public static bool Intersect(Segment s0, Segment s1, out Intersection2D interObj)
{
// (Ay-Cy)(Dx-Cx)-(Ax-Cx)(Dy-Cy)
//r = ----------------------------- (eqn 1)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
// (Ay-Cy)(Bx-Ax)-(Ax-Cx)(By-Ay)
//s = ----------------------------- (eqn 2)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
double den = (s0.P1.X - s0.P0.X) * (s1.P1.Y - s1.P0.Y) - (s0.P1.Y - s0.P0.Y) * (s1.P1.X - s1.P0.X);
double r = (s0.P0.Y - s1.P0.Y) * (s1.P1.X - s1.P0.X) - (s0.P0.X - s1.P0.X) * (s1.P1.Y - s1.P0.Y);
double s = (s0.P0.Y - s1.P0.Y) * (s0.P1.X - s0.P0.X) - (s0.P0.X - s1.P0.X) * (s0.P1.Y - s0.P0.Y);
// If the denominator in eqn 1 is zero, AB & CD are parallel
if (System.Math.Abs(den) < MathFunctions.EpsilonF)
{
// If the numerator in eqn 1 is also zero, AB & CD are collinear.
if (System.Math.Abs(r) < MathFunctions.EpsilonF)
{
Interval i0 = new Interval(Interval.Type.Closed, System.Math.Min(s0.P0.X, s0.P1.X), System.Math.Max(s0.P0.X, s0.P1.X));
Interval i1 = new Interval(Interval.Type.Closed, System.Math.Min(s1.P0.X, s1.P1.X), System.Math.Max(s1.P0.X, s1.P1.X));
// check if interval overlaps
if ((i0.Max < i1.Min) || (i1.Max < i0.Min))
{
interObj = new Intersection2D();
return(false);
}
else
{
Interval i2 = new Interval(Interval.Type.Closed, System.Math.Max(i0.Min, i1.Min), System.Math.Min(i0.Max, i1.Max));
interObj = new Intersection2D(new Segment());
return(true);
}
}
else
{
interObj = new Intersection2D();
return(false);
}
}
else
{
r /= den;
s /= den;
// Let P be the position vector of the intersection point, then
// P=A+r(B-A)
if (0 <= r && r <= 1 && 0 <= s && s <= 1)
{
interObj = new Intersection2D(new Vector2D(s0.P0 + r * (s0.P1 - s0.P0)));
return(true);
}
}
interObj = new Intersection2D();
return(false);
}
public static bool Intersect(Segment seg, Ray ray, out Intersection2D interObj)
{
// (Ay-Cy)(Dx-Cx)-(Ax-Cx)(Dy-Cy)
//r = ----------------------------- (eqn 1)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
// (Ay-Cy)(Bx-Ax)-(Ax-Cx)(By-Ay)
//s = ----------------------------- (eqn 2)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
double den = (seg.P1.X - seg.P0.X) * ray.Direction.Y - (seg.P1.Y - seg.P0.Y) * ray.Direction.X;
double r = (seg.P0.Y - ray.Origin.Y) * ((ray.Origin + ray.Direction).X - ray.Origin.X) - (seg.P0.X - ray.Origin.X) * ((ray.Origin + ray.Direction).Y - ray.Origin.Y);
// If the denominator in eqn 1 is zero, AB & CD are parallel
if (System.Math.Abs(den) < MathFunctions.EpsilonF)
{
// If the numerator in eqn 1 is also zero, AB & CD are collinear.
if (System.Math.Abs(r) < MathFunctions.EpsilonF)
{
interObj = new Intersection2D(new Segment(seg));
return(true);
}
else
{
interObj = new Intersection2D();
return(false);
}
}
else
{
r /= den;
// Let P be the position vector of the intersection point, then
// P=A+r(B-A)
if (0 <= r && r <= 1)
{
interObj = new Intersection2D(new Vector2D(seg.P0 + r * (seg.P1 - seg.P0)));
return(true);
}
}
interObj = new Intersection2D();
return(false);
}
public static bool IntersectLines(Segment s0, Segment s1, out Intersection2D interObj)
{
// (Ay-Cy)(Dx-Cx)-(Ax-Cx)(Dy-Cy)
//r = ----------------------------- (eqn 1)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
// (Ay-Cy)(Bx-Ax)-(Ax-Cx)(By-Ay)
//s = ----------------------------- (eqn 2)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
double den = (s0.P1.X - s0.P0.X) * (s1.P1.Y - s1.P0.Y) - (s0.P1.Y - s0.P0.Y) * (s1.P1.X - s1.P0.X);
double r = (s0.P0.Y - s1.P0.Y) * (s1.P1.X - s1.P0.X) - (s0.P0.X - s1.P0.X) * (s1.P1.Y - s1.P0.Y);
double s = (s0.P0.Y - s1.P0.Y) * (s0.P1.X - s0.P0.X) - (s0.P0.X - s1.P0.X) * (s0.P1.Y - s0.P0.Y);
// If the denominator in eqn 1 is zero, AB & CD are parallel
if (System.Math.Abs(den) > MathFunctions.EpsilonF)
{
r /= den;
s /= den;
// Let P be the position vector of the intersection point, then
// P=A+r(B-A)
interObj = new Intersection2D(new Vector2D(s0.P0 + r * (s0.P1 - s0.P0)));
return true;
}
else
{
// If the numerator in eqn 1 is also zero, AB & CD are collinear.
if (System.Math.Abs(r) < MathFunctions.EpsilonF)
{
}
else
{
}
}
interObj = new Intersection2D();
return false;
}
public static bool IntersectLines(Segment s0, Segment s1, out Intersection2D interObj)
{
// (Ay-Cy)(Dx-Cx)-(Ax-Cx)(Dy-Cy)
//r = ----------------------------- (eqn 1)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
// (Ay-Cy)(Bx-Ax)-(Ax-Cx)(By-Ay)
//s = ----------------------------- (eqn 2)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
double den = (s0.P1.X - s0.P0.X) * (s1.P1.Y - s1.P0.Y) - (s0.P1.Y - s0.P0.Y) * (s1.P1.X - s1.P0.X);
double r = (s0.P0.Y - s1.P0.Y) * (s1.P1.X - s1.P0.X) - (s0.P0.X - s1.P0.X) * (s1.P1.Y - s1.P0.Y);
double s = (s0.P0.Y - s1.P0.Y) * (s0.P1.X - s0.P0.X) - (s0.P0.X - s1.P0.X) * (s0.P1.Y - s0.P0.Y);
// If the denominator in eqn 1 is zero, AB & CD are parallel
if (System.Math.Abs(den) > MathFunctions.EpsilonF)
{
r /= den;
s /= den;
// Let P be the position vector of the intersection point, then
// P=A+r(B-A)
interObj = new Intersection2D(new Vector2D(s0.P0 + r * (s0.P1 - s0.P0)));
return(true);
}
else
{
// If the numerator in eqn 1 is also zero, AB & CD are collinear.
if (System.Math.Abs(r) < MathFunctions.EpsilonF)
{
}
else
{
}
}
interObj = new Intersection2D();
return(false);
}
public static bool Intersect(Segment s0, Segment s1, out Intersection2D interObj)
{
// (Ay-Cy)(Dx-Cx)-(Ax-Cx)(Dy-Cy)
//r = ----------------------------- (eqn 1)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
// (Ay-Cy)(Bx-Ax)-(Ax-Cx)(By-Ay)
//s = ----------------------------- (eqn 2)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
double den = (s0.P1.X - s0.P0.X) * (s1.P1.Y - s1.P0.Y) - (s0.P1.Y - s0.P0.Y) * (s1.P1.X - s1.P0.X);
double r = (s0.P0.Y - s1.P0.Y) * (s1.P1.X - s1.P0.X) - (s0.P0.X - s1.P0.X) * (s1.P1.Y - s1.P0.Y);
double s = (s0.P0.Y - s1.P0.Y) * (s0.P1.X - s0.P0.X) - (s0.P0.X - s1.P0.X) * (s0.P1.Y - s0.P0.Y);
// If the denominator in eqn 1 is zero, AB & CD are parallel
if (System.Math.Abs(den) < MathFunctions.EpsilonF)
{
// If the numerator in eqn 1 is also zero, AB & CD are collinear.
if (System.Math.Abs(r) < MathFunctions.EpsilonF)
{
Interval i0 = new Interval(Interval.Type.Closed, System.Math.Min(s0.P0.X, s0.P1.X), System.Math.Max(s0.P0.X, s0.P1.X));
Interval i1 = new Interval(Interval.Type.Closed, System.Math.Min(s1.P0.X, s1.P1.X), System.Math.Max(s1.P0.X, s1.P1.X));
// check if interval overlaps
if ((i0.Max < i1.Min) || (i1.Max < i0.Min))
{
interObj = new Intersection2D();
return false;
}
else
{
Interval i2 = new Interval(Interval.Type.Closed, System.Math.Max(i0.Min, i1.Min), System.Math.Min(i0.Max, i1.Max));
interObj = new Intersection2D(new Segment());
return true;
}
}
else
{
interObj = new Intersection2D();
return false;
}
}
else
{
r /= den;
s /= den;
// Let P be the position vector of the intersection point, then
// P=A+r(B-A)
if (0 <= r && r <= 1 && 0 <= s && s <= 1)
{
interObj = new Intersection2D(new Vector2D(s0.P0+r*(s0.P1-s0.P0)));
return true;
}
}
interObj = new Intersection2D();
return false;
}
public static bool Intersect(Segment seg, Ray ray, out Intersection2D interObj)
{
// (Ay-Cy)(Dx-Cx)-(Ax-Cx)(Dy-Cy)
//r = ----------------------------- (eqn 1)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
// (Ay-Cy)(Bx-Ax)-(Ax-Cx)(By-Ay)
//s = ----------------------------- (eqn 2)
// (Bx-Ax)(Dy-Cy)-(By-Ay)(Dx-Cx)
double den = (seg.P1.X - seg.P0.X) * ray.Direction.Y - (seg.P1.Y - seg.P0.Y) * ray.Direction.X;
double r = (seg.P0.Y - ray.Origin.Y) * ((ray.Origin + ray.Direction).X - ray.Origin.X) - (seg.P0.X - ray.Origin.X) * ((ray.Origin + ray.Direction).Y - ray.Origin.Y);
// If the denominator in eqn 1 is zero, AB & CD are parallel
if (System.Math.Abs(den) < MathFunctions.EpsilonF)
{
// If the numerator in eqn 1 is also zero, AB & CD are collinear.
if (System.Math.Abs(r) < MathFunctions.EpsilonF)
{
interObj = new Intersection2D(new Segment(seg));
return true;
}
else
{
interObj = new Intersection2D();
return false;
}
}
else
{
r /= den;
// Let P be the position vector of the intersection point, then
// P=A+r(B-A)
if (0 <= r && r <= 1)
{
interObj = new Intersection2D(new Vector2D(seg.P0 + r * (seg.P1 - seg.P0)));
return true;
}
}
interObj = new Intersection2D();
return false;
}
