/// <summary>
/// This method calculates the distance to a point Pt.
/// The parameter Lam can be used to calculate the nearest point of the LineType, which is
/// also returned by the outvalue Nearest
/// </summary>
/// <param name="Pt">Point to calculate the distance to the LineType</param>
/// <param name="Lam">Parameter to calculate the nearest point</param>
/// <param name="Nearest">Point on the Line, with the lowest distance to Pt</param>
/// <returns>Returns the distance from the line to the point Pt</returns>
public double Distance(xyz Pt, out double Lam, out xyz Nearest)
{
if (Utils.Equals(Direction.length(), 0))
{
Lam = 0;
Nearest = P;
return(Pt.dist(P));
}
Lam = Direction.normalized().Scalarproduct(Pt.sub(P)) / Direction.length();
Nearest = P.add(Direction.mul(Lam));
return(Nearest.dist(Pt));
}
//public override void Compile(OpenGlDevice Device)
//{
// bool Inverted = false;
// base.Compile(Device);
// if (Inverted) BoundedCurves.Invert();
//}
/// <summary>
/// is a constructor, which has thre points of the plane.
/// </summary>
/// <param name="A">the first point.</param>
/// <param name="B">the second point.</param>
/// <param name="C">the third point.</param>
public PlaneSurface(xyz A, xyz B, xyz C)
{
xyz BA = B - A;
xyz CA = C - A;
xyz BaseZ = BA & CA;
BaseZ = BaseZ.normalized();
if (BaseZ.length() < 0.000001)
{
Base BB = Base.UnitBase;
BB.BaseO = A;
Base = BB;
return;
}
xyz BaseX = (CA & BaseZ).normalized();
xyz BaseY = BaseZ & BaseX;
Base __Base = new Base();
__Base.BaseO = A;
__Base.BaseX = BaseX;
__Base.BaseY = BaseY;
__Base.BaseZ = BaseZ;
Base = __Base;
}
/// <summary>
/// Transforms the plane with a transformation matrix
/// </summary>
/// <param name="T"></param>
public void Transform(Matrix T)
{
P = T * P;
double l = NormalUnit.length();
NormalUnit = T * NormalUnit - T * new xyz(0, 0, 0);
l = NormalUnit.length();
}
/// <summary>
/// Calculates the absolute coordinates of the point, whose coordinates are related to the Base.
/// The base is assumed to be normalized.
/// The invert method is <see cref="Relativ"/>.
/// </summary>
/// <param name="pt">Point</param>
/// <returns>returns the absolut coordinates in a worldbase</returns>
public xyz Absolut(xyz pt)
{
//xyz d=pt.sub(BaseO);
if ((!Utils.Equals(BaseX.length(), 1f)) || (!Utils.Equals(BaseY.length(), 1f)) || (!Utils.Equals(BaseZ.length(), 1f)))
{
}
return(BaseO.add(BaseX.mul(pt.x)).add(BaseY.mul(pt.y)).add(BaseZ.mul(pt.z)));
}
/// <summary>
/// Produce an orthogonal base with Origin a z-axis,the x-axis and a y-axis, which is normal to XAxis cross YVector
/// </summary>
/// <param name="Origin">The origin</param>
/// <param name="XAxis">the x axis</param>
/// <param name="YVector">the x axis is normal to XAxis cross YVector</param>
/// <returns>orthogonal base</returns>
public static Base DoComplete(xyz Origin, xyz XAxis, xyz YVector)
{
Base Result = new Base();
if (YVector.length() == 0)
{
YVector = XAxis & new xyz(0, 0, 1);
if (YVector.length() == 0)
{
YVector = XAxis & new xyz(0, 1, 0);
}
if (YVector.length() == 0)
{
YVector = XAxis & new xyz(1, 0, 0);
}
}
Result.BaseO = Origin;
Result.BaseX = XAxis.normalized();
Result.BaseZ = (XAxis & YVector).normalized();
Result.BaseY = Result.BaseZ & Result.BaseX;
return(Result);
}
/// <summary>
/// calculates the barycentric coordinates, which wil be returned.
/// The point A*result.x +B*result.y+C*result.z is the normalprojection of P to
/// the plane spanned by A,B and C. If A,B and C are in a line 0,0,0 wil be returned.
/// </summary>
/// <param name="A">Edge point of the triangle</param>
/// <param name="B">Edge point of the triangle</param>
/// <param name="C">Edge point of the triangle</param>
/// <param name="P">Base point in the ABC plane </param>
/// <returns></returns>
public static xyz BaryCentric(xyz A, xyz B, xyz C, xyz P)
{
xyz F = (B - A) & (C - A);
if (F.length() < 0.000000001)
{
return(new xyz(0, 0, 0));
}
xyz N = F.normalized();
double TrABC = F * N;
double TrCAP = ((C - P) & (A - P)) * N;
double TrABP = ((A - P) & (B - P)) * N;
double TrBCP = ((B - P) & (C - P)) * N;
return(new xyz(TrBCP / TrABC, TrCAP / TrABC, TrABP / TrABC));
}
/// <summary>
/// Overrides the method <see cref="Surface.getCross"/> and implements a method for get the crosspoint with a Line <b>L</b>, which is
/// nearer to L.Q.
/// </summary>
/// <param name="L">The line, which will be crossed with the sphere</param>
/// <param name="u">gets the u parameter of the cross point</param>
/// <param name="v">gets the v parameter of the cross point</param>
/// <returns>false if there is no cross point.</returns>
public override bool getCross(LineType L, ref double u, ref double v)
{
xyz Direction = L.Direction.normalized();
xyz P = Base.Relativ(L.P);
xyz NDirection = ((Direction & P) & (Direction));
double bb = NDirection.length();
xyz S = new xyz(0, 0, 0);
if (Radius > bb)
{
S = NDirection - Direction * System.Math.Sqrt(Radius * Radius - bb * bb);
}
else
{
return(false);
}
xy Param = this.ProjectPoint(Base.Absolut(S));
u = Param.x;
v = Param.Y;
return(true);
}