/// <summary>Calculates the orientation of the triangle formed by p->q->r.</summary>
/// <remarks>
/// Calculates the orientation of the triangle formed by p->q->r. Returns 1
/// for counter-clockwise, -1 for clockwise, and 0 for collinear. May use
/// high precision arithmetics for some special degenerate cases.
/// </remarks>
public static int OrientationRobust(com.epl.geometry.Point2D p, com.epl.geometry.Point2D q, com.epl.geometry.Point2D r)
{
com.epl.geometry.ECoordinate det_ec = new com.epl.geometry.ECoordinate();
det_ec.Set(q.x);
det_ec.Sub(p.x);
com.epl.geometry.ECoordinate rp_y_ec = new com.epl.geometry.ECoordinate();
rp_y_ec.Set(r.y);
rp_y_ec.Sub(p.y);
com.epl.geometry.ECoordinate qp_y_ec = new com.epl.geometry.ECoordinate();
qp_y_ec.Set(q.y);
qp_y_ec.Sub(p.y);
com.epl.geometry.ECoordinate rp_x_ec = new com.epl.geometry.ECoordinate();
rp_x_ec.Set(r.x);
rp_x_ec.Sub(p.x);
det_ec.Mul(rp_y_ec);
qp_y_ec.Mul(rp_x_ec);
det_ec.Sub(qp_y_ec);
if (!det_ec.IsFuzzyZero())
{
double det_ec_value = det_ec.Value();
if (det_ec_value < 0.0)
{
return(-1);
}
if (det_ec_value > 0.0)
{
return(1);
}
return(0);
}
// Need extended precision
decimal det_mp = new decimal(q.x);
decimal px_mp = new decimal(p.x);
decimal py_mp = new decimal(p.y);
det_mp = decimal.Subtract(det_mp, px_mp);
decimal rp_y_mp = new decimal(r.y);
rp_y_mp = decimal.Subtract(rp_y_mp, py_mp);
decimal qp_y_mp = new decimal(q.y);
qp_y_mp = decimal.Subtract(qp_y_mp, py_mp);
decimal rp_x_mp = new decimal(r.x);
rp_x_mp = decimal.Subtract(rp_x_mp, px_mp);
det_mp = decimal.Multiply(det_mp, rp_y_mp);
qp_y_mp = decimal.Multiply(qp_y_mp, rp_x_mp);
det_mp = decimal.Subtract(det_mp, qp_y_mp);
return(System.Math.Sign(det_mp));
}
// Orientation predicates
private static com.epl.geometry.ECoordinate Determinant_(com.epl.geometry.Point2D p, com.epl.geometry.Point2D q, com.epl.geometry.Point2D r)
{
com.epl.geometry.ECoordinate det_ec = new com.epl.geometry.ECoordinate();
det_ec.Set(q.x);
det_ec.Sub(p.x);
com.epl.geometry.ECoordinate rp_y_ec = new com.epl.geometry.ECoordinate();
rp_y_ec.Set(r.y);
rp_y_ec.Sub(p.y);
com.epl.geometry.ECoordinate qp_y_ec = new com.epl.geometry.ECoordinate();
qp_y_ec.Set(q.y);
qp_y_ec.Sub(p.y);
com.epl.geometry.ECoordinate rp_x_ec = new com.epl.geometry.ECoordinate();
rp_x_ec.Set(r.x);
rp_x_ec.Sub(p.x);
det_ec.Mul(rp_y_ec);
qp_y_ec.Mul(rp_x_ec);
det_ec.Sub(qp_y_ec);
return(det_ec);
}
/// <summary>Calculates if the point s is inside of the circumcircle inscribed by the clockwise oriented triangle p-q-r.</summary>
/// <remarks>
/// Calculates if the point s is inside of the circumcircle inscribed by the clockwise oriented triangle p-q-r.
/// Returns 1 for outside, -1 for inside, and 0 for cocircular.
/// Note that the convention used here differs from what is commonly found in literature, which can define the relation
/// in terms of a counter-clockwise oriented circle, and this flips the sign (think of the signed volume of the tetrahedron).
/// May use high precision arithmetics for some special cases.
/// </remarks>
internal static int InCircleRobust(com.epl.geometry.Point2D p, com.epl.geometry.Point2D q, com.epl.geometry.Point2D r, com.epl.geometry.Point2D s)
{
com.epl.geometry.ECoordinate psx_ec = new com.epl.geometry.ECoordinate();
com.epl.geometry.ECoordinate psy_ec = new com.epl.geometry.ECoordinate();
psx_ec.Set(p.x);
psx_ec.Sub(s.x);
psy_ec.Set(p.y);
psy_ec.Sub(s.y);
com.epl.geometry.ECoordinate qsx_ec = new com.epl.geometry.ECoordinate();
com.epl.geometry.ECoordinate qsy_ec = new com.epl.geometry.ECoordinate();
qsx_ec.Set(q.x);
qsx_ec.Sub(s.x);
qsy_ec.Set(q.y);
qsy_ec.Sub(s.y);
com.epl.geometry.ECoordinate rsx_ec = new com.epl.geometry.ECoordinate();
com.epl.geometry.ECoordinate rsy_ec = new com.epl.geometry.ECoordinate();
rsx_ec.Set(r.x);
rsx_ec.Sub(s.x);
rsy_ec.Set(r.y);
rsy_ec.Sub(s.y);
com.epl.geometry.ECoordinate psx_ec_qsy_ec = new com.epl.geometry.ECoordinate();
psx_ec_qsy_ec.Set(psx_ec);
psx_ec_qsy_ec.Mul(qsy_ec);
com.epl.geometry.ECoordinate psy_ec_qsx_ec = new com.epl.geometry.ECoordinate();
psy_ec_qsx_ec.Set(psy_ec);
psy_ec_qsx_ec.Mul(qsx_ec);
com.epl.geometry.ECoordinate qsx_ec_rsy_ec = new com.epl.geometry.ECoordinate();
qsx_ec_rsy_ec.Set(qsx_ec);
qsx_ec_rsy_ec.Mul(rsy_ec);
com.epl.geometry.ECoordinate qsy_ec_rsx_ec = new com.epl.geometry.ECoordinate();
qsy_ec_rsx_ec.Set(qsy_ec);
qsy_ec_rsx_ec.Mul(rsx_ec);
com.epl.geometry.ECoordinate psx_ec_rsy_ec = new com.epl.geometry.ECoordinate();
psx_ec_rsy_ec.Set(psx_ec);
psx_ec_rsy_ec.Mul(rsy_ec);
com.epl.geometry.ECoordinate psy_ec_rsx_ec = new com.epl.geometry.ECoordinate();
psy_ec_rsx_ec.Set(psy_ec);
psy_ec_rsx_ec.Mul(rsx_ec);
com.epl.geometry.ECoordinate pq_det_ec = new com.epl.geometry.ECoordinate();
pq_det_ec.Set(psx_ec_qsy_ec);
pq_det_ec.Sub(psy_ec_qsx_ec);
com.epl.geometry.ECoordinate qr_det_ec = new com.epl.geometry.ECoordinate();
qr_det_ec.Set(qsx_ec_rsy_ec);
qr_det_ec.Sub(qsy_ec_rsx_ec);
com.epl.geometry.ECoordinate pr_det_ec = new com.epl.geometry.ECoordinate();
pr_det_ec.Set(psx_ec_rsy_ec);
pr_det_ec.Sub(psy_ec_rsx_ec);
com.epl.geometry.ECoordinate psx_ec_psx_ec = new com.epl.geometry.ECoordinate();
psx_ec_psx_ec.Set(psx_ec);
psx_ec_psx_ec.Mul(psx_ec);
com.epl.geometry.ECoordinate psy_ec_psy_ec = new com.epl.geometry.ECoordinate();
psy_ec_psy_ec.Set(psy_ec);
psy_ec_psy_ec.Mul(psy_ec);
com.epl.geometry.ECoordinate qsx_ec_qsx_ec = new com.epl.geometry.ECoordinate();
qsx_ec_qsx_ec.Set(qsx_ec);
qsx_ec_qsx_ec.Mul(qsx_ec);
com.epl.geometry.ECoordinate qsy_ec_qsy_ec = new com.epl.geometry.ECoordinate();
qsy_ec_qsy_ec.Set(qsy_ec);
qsy_ec_qsy_ec.Mul(qsy_ec);
com.epl.geometry.ECoordinate rsx_ec_rsx_ec = new com.epl.geometry.ECoordinate();
rsx_ec_rsx_ec.Set(rsx_ec);
rsx_ec_rsx_ec.Mul(rsx_ec);
com.epl.geometry.ECoordinate rsy_ec_rsy_ec = new com.epl.geometry.ECoordinate();
rsy_ec_rsy_ec.Set(rsy_ec);
rsy_ec_rsy_ec.Mul(rsy_ec);
com.epl.geometry.ECoordinate p_parab_ec = new com.epl.geometry.ECoordinate();
p_parab_ec.Set(psx_ec_psx_ec);
p_parab_ec.Add(psy_ec_psy_ec);
com.epl.geometry.ECoordinate q_parab_ec = new com.epl.geometry.ECoordinate();
q_parab_ec.Set(qsx_ec_qsx_ec);
q_parab_ec.Add(qsy_ec_qsy_ec);
com.epl.geometry.ECoordinate r_parab_ec = new com.epl.geometry.ECoordinate();
r_parab_ec.Set(rsx_ec_rsx_ec);
r_parab_ec.Add(rsy_ec_rsy_ec);
p_parab_ec.Mul(qr_det_ec);
q_parab_ec.Mul(pr_det_ec);
r_parab_ec.Mul(pq_det_ec);
com.epl.geometry.ECoordinate det_ec = new com.epl.geometry.ECoordinate();
det_ec.Set(p_parab_ec);
det_ec.Sub(q_parab_ec);
det_ec.Add(r_parab_ec);
if (!det_ec.IsFuzzyZero())
{
double det_ec_value = det_ec.Value();
if (det_ec_value < 0.0)
{
return(-1);
}
if (det_ec_value > 0.0)
{
return(1);
}
return(0);
}
return(InCircleRobustMP_(p, q, r, s));
}