FlatEllipse::FlatEllipse(const FlatPoint &_f1, const FlatPoint &_f2,
const FlatPoint &_ap)
:f1(_f1),f2(_f2),ap(_ap)
{
const FlatLine f12(f1, f2);
p = f12.ave();
theta = f12.angle();
const fixed csq = f12.dsq();
a = (f1.d(ap) + f2.d(ap));
b = half(sqrt(a * a - csq));
a = half(a);
// a.sin(t) = ap.x
// b.cos(t) = ap.y
FlatPoint op = ap;
op.sub(p);
op.rotate(-theta);
theta_initial = Angle::radians(atan2(op.y * a, op.x * b)).as_delta();
}
FlatEllipse::FlatEllipse(const FlatPoint &_f1, const FlatPoint &_f2,
const FlatPoint &_ap)
:f1(_f1),f2(_f2),ap(_ap)
{
const FlatLine f12(f1, f2);
p = f12.ave();
theta = f12.angle();
const fixed csq = f12.dsq();
a = (f1.Distance(ap) + f2.Distance(ap));
b = half(sqrt(sqr(a) - csq));
a = half(a);
// a.sin(t) = ap.x
// b.cos(t) = ap.y
FlatPoint op = ap;
op.Subtract(p);
op.Rotate(-theta);
theta_initial = Angle::Radians(atan2(op.y * a, op.x * b)).AsDelta();
}
bool
FlatEllipse::intersect(const FlatLine &line, FlatPoint &i1, FlatPoint &i2) const
{
const fixed er = ab();
const fixed ier = ba();
FlatLine s_line = line;
s_line.sub(p);
s_line.rotate(theta.Reciprocal());
s_line.mul_y(er);
if (s_line.intersect_czero(a, i1, i2)) {
i1.mul_y(ier);
i1.rotate(theta);
i1.add(p);
i2.mul_y(ier);
i2.rotate(theta);
i2.add(p);
return true;
}
return false;
}
FlatEllipse::FlatEllipse(const FlatPoint &_f1, const FlatPoint &_f2,
const FlatPoint &_ap)
:f1(_f1),f2(_f2),ap(_ap)
{
const FlatLine f12(f1, f2);
p = f12.GetMiddle();
theta = f12.GetAngle();
const auto csq = f12.GetSquaredDistance();
a = (f1.Distance(ap) + f2.Distance(ap));
assert(Square(a) >= csq);
b = sqrt(Square(a) - csq) / 2;
a /= 2;
// a.sin(t) = ap.x
// b.cos(t) = ap.y
FlatPoint op = ap;
op -= p;
op.Rotate(-theta);
theta_initial = Angle::FromXY(op.x * b, op.y * a).AsDelta();
}
bool
FlatEllipse::Intersect(const FlatLine &line, FlatPoint &i1, FlatPoint &i2) const
{
const double er = ab();
const double ier = ba();
FlatLine s_line = line - p;
s_line.Rotate(theta.Reciprocal());
s_line.MultiplyY(er);
if (s_line.IntersectOriginCircle(a, i1, i2)) {
i1.MultiplyY(ier);
i1.Rotate(theta);
i1 += p;
i2.MultiplyY(ier);
i2.Rotate(theta);
i2 += p;
return true;
}
return false;
}