/// <summary>
/// Obtains barycentric coordinate relative to this triangle.
/// </summary>
/// <param name="input">The vector that lies in triangle plane.</param>
/// <returns></returns>
public Vector2f GetBarycentric(Vector2f input)
{
// Automatic Z-projection for 2D.
return(LinearSolver.SolveSystem(B.X - A.X, C.X - A.X,
B.Y - A.Y, C.Y - A.Y,
input.X - A.X, input.Y - A.Y));
}
/// <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(LineSegment2d one, LineSegment2d 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 (!Vector2d.NearEqual(one.Sample(r.X), other.Sample(r.Y)))
{
return(false);
}
// We copy interpolation.
t1 = r.X;
t2 = r.Y;
return(true);
}
/// <summary>
/// Obtains barycentric coordinate relative to this triangle.
/// </summary>
/// <param name="input">The vector that lies in triangle plane.</param>
/// <returns></returns>
public Vector2f GetBarycentric(Vector3f input)
{
//#ifdef 3D
// We need positive components of normal, only magnitude relavant.
Vector3f normal = this.Normal;
normal = Vector3f.ComponentMultiply(normal, normal);
if (normal.X > normal.Y)
{
if (normal.X > normal.Y)
{
// We project to x axis, all xs are the same.
return(LinearSolver.SolveSystem(B.Y - A.Y, C.Y - A.Y,
B.Z - A.Z, C.Z - A.Z,
input.Y - A.Y, input.Z - A.Z));
}
else
{
// We project to z axis, all zs are the same.
return(LinearSolver.SolveSystem(B.X - A.X, C.X - A.X,
B.Y - A.Y, C.Y - A.Y,
input.X - A.X, input.Y - A.Y));
}
}
else
{
if (normal.Y > normal.Z)
{
// We project to y axis, all ys are the same.
return(LinearSolver.SolveSystem(B.X - A.X, C.X - A.X,
B.Z - A.Z, C.Z - A.Z,
input.X - A.X, input.Z - A.Z));
}
else
{
// We project to z axis, all zs are the same.
return(LinearSolver.SolveSystem(B.X - A.X, C.X - A.X,
B.Y - A.Y, C.Y - A.X,
input.X - A.X, input.Y - A.Y));
}
}
//#endif
}