int LineArcIntof(const Span& line, const Span& arc, Point& p0, Point& p1, double t[4]) {
// inters of line arc
// solving x = x0 + dx * t x = y0 + dy * t
// x = xc + R * cos(a) y = yc + R * sin(a) for t
// gives :- t² (dx² + dy²) + 2t(dx*dx0 + dy*dy0) + (x0-xc)² + (y0-yc)² - R² = 0
int nRoots;
Vector2d v0(arc.pc, line.p0);
Vector2d v1(line.p0, line.p1);
double s = v1.magnitudesqd();
p0.ok = p1.ok = false;
if((nRoots = quadratic(s, 2 * (v0 * v1), v0.magnitudesqd() - arc.radius * arc.radius, t[0], t[1])) != 0) {
double toler = geoff_geometry::TOLERANCE / sqrt(s); // calc a parametric tolerance
if(t[0] > -toler && t[0] < 1 + toler) {
p0 = v1 * t[0] + line.p0;
p0.ok = arc.OnSpan(p0, &t[2]);
}
if(nRoots == 2) {
if(t[1] > -toler && t[1] < 1 + toler) {
p1 = v1 * t[1] + line.p0;
p1.ok = arc.OnSpan(p1, &t[3]);
}
}
if(!p0.ok && p1.ok) {
p0 = p1;
p1.ok = false;
}
nRoots = (int)p0.ok + (int)p1.ok;
}
return nRoots;
}
int ArcArcIntof(const Span& arc0, const Span& arc1, Point& pLeft, Point& pRight) {
// Intof 2 arcs
int numInts = Intof(Circle(arc0.pc, arc0.radius), Circle(arc1.pc, arc1.radius), pLeft, pRight);
if(numInts == 0) {
pLeft = arc0.p1;
pLeft.ok = false;
return 0;
}
int nLeft = arc0.OnSpan(pLeft) && arc1.OnSpan(pLeft);
int nRight = (numInts == 2)?arc0.OnSpan(pRight) && arc1.OnSpan(pRight) : 0;
if(nLeft == 0 && nRight) pLeft = pRight;
return nLeft + nRight;
}
double Dist(const Span& sp, const Point& p , Point& pnear ) {
// returns distance of p from span, pnear is the nearpoint on the span (or endpoint)
if(!sp.dir) {
double d, t;
Point3d unused_pnear;
d = Dist(Line(sp), Point3d(p), unused_pnear, t);
if(t < -geoff_geometry::TOLERANCE) {
pnear = sp.p0; // nearpoint
d = pnear.Dist(p);
}
else if(t > sp.length + geoff_geometry::TOLERANCE) {
pnear = sp.p1;
d = pnear.Dist(p);
}
return d;
}
else {
// put pnear on the circle
double radiusp;
Vector2d v(sp.pc, p);
if((radiusp = v.magnitude()) < geoff_geometry::TOLERANCE) {
// point specified on circle centre - use first point as near point
pnear = sp.p0; // nearpoint
return sp.radius;
}
else {
pnear = v * (sp.radius / radiusp) + sp.pc;
// check if projected point is on the arc
if(sp.OnSpan(pnear)) return fabs(radiusp - sp.radius);
// double h1 = pnear.x - sp.p0.x ;
// double v1 = pnear.y - sp.p0.y ;
// double h2 = sp.p1.x - pnear.x ;
// double v2 = sp.p1.y - pnear.y ;
// if ( sp.dir * ( h1 * v2 - h2 * v1 ) >= 0 )return fabs(radiusp - sp.radius);
// point not on arc so calc nearest end-point
double ndist = p.Dist(sp.p0);
double dist = p.Dist(sp.p1);
if(ndist >= dist) {
// sp.p1 is near point
pnear = sp.p1;
return dist;
}
// sp.p0 is near point
pnear = sp.p0; // nearpoint
return ndist ;
}
}
}
bool OnSpan(const Span& sp, const Point& p, bool nearPoints, Point& pNear, Point& pOnSpan) {
// function returns true if pNear == pOnSpan
// returns pNear & pOnSpan if nearPoints true
// pNear (nearest on unbound span)
// pOnSpan (nearest on finite span)
if(sp.dir) {
// arc
if(fabs(p.Dist(sp.pc) - sp.radius) > geoff_geometry::TOLERANCE) {
if(!nearPoints) return false;
}
pNear = On(Circle(sp.pc, sp.radius), p);
if(sp.OnSpan(pNear)) {
if(nearPoints) pOnSpan = pNear;
return true; // near point is on arc - already calculated
}
// point not on arc return the nearest end-point
if(nearPoints) pOnSpan = (p.Dist(sp.p0) >= p.Dist(sp.p1)) ?sp.p1 : sp.p0;
return false;
}
else {
// straight
if(fabs(CLine(sp.p0, sp.vs).Dist(p)) > geoff_geometry::TOLERANCE) {
if(!nearPoints) return false;
}
Vector2d v(sp.p0, p);
double t = v * sp.vs;
if(nearPoints) pNear = sp.vs * t + sp.p0;
bool onSpan = (t > - geoff_geometry::TOLERANCE && t < sp.length + geoff_geometry::TOLERANCE);
if(! onSpan) {
if(nearPoints) pOnSpan = (p.Dist(sp.p0) >= p.Dist(sp.p1))?sp.p1 : sp.p0;
}
else {
if(nearPoints) pOnSpan = pNear;
}
return onSpan;
}
}
