[0].p1.x;
rect->top = rect->bottom = pts[0].p1.y;
/* First, we build derived BBExtras structures, so we have something to feed
the primitives. */
if (!closed) {
start_lextra.start_long = extra->start_long;
start_lextra.start_trans = MAX(extra->start_trans,extra->middle_trans);
start_lextra.end_long = 0;
start_lextra.end_trans = extra->middle_trans;
end_lextra.start_long = 0;
end_lextra.start_trans = extra->middle_trans;
end_lextra.end_long = extra->end_long;
end_lextra.end_trans = MAX(extra->end_trans,extra->middle_trans);
}
full_lextra.start_long = extra->start_long;
full_lextra.start_trans = MAX(extra->start_trans,extra->middle_trans);
full_lextra.end_long = extra->end_long;
full_lextra.end_trans = MAX(extra->end_trans,extra->middle_trans);
if (!closed) {
lextra.start_long = 0;
lextra.start_trans = extra->middle_trans;
lextra.end_long = 0;
lextra.end_trans = extra->middle_trans;
start_bextra.start_long = extra->start_long;
start_bextra.start_trans = extra->start_trans;
start_bextra.middle_trans = extra->middle_trans;
start_bextra.end_long = 0;
start_bextra.end_trans = extra->middle_trans;
end_bextra.start_long = 0;
end_bextra.start_trans = extra->middle_trans;
end_bextra.middle_trans = extra->middle_trans;
end_bextra.end_long = extra->end_long;
end_bextra.end_trans = extra->end_trans;
}
bextra.start_long = 0;
bextra.start_trans = extra->middle_trans;
bextra.middle_trans = extra->middle_trans;
bextra.end_long = 0;
bextra.end_trans = extra->middle_trans;
for (i=1;i<numpoints;i++) {
next = (i+1) % numpoints;
prev = (i-1) % numpoints;
if (closed && (next == 0)) next=1;
if (closed && (prev == 0)) prev=numpoints-1;
/* We have now:
i = index of current vertex.
prev,next: index of previous/next vertices (of the control polygon)
We want:
vp, vx, vn: the previous, current and next vertices;
start, end: TRUE if we're at an end of poly (then, vp and/or vn are not
valid, respectively).
Some values *will* be recomputed a few times across iterations (but stored in
different boxes). Either gprof says it's a real problem, or gcc finally gets
a clue.
*/
if (pts[i].type == BEZ_MOVE_TO) {
continue;
}
switch(pts[i].type) {
case BEZ_MOVE_TO:
g_assert_not_reached();
break;
case BEZ_LINE_TO:
point_copy(&vx,&pts[i].p1);
switch(pts[prev].type) {
case BEZ_MOVE_TO:
case BEZ_LINE_TO:
point_copy(&vsc,&pts[prev].p1);
point_copy(&vp,&pts[prev].p1);
break;
case BEZ_CURVE_TO:
point_copy(&vsc,&pts[prev].p3);
point_copy(&vp,&pts[prev].p3);
break;
}
break;
case BEZ_CURVE_TO:
point_copy(&vx,&pts[i].p3);
point_copy(&vp,&pts[i].p2);
switch(pts[prev].type) {
case BEZ_MOVE_TO:
case BEZ_LINE_TO:
point_copy(&vsc,&pts[prev].p1);
break;
case BEZ_CURVE_TO:
point_copy(&vsc,&pts[prev].p3);
break;
} /* vsc is the start of the curve. */
break;
}
start = (pts[prev].type == BEZ_MOVE_TO);
end = (pts[next].type == BEZ_MOVE_TO);
point_copy(&vn,&pts[next].p1); /* whichever type pts[next] is. */
/* Now, we know about a few vertices around the one we're dealing with.
Depending on the shape of the (previous,current) segment, and whether
it's a middle or end segment, we'll be doing different stuff. */
if (closed) {
if (pts[i].type == BEZ_LINE_TO) {
line_bbox(&vsc,&vx,&full_lextra,&rt);
} else {
bicubicbezier2D_bbox(&vsc,
&pts[i].p1,&pts[i].p2,&pts[i].p3,
&bextra,
&rt);
}
} else if (start) {
if (pts[i].type == BEZ_LINE_TO) {
if (end) {
line_bbox(&vsc,&vx,&full_lextra,&rt);
} else {
line_bbox(&vsc,&vx,&start_lextra,&rt);
}
} else { /* BEZ_MOVE_TO */
if (end) {
bicubicbezier2D_bbox(&vsc,
&pts[i].p1,&pts[i].p2,&pts[i].p3,
extra,
&rt);
} else {
bicubicbezier2D_bbox(&vsc,
&pts[i].p1,&pts[i].p2,&pts[i].p3,
&start_bextra,
&rt);
}
}
} else if (end) { /* end but not start. Not closed anyway. */
if (pts[i].type == BEZ_LINE_TO) {
line_bbox(&vsc,&vx,&end_lextra,&rt);
} else {
bicubicbezier2D_bbox(&vsc,
&pts[i].p1,&pts[i].p2,&pts[i].p3,
&end_bextra,
&rt);
}
} else { /* normal case : middle segment (not closed shape). */
if (pts[i].type == BEZ_LINE_TO) {
line_bbox(&vsc,&vx,&lextra,&rt);
} else {
bicubicbezier2D_bbox(&vsc,
&pts[i].p1,&pts[i].p2,&pts[i].p3,
&bextra,
&rt);
}
}
rectangle_union(rect,&rt);
/* The following code enlarges a little the bounding box (if necessary) to
account with the "pointy corners" X (and PS) add when LINEJOIN_MITER mode is
in force. */
if ((!start) && (!end)) { /* We have a non-extremity vertex. */
Point vpx,vxn;
real co,alpha;
point_copy_add_scaled(&vpx,&vx,&vp,-1);
point_normalize(&vpx);
point_copy_add_scaled(&vxn,&vn,&vx,-1);
point_normalize(&vxn);
co = point_dot(&vpx,&vxn);
alpha = acos(-co);
if (co > -0.9816) { /* 0.9816 = cos(11deg) */
/* we have a pointy join. */
real overshoot;
Point vovs,pto;
if (finite(alpha))
overshoot = extra->middle_trans / sin(alpha/2.0);
else /* prependicular? */
overshoot = extra->middle_trans;
point_copy_add_scaled(&vovs,&vpx,&vxn,-1);
point_normalize(&vovs);
point_copy_add_scaled(&pto,&vx,&vovs,overshoot);
rectangle_add_point(rect,&pto);
} else {
/* we don't have a pointy join. */
Point vpxt,vxnt,tmp;
point_get_perp(&vpxt,&vpx);
point_get_perp(&vxnt,&vxn);
point_copy_add_scaled(&tmp,&vx,&vpxt,1);
rectangle_add_point(rect,&tmp);
point_copy_add_scaled(&tmp,&vx,&vpxt,-1);
rectangle_add_point(rect,&tmp);
point_copy_add_scaled(&tmp,&vx,&vxnt,1);
rectangle_add_point(rect,&tmp);
point_copy_add_scaled(&tmp,&vx,&vxnt,-1);
rectangle_add_point(rect,&tmp);
}
}
}
}
void polybezier_bbox(const BezPoint *pts, int numpoints,
const PolyBBExtras *extra, bool closed,
Rectangle *rect)
{
Point vx,vp,vn,vsc;
int i,prev,next;
Rectangle rt;
PolyBBExtras bextra,start_bextra,end_bextra;
LineBBExtras lextra,start_lextra,end_lextra,full_lextra;
bool start,end;
rect->setLeft(pts[0].p1.x());
rect->setRight(pts[0].p1.x());
rect->setTop(pts[0].p1.y());
rect->setBottom(pts[0].p1.y());
if (!closed) {
start_lextra.startLong = extra->startLong;
start_lextra.startTrans = qMax(extra->startTrans,extra->middleTrans);
start_lextra.endLong = 0;
start_lextra.endTrans = extra->middleTrans;
end_lextra.startLong = 0;
end_lextra.startTrans = extra->middleTrans;
end_lextra.endLong = extra->endLong;
end_lextra.endTrans = qMax(extra->endTrans,extra->middleTrans);
}
full_lextra.startLong = extra->startLong;
full_lextra.startTrans = qMax(extra->startTrans,extra->middleTrans);
full_lextra.endLong = extra->endLong;
full_lextra.endTrans = qMax(extra->endTrans,extra->middleTrans);
if (!closed) {
lextra.startLong = 0;
lextra.startTrans = extra->middleTrans;
lextra.endLong = 0;
lextra.endTrans = extra->middleTrans;
start_bextra.startLong = extra->startLong;
start_bextra.startTrans = extra->startTrans;
start_bextra.middleTrans = extra->middleTrans;
start_bextra.endLong = 0;
start_bextra.endTrans = extra->middleTrans;
end_bextra.startLong = 0;
end_bextra.startTrans = extra->middleTrans;
end_bextra.middleTrans = extra->middleTrans;
end_bextra.endLong = extra->endLong;
end_bextra.endTrans = extra->endTrans;
}
bextra.startLong = 0;
bextra.startTrans = extra->middleTrans;
bextra.middleTrans = extra->middleTrans;
bextra.endLong = 0;
bextra.endTrans = extra->middleTrans;
for (i=1;i<numpoints;i++) {
next = (i+1) % numpoints;
prev = (i-1) % numpoints;
if (closed && (next == 0)) next=1;
if (closed && (prev == 0)) prev=numpoints-1;
if (pts[i].type == BezPoint::BEZ_MOVE_TO) {
continue;
}
switch(pts[i].type) {
case BezPoint::BEZ_MOVE_TO:
break;
case BezPoint::BEZ_LINE_TO:
vx = pts[i].p1;
switch(pts[prev].type) {
case BezPoint::BEZ_MOVE_TO:
case BezPoint::BEZ_LINE_TO:
vsc = pts[prev].p1;
vp = pts[prev].p1;
break;
case BezPoint::BEZ_CURVE_TO:
vsc = pts[prev].p3;
vp = pts[prev].p3;
break;
}
break;
case BezPoint::BEZ_CURVE_TO:
vx = pts[i].p3;
vp = pts[i].p2;
switch(pts[prev].type) {
case BezPoint::BEZ_MOVE_TO:
case BezPoint::BEZ_LINE_TO:
vsc = pts[prev].p1;
break;
case BezPoint::BEZ_CURVE_TO:
vsc = pts[prev].p3;
break;
}
break;
}
start = (pts[prev].type == BezPoint::BEZ_MOVE_TO);
end = (pts[next].type == BezPoint::BEZ_MOVE_TO);
vn = pts[next].p1;
if (closed) {
if (pts[i].type == BezPoint::BEZ_LINE_TO) {
line_bbox(&vsc,&vx,&full_lextra,&rt);
} else {
bicubicbezier2D_bbox(&vsc,
&pts[i].p1,&pts[i].p2,&pts[i].p3,
&bextra,
&rt);
}
} else if (start) {
if (pts[i].type == BezPoint::BEZ_LINE_TO) {
if (end) {
line_bbox(&vsc,&vx,&full_lextra,&rt);
} else {
line_bbox(&vsc,&vx,&start_lextra,&rt);
}
} else {
if (end) {
bicubicbezier2D_bbox(&vsc,
&pts[i].p1,&pts[i].p2,&pts[i].p3,
extra,
&rt);
} else {
bicubicbezier2D_bbox(&vsc,
&pts[i].p1,&pts[i].p2,&pts[i].p3,
&start_bextra,
&rt);
}
}
} else if (end) {
if (pts[i].type == BezPoint::BEZ_LINE_TO) {
line_bbox(&vsc,&vx,&end_lextra,&rt);
} else {
bicubicbezier2D_bbox(&vsc,
&pts[i].p1,&pts[i].p2,&pts[i].p3,
&end_bextra,
&rt);
}
} else {
if (pts[i].type == BezPoint::BEZ_LINE_TO) {
line_bbox(&vsc,&vx,&lextra,&rt);
} else {
bicubicbezier2D_bbox(&vsc,
&pts[i].p1,&pts[i].p2,&pts[i].p3,
&bextra,
&rt);
}
}
*rect = rect->united(rt);
if ((!start) && (!end)) {
Point vpx,vxn;
double co,alpha;
point_copy_add_scaled(&vpx,&vx,&vp,-1);
point_normalize(&vpx);
point_copy_add_scaled(&vxn,&vn,&vx,-1);
point_normalize(&vxn);
co = point_dot(&vpx,&vxn);
alpha = acos(-co);
if ((co > -0.9816) && (finite(alpha))) {
double overshoot = extra->middleTrans / sin(alpha/2.0);
Point vovs,pto;
point_copy_add_scaled(&vovs,&vpx,&vxn,-1);
point_normalize(&vovs);
point_copy_add_scaled(&pto,&vx,&vovs,overshoot);
rectangle_add_point(rect,&pto);
} else {
Point vpxt,vxnt,tmp;
point_get_perp(&vpxt,&vpx);
point_get_perp(&vxnt,&vxn);
point_copy_add_scaled(&tmp,&vx,&vpxt,1);
rectangle_add_point(rect,&tmp);
point_copy_add_scaled(&tmp,&vx,&vpxt,-1);
rectangle_add_point(rect,&tmp);
point_copy_add_scaled(&tmp,&vx,&vxnt,1);
rectangle_add_point(rect,&tmp);
point_copy_add_scaled(&tmp,&vx,&vxnt,-1);
rectangle_add_point(rect,&tmp);
}
}
}
}
/*!
* \brief Calculate crossing points of two bezier segments
*
* Beware two bezier segments can intersect more than once, but this
* function only returns the first or no intersection. It is the
* responsibility of the caller to further split segments until there
* is no intersection left.
*/
static gboolean
bezier_bezier_intersection (GArray *crossing,
const BezierSegment *a,
const BezierSegment *b,
int depth,
real asplit,
real bsplit)
{
Rectangle abox, bbox;
PolyBBExtras extra = { 0, };
gboolean small_a, small_b;
/* Avoid intersection overflow: if start and end are on the other segment
* assume full overlap and no crossing.
*/
if ( (_segment_has_point (a, &b->p0) && _segment_has_point (a, &b->p3))
|| (_segment_has_point (b, &a->p0) && _segment_has_point (b, &a->p3)))
return FALSE; /* XXX: more variants pending, partial overlap */
/* With very similar segments we would create a lot of points with not
* a very deep recursion (test with ying-yang symbol).
* Just comparing the segments on depth=1 is not good enough, so for
* now we are limiting the number of intersections
*/
if (crossing->len > 127) { /* XXX: arbitrary limit */
g_warning ("Crossing limit (%d) reached", crossing->len);
return FALSE;
}
bicubicbezier2D_bbox (&a->p0, &a->p1, &a->p2, &a->p3, &extra, &abox);
bicubicbezier2D_bbox (&b->p0, &b->p1, &b->p2, &b->p3, &extra, &bbox);
if (!rectangle_intersects (&abox, &bbox))
return FALSE;
small_a = (abox.right - abox.left) < EPSILON && (abox.bottom - abox.top) < EPSILON;
small_b = (bbox.right - bbox.left) < EPSILON && (bbox.bottom - bbox.top) < EPSILON;
/* if the boxes are small enough we can calculate the point */
if (small_a && small_b) {
/* intersecting and both small, should not matter which one is used */
Point pt = { (abox.right + abox.left + bbox.right + bbox.left) / 4,
(abox.bottom + abox.top + bbox.bottom + bbox.top) / 4 };
Intersection is;
int i;
for (i = 0; i < crossing->len; ++i) {
/* if it's already included we are done */
if (distance_point_point (&g_array_index (crossing, Intersection, i).pt, &pt) < 1.4142*EPSILON)
return TRUE; /* although we did not add it */
}
is.split_one = asplit;
is.split_two = bsplit;
is.pt = pt;
g_print ("d=%d; as=%g; bs=%g; ", depth, asplit, bsplit);
g_array_append_val (crossing, is);
return TRUE;
} else {
/* further splitting of a and b; it could be smart to only search in the
* intersection of a-box and b-box ... */
BezierSegment a1, a2;
BezierSegment b1, b2;
real ofs = 1.0/(1<<(depth+1));
gboolean ret = FALSE;
bezier_split (a, &a1, &a2);
bezier_split (b, &b1, &b2);
ret |= bezier_bezier_intersection (crossing, &a1, &b1, depth+1, asplit-ofs, bsplit-ofs);
ret |= bezier_bezier_intersection (crossing, &a2, &b1, depth+1, asplit+ofs, bsplit-ofs);
ret |= bezier_bezier_intersection (crossing, &a1, &b2, depth+1, asplit-ofs, bsplit+ofs);
ret |= bezier_bezier_intersection (crossing, &a2, &b2, depth+1, asplit+ofs, bsplit+ofs);
/* XXX: check !ret case, not sure if it should happen */
return ret;
}
}