/// <summary>
/// Intersection test.
/// </summary>
/// <remarks>Test does not handle parallel lines.</remarks>
/// <param name="one">The first line segment.</param>
/// <param name="other">The second line segment.</param>
/// <param name="t1">The interpolation for first line segment, only if intersects is true.</param>
/// <param name="t2">The interpolation for second line segment, only if intersects is true.</param>
/// <returns>Do lines intersect.</returns>
public static bool Intersect(LineSegment3d one, LineSegment3d other,
out double t1, out double t2)
{
t1 = t2 = 0.0;
// We solve 2x2 system and then check if it is ok for the third argument.
Vector2d r = LinearSolver.SolveSystem(
new Matrix2x2d(one.Direction.X, -other.Direction.X,
one.Direction.Y, -other.Direction.Y),
new Vector2d(other.A.X - one.A.X, other.A.Y - one.A.Y));
// If system has the solution, it must be in range [0,1].
if (r.X < 0.0 || r.X > 0.0)
{
return(false);
}
if (r.Y < 0.0 || r.Y > 0.0)
{
return(false);
}
// We check if the last line satisfies.
if (!Vector3d.NearEqual(one.Sample(r.X), other.Sample(r.Y)))
{
return(false);
}
// We copy interpolation.
t1 = r.X;
t2 = r.Y;
return(true);
}
/// <summary>
/// Intersection test.
/// </summary>
/// <remarks>Test does not handle parallel lines.</remarks>
/// <param name="one">The first line segment.</param>
/// <param name="other">The second line segment.</param>
/// <param name="result">The resulting intersection point, only if it returns true.</param>
/// <returns>Do lines intersect.</returns>
public static bool Intersect(LineSegment3d one, LineSegment3d other, out Vector3d result)
{
double t1, t2;
if (!Intersect(one, other, out t1, out t2))
{
result = Vector3d.Zero;
return(false);
}
else
{
result = one.Sample(t1);
return(true);
}
}
//#endfor instanced to '3Df'
#endregion
#region LineSeg-Triangle Intersection
//#foreach instanced to '3Dd'
//#ifdef 3D
/// <summary>
/// A line-triangle intersection.
/// </summary>
/// <remarks>Only point is returned. In case of line segment lying on top of triangle, one
/// point is only returned.</remarks>
/// <param name="line">The line segment</param>
/// <param name="triangle">The triangle</param>
/// <param name="point">The intersection point.</param>
/// <returns>Does intersection occur</returns>
private static bool Intersect(LineSegment3d line, Triangle3d triangle, out Vector3d point)
{
// We compute distance of ray of plane.
double d = -((line.A - triangle.A) * triangle.Normal) / (line.Direction * triangle.Normal);
// We exit quickly if intersection does not occur on line.
if (d < 0.0 || d > 1.0)
{
point = Vector3d.Zero;
return(false);
}
// We now compute the actual point on the plane.
point = line.A + d * line.Direction;
// We have to determine if point lies inside triangle. We do it using barycentric
// coordinates. We solve the system with two unknowns.
Vector2d uv = triangle.GetBarycentric(point);
// Is it inside.
return(Triangle3d.IsBaryCentricInside(uv));
}
//#endfor instanced to '2Df'
//#foreach instanced to '3Dd'
/// <summary>
/// Pure intersection test.
/// </summary>
/// <remarks>Test does not handle parallel lines.</remarks>
/// <param name="one">The first line segment.</param>
/// <param name="other">The second line segment.</param>
/// <returns>Do lines intersect.</returns>
public static bool Intersect(LineSegment3d one, LineSegment3d other)
{
double t1, t2;
return(Intersect(one, other, out t1, out t2));
}