void bicubicbezier2D_bbox(const Point *p0,const Point *p1,
const Point *p2,const Point *p3,
const PolyBBExtras *extra,
Rectangle *rect)
{
double x[4],y[4];
Point vl,vt,p,tt;
double *xy;
int i,extr;
double u[2];
rect->setLeft(p0->x());
rect->setRight(p0->x());
rect->setTop(p0->y());
rect->setBottom(p0->y());
rectangle_add_point(rect,p3);
point_copy_add_scaled(&vl,p0,p1,-1);
point_normalize(&vl);
add_arrow_rectangle(rect,p0,&vl,extra->startLong,
qMax(extra->startTrans, extra->middleTrans));
point_copy_add_scaled(&vl,p3,p2,-1);
point_normalize(&vl);
add_arrow_rectangle(rect,p3,&vl,extra->endLong,
qMax(extra->endTrans, extra->middleTrans));
x[0] = p0->x(); x[1] = p1->x(); x[2] = p2->x(); x[3] = p3->x();
y[0] = p0->y(); y[1] = p1->y(); y[2] = p2->y(); y[3] = p3->y();
for (xy = x; xy ; xy=(xy==x?y:NULL) ) {
extr = bicubicbezier_extrema(xy,u);
for (i=0;i<extr;i++) {
if ((u[i]<0) || (u[i]>1)) continue;
p.setX(bezier_eval(x,u[i]));
vl.setX(bezier_eval_tangent(x,u[i]));
p.setY(bezier_eval(y,u[i]));
vl.setY(bezier_eval_tangent(y,u[i]));
point_normalize(&vl);
point_get_perp(&vt,&vl);
point_copy_add_scaled(&tt,&p,&vt,extra->middleTrans);
rectangle_add_point(rect,&tt);
point_copy_add_scaled(&tt,&p,&vt,-extra->middleTrans);
rectangle_add_point(rect,&tt);
}
}
}
/** Calculate the boundingbox for a 2D bezier curve segment.
* @param p0 start point
* @param p1 1st control point
* @param p2 2nd control point
* @param p3 end point
* @param extra information about extra space from linewidth and arrow to add to the bounding box
* @param rect The rectangle that the segment fits inside.
*/
void
bicubicbezier2D_bbox(const Point *p0,const Point *p1,
const Point *p2,const Point *p3,
const PolyBBExtras *extra,
Rectangle *rect)
{
real x[4],y[4];
Point vl,vt,p,tt;
real *xy;
int i,extr;
real u[2];
rect->left = rect->right = p0->x;
rect->top = rect->bottom = p0->y;
rectangle_add_point(rect,p3);
/* start point */
point_copy_add_scaled(&vl,p0,p1,-1);
point_normalize(&vl);
add_arrow_rectangle(rect,p0,&vl,extra->start_long,MAX(extra->start_trans,
extra->middle_trans));
/* end point */
point_copy_add_scaled(&vl,p3,p2,-1);
point_normalize(&vl);
add_arrow_rectangle(rect,p3,&vl,extra->end_long,MAX(extra->end_trans,
extra->middle_trans));
/* middle part */
x[0] = p0->x; x[1] = p1->x; x[2] = p2->x; x[3] = p3->x;
y[0] = p0->y; y[1] = p1->y; y[2] = p2->y; y[3] = p3->y;
for (xy = x; xy ; xy=(xy==x?y:NULL) ) { /* sorry */
extr = bicubicbezier_extrema(xy,u);
for (i=0;i<extr;i++) {
if ((u[i]<0) || (u[i]>1)) continue;
p.x = bezier_eval(x,u[i]);
vl.x = bezier_eval_tangent(x,u[i]);
p.y = bezier_eval(y,u[i]);
vl.y = bezier_eval_tangent(y,u[i]);
point_normalize(&vl);
point_get_perp(&vt,&vl);
point_copy_add_scaled(&tt,&p,&vt,extra->middle_trans);
rectangle_add_point(rect,&tt);
point_copy_add_scaled(&tt,&p,&vt,-extra->middle_trans);
rectangle_add_point(rect,&tt);
}
}
}
static Point
bezier_line_eval(BezPoint *line,int p,real u)
{
real bx[4],by[4];
Point res;
bx[0]=line[p-1].p3.x;
bx[1]=line[p].p1.x;
bx[2]=line[p].p2.x;
bx[3]=line[p].p3.x;
by[0]=line[p-1].p3.y;
by[1]=line[p].p1.y;
by[2]=line[p].p2.y;
by[3]=line[p].p3.y;
res.x=bezier_eval(bx,u);
res.y=bezier_eval(by,u);
return res;
}
/* compute bezier for Dependency */
static void compute_dependency(BezPoint *line, BezPoint *bpl) {
Point ref;
double dx,dy,dxp,dyp,k;
real bx[4],by[4];
/* computing anchor point and tangent */
bx[0]=line[1].p3.x;
bx[1]=line[2].p1.x;
bx[2]=line[2].p2.x;
bx[3]=line[2].p3.x;
by[0]=line[1].p3.y;
by[1]=line[2].p1.y;
by[2]=line[2].p2.y;
by[3]=line[2].p3.y;
ref.x=bezier_eval(bx,0.25);
ref.y=bezier_eval(by,0.25);
dx=bezier_eval_tangent(bx,0.25);
dy=bezier_eval_tangent(by,0.25);
k=sqrt(dx*dx+dy*dy);
/* normalizing */
if (k!=0) {
dx=dx/k;
dy=dy/k;
dxp=dy;
dyp=-dx;
} else {
dx=0;
dy=1;
dxp=1;
dyp=0;
}
/* more offset for origin */
ref.x -= LINK_DEP_HEIGHT * dx;
ref.y -= LINK_DEP_HEIGHT * dy;
/* bezier */
bpl[0].type=BEZ_MOVE_TO;
bpl[0].p1.x = ref.x + LINK_DEP_WIDTH/2.0 * dxp;
bpl[0].p1.y = ref.y + LINK_DEP_WIDTH/2.0 * dyp;
bpl[1].type=BEZ_CURVE_TO;
bpl[1].p3.x = ref.x + LINK_DEP_HEIGHT * dx;
bpl[1].p3.y = ref.y + LINK_DEP_HEIGHT * dy;
bpl[1].p1.x = ref.x + LINK_DEP_WIDTH/2.0 * dxp + LINK_DEP_HEIGHT * dx;
bpl[1].p1.y = ref.y + LINK_DEP_WIDTH/2.0 * dyp + LINK_DEP_HEIGHT * dy;
bpl[1].p2.x = bpl[1].p1.x;
bpl[1].p2.y = bpl[1].p1.y;
bpl[2].type=BEZ_CURVE_TO;
bpl[2].p3.x = ref.x - LINK_DEP_WIDTH/2.0 * dxp;
bpl[2].p3.y = ref.y - LINK_DEP_WIDTH/2.0 * dyp;
bpl[2].p1.x = ref.x - LINK_DEP_WIDTH/2.0 * dxp + LINK_DEP_HEIGHT * dx;
bpl[2].p1.y = ref.y - LINK_DEP_WIDTH/2.0 * dyp + LINK_DEP_HEIGHT * dy;
bpl[2].p2.x = bpl[2].p1.x;
bpl[2].p2.y = bpl[2].p1.y;
bpl[3].type=BEZ_LINE_TO;
bpl[3].p1.x=bpl[0].p1.x;
bpl[3].p1.y=bpl[0].p1.y;
}