/// <summary>
/// implements the <see cref="INurbs3d.getUKnots"/> method.
/// </summary>
/// <returns></returns>
public override xyz[,] getCtrlPoints()
{
double Factor = 0.0000;
xyz[,] ControlPoints = new xyz[, ] {
{ new xyz(0, Factor, -Radius), new xyz(0, Radius, -Radius), new xyz(0, Radius, 0), new xyz(0, Radius, Radius), new xyz(0, Factor, Radius) },
{ new xyz(-Factor, Factor, -Radius), new xyz(-Radius, Radius, -Radius), new xyz(-Radius, Radius, 0), new xyz(-Radius, Radius, Radius), new xyz(-Factor, Factor, Radius) },
{ new xyz(-Factor, 0, -Radius), new xyz(-Radius, 0, -Radius), new xyz(-Radius, 0, 0), new xyz(-Radius, 0, Radius), new xyz(-Factor, 0, Radius) },
{ new xyz(-Factor, -Factor, -Radius), new xyz(-Radius, -Radius, -Radius), new xyz(-Radius, -Radius, 0), new xyz(-Radius, -Radius, Radius), new xyz(-Factor, -Factor, Radius) },
{ new xyz(0, -Factor, -Radius), new xyz(0, -Radius, -Radius), new xyz(0, -Radius, 0), new xyz(0, -Radius, Radius), new xyz(0, -Factor, Radius) },
{ new xyz(Factor, -Factor, -Radius), new xyz(Radius, -Radius, -Radius), new xyz(Radius, -Radius, 0), new xyz(Radius, -Radius, Radius), new xyz(Factor, -Factor, Radius) },
{ new xyz(Factor, 0, -Radius), new xyz(Radius, 0, -Radius), new xyz(Radius, 0, 0), new xyz(Radius, 0, Radius), new xyz(Factor, 0, Radius) },
{ new xyz(Factor, Factor, -Radius), new xyz(Radius, Radius, -Radius), new xyz(Radius, Radius, 0), new xyz(Radius, Radius, Radius), new xyz(Factor, Factor, Radius) },
{ new xyz(0, Factor, -Radius), new xyz(0, Radius, -Radius), new xyz(0, Radius, 0), new xyz(0, Radius, Radius), new xyz(0, Factor, Radius) }
};
for (int i = 0; i < ControlPoints.GetLength(0); i++)
{
for (int j = 0; j < ControlPoints.GetLength(1); j++)
{
ControlPoints[i, j] = Base.Absolut(ControlPoints[i, j]);
}
}
return(ControlPoints);
}
/// <summary>
/// implements the <see cref="INurbs3d.getUKnots"/> method.
/// </summary>
/// <returns></returns>
public override xyz[,] getCtrlPoints()
{
RefreshEnvBox();
double BaseRadius = Radius;
double Max = Env.Y + Env.Height;
double Min = Env.Y;
xyz[,] CP = new xyz[, ]
{
{ new xyz(BaseRadius, 0, 0), new xyz(BaseRadius, 0, Height) },
{ new xyz(BaseRadius, BaseRadius, 0), new xyz(BaseRadius, BaseRadius, Height) },
{ new xyz(0, BaseRadius, 0), new xyz(0, BaseRadius, Height) },
{ new xyz(-BaseRadius, BaseRadius, 0), new xyz(-BaseRadius, BaseRadius, Height) },
{ new xyz(-BaseRadius, 0, 0), new xyz(-BaseRadius, 0, Height) },
{ new xyz(-BaseRadius, -BaseRadius, 0), new xyz(-BaseRadius, -BaseRadius, Height) },
{ new xyz(0, -BaseRadius, 0), new xyz(0, -BaseRadius, Height) },
{ new xyz(BaseRadius, -BaseRadius, 0), new xyz(BaseRadius, -BaseRadius, Height) },
{ new xyz(BaseRadius, 0, 0), new xyz(BaseRadius, 0, Height) },
};
for (int i = 0; i < CP.GetLength(0); i++)
{
for (int j = 0; j < CP.GetLength(1); j++)
{
CP[i, j] = Base.Absolut(CP[i, j]);
}
}
return(CP);
}
/// <summary>
/// Calculates the partial v derivation of the <see cref="BSplineSurface"/>.
/// </summary>
/// <param name="u">Parameter u.</param>
/// <param name="v">Parameter v.</param>
/// <returns>The partial v derivation.</returns>
public override xyz vDerivation(double u, double v)
{
if ((UKnots == null) || (VKnots == null))
{
return(new xyz(0, 0, 0));
}
Utils.SplineExValue[] VCoeffs = Utils.CoeffSplineEx(VKnots, ControlPoints.GetLength(1), VDegree, VPeriodicity, v);
double[] UCoeffs = Utils.CoeffSpline(UKnots, ControlPoints.GetLength(0), UDegree, UPeriodicity, u);
double WDerived = 0;
double W = 0;
for (int i = 0; i < UCoeffs.Length; i++)
{
for (int j = 0; j < VCoeffs.Length; j++)
{
W = W + Weights[i, j] * UCoeffs[i] * VCoeffs[j].Value;
WDerived = WDerived + Weights[i, j] * UCoeffs[i] * VCoeffs[j].Derivation;
}
}
xyz Result = new xyz();
for (int i = 0; i < ControlPoints.GetLength(0); i++)
{
for (int k = 0; k < ControlPoints.GetLength(1); k++)
{
Result = Result + ControlPoints[i, k] * (Weights[i, k] * UCoeffs[i] * (VCoeffs[k].Derivation * W - WDerived * VCoeffs[k].Value) / (W * W));
}
}
return(Base.Absolut(Result) - Base.BaseO);
}
/// <summary>
/// Calculates partial uderivation of the <see cref="Torus"/>.
/// </summary>
/// <param name="u">Parameter u.</param>
/// <param name="v">Parameter v.</param>
/// <returns>The partial u-derivation for the torus.</returns>
public override xyz uDerivation(double u, double v)
{
double x = -(InnerRadius * System.Math.Cos(v * VFactor) + OuterRadius) * System.Math.Sin(u * UFactor) * UFactor;
double y = (InnerRadius * System.Math.Cos(v * VFactor) + OuterRadius) * System.Math.Cos(u * UFactor) * UFactor;
double z = 0;
return(Base.Absolut(new xyz(x, y, z)) - Base.BaseO);
}
/// <summary>
/// Calculates the partial vDerivation
/// </summary>
/// <param name="u">first parameter</param>
/// <param name="v">second parameter</param>
/// <returns>value of the partial vDerivation</returns>
public override xyz vDerivation(double u, double v)
{
double x = Radius * System.Math.Cos((u) * UFactor + 0.25 * System.Math.PI * 2) * System.Math.Cos(v * VFactor);
double y = Radius * System.Math.Sin((u) * UFactor + 0.25 * System.Math.PI * 2) * System.Math.Cos(v * VFactor);
double z = Radius * System.Math.Sin(v * VFactor);
return(Base.Absolut(new xyz(x, y, z)) - Base.BaseO);
}
/// <summary>
/// overrides <see cref="Surface.vDerivation(double, double)"/>.
/// </summary>
/// <param name="u">first parameter.</param>
/// <param name="v">second parameter.</param>
/// <returns>is the partial v deriavation.</returns>
public override xyz vDerivation(double u, double v)
{
double x = -System.Math.Sin(v * Math.PI * 2 * (ToAngle / VFactor + (1 - v) * FromAngle / VFactor)) * Curve.Value(u).x;
double y = System.Math.Cos(v * Math.PI * 2 * (ToAngle / VFactor + (1 - v) * FromAngle / VFactor)) * Curve.Value(u).x;
double z = 0;
xyz Q = new xyz(x, y, z);
return(Base.Absolut(Q) - Base.BaseO);
}
/// <summary>
/// Calculates the circle in the center of the torus.
/// </summary>
/// <param name="u">Specifies a parameter in [0,1] for which a circle points will be calculated.</param>
/// <returns>Returns a point on the center circle of the torus.</returns>
public xyz CenterCircle(double u)
{
double x = OuterRadius * System.Math.Cos(u * UFactor);
double y = OuterRadius * System.Math.Sin(u * UFactor);
double z = 0;
return(Base.Absolut(new xyz(x, y, z)));
// double dummy = x;
}
/// <summary>
/// overrides the <see cref="Surface.uDerivation(double, double)"/>.
/// </summary>
/// <param name="u">first paramter.</param>
/// <param name="v">second paramter.</param>
/// <returns>is the partial u deriavation.</returns>
public override xyz uDerivation(double u, double v)
{
xyz CurveDerive = Curve.Derivation(u);
double x = System.Math.Cos(v * VFactor) * Curve.Derivation(u).x - Math.Sin(v * VFactor) * (Curve.Derivation(u).y);
double y = Math.Sin(v * VFactor) * Curve.Derivation(u).x + System.Math.Cos(v * VFactor) * (Curve.Derivation(u).y);
double z = Curve.Derivation(u).z;
return(Base.Absolut(new xyz(x, y, z)) - Base.BaseO);
}
/// <summary>
/// Calculates partial v-derivation of the <see cref="Torus"/>.
/// </summary>
/// <param name="u">Parameter u.</param>
/// <param name="v">Parameter v.</param>
/// <returns>The partial v-derivation for the torus.</returns>
public override xyz vDerivation(double u, double v)
{
double x = -InnerRadius *System.Math.Sin(v *VFactor) * VFactor * System.Math.Cos(u * UFactor);
double y = -InnerRadius *System.Math.Sin(v *VFactor) * VFactor * System.Math.Sin(u * UFactor);
double z = InnerRadius * System.Math.Cos(v * VFactor) * VFactor;
return(Base.Absolut(new xyz(x, y, z)) - Base.BaseO);
}
/// <summary>
/// overrides the <see cref="Surface.vDerivation(double, double)"/>.
/// </summary>
/// <param name="u">first paramter.</param>
/// <param name="v">second paramter.</param>
/// <returns>is the partial v deriavation.</returns>
public override xyz vDerivation(double u, double v)
{
xyz P = Curve.Value(u);
double x = -System.Math.Sin(v * VFactor) * VFactor * Curve.Value(u).x - Math.Cos(v * VFactor) * VFactor * (Curve.Value(u).y);
double y = Math.Cos(v * VFactor) * VFactor * Curve.Value(u).x - System.Math.Sin(v * VFactor) * VFactor * Curve.Value(u).y;
double z = 0;
xyz Q = new xyz(x, y, z);
return(Base.Absolut(Q) - Base.BaseO);
}
/// <summary>
/// overrides the <see cref="Value(double, double)"/> method.
/// </summary>
/// <param name="u">the u parameter.</param>
/// <param name="v">the v parameter.</param>
/// <returns></returns>
public override xyz Value(double u, double v)
{
if (ZHeight(u, v) != 0)
{
return(Base.Absolut(Utils.BezierSurfacePt(ControlPoints, u, v) + Normal(u, v) * ZHeight(u, v)));
}
else
{
return(Base.Absolut(Utils.BezierSurfacePt(ControlPoints, u, v)));
}
}
/// <summary>
/// Overrides the Value function and implements the Cylinder calulations.
/// </summary>
/// <param name="u">Specifies the u parameter int [0,1]</param>
/// <param name="v">Specifies the v parameter int [0,1]</param>
/// <returns>returns a xyz Point</returns>
public override xyz Value(double u, double v)
{
double x = Radius * System.Math.Cos(u * UFactor);
double y = Radius * System.Math.Sin(u * UFactor);
double z = Height * v;
if (ZHeight(u, v) > 0)
{
return(Base.Absolut(new xyz(x, y, z) + Normal(u, v) * ZHeight(u, v)));
}
return(Base.Absolut(new xyz(x, y, z)));
}
/// <summary>
/// Calculates the value of the <see cref="Torus"/>.
/// </summary>
/// <param name="u">Parameter u.</param>
/// <param name="v">Parameter v.</param>
/// <returns>The Evaluation for the torus.</returns>
public override xyz Value(double u, double v)
{
double IR = InnerRadius;
double OR = OuterRadius;
double x = (IR * System.Math.Cos(v * VFactor) + OR) * System.Math.Cos(u * UFactor);
double y = (IR * System.Math.Cos(v * VFactor) + OR) * System.Math.Sin(u * UFactor);
double z = IR * System.Math.Sin(v * VFactor);
if (ZHeight(u, v) > 0)
{
return(Base.Absolut(new xyz(x, y, z) + Normal(u, v) * ZHeight(u, v)));
}
return(Base.Absolut(new xyz(x, y, z)));
}
/// <summary>
/// Overrides the Value function and implements the cone calulations.
/// </summary>
/// <param name="u">Specifies the u parameter int [0,1]</param>
/// <param name="v">Specifies the v parameter int [0,1]</param>
/// <returns>returns a xyz Point</returns>
public override xyz Value(double u, double v)
{
double Factor = Radius - v * VFactor * System.Math.Tan(HalfAngle);
double x = System.Math.Cos(u * UFactor) * Factor;
double y = System.Math.Sin(u * UFactor) * Factor;
double z = v * VFactor;
if (ZHeight(u, v) != 0)
{
return(Base.Absolut(new xyz(x, y, z) + Normal(u, v) * (ZHeight(u, v))));
}
else
{
return(Base.Absolut(new xyz(x, y, z)));
}
}
/// <summary>
/// overrides the <see cref="Surface.Normal(double, double)"/> method.
/// </summary>
/// <param name="u">the parameter u.</param>
/// <param name="v">the parameter v.</param>
/// <returns>the normal vector.</returns>
public override xyz Normal(double u, double v)
{
double x = (Math.Cos(v * VFactor)) * Math.Cos(u * UFactor);
double y = (System.Math.Cos(v * VFactor)) * System.Math.Sin(u * UFactor);
double z = System.Math.Sin(v * VFactor);
{
if (SameSense)
{
return(Base.Absolut(new xyz(x, y, z)) - Base.BaseO);
}
else
{
return((Base.Absolut(new xyz(x, y, z)) - Base.BaseO) * (-1));
}
}
}
/// <summary>
/// paramtisizes the sphere for the to parameters u and v which are given in the interval [0, 1]
/// </summary>
/// <param name="u">first parameter</param>
/// <param name="v">second parameter</param>
/// <returns>Spherecoordinate</returns>
public override xyz Value(double u, double v)
{
double x = Radius * System.Math.Cos((u) * UFactor + 0.25 * System.Math.PI * 2) * System.Math.Sin(v * VFactor);
double y = Radius * System.Math.Sin((u) * UFactor + 0.25 * System.Math.PI * 2) * System.Math.Sin(v * VFactor);
double z = -Radius *System.Math.Cos(v *VFactor);
if (ZHeight(u, v) > 0)
{
return(Base.Absolut(new xyz(x, y, z) +
new xyz(
System.Math.Cos((u) * UFactor + 0.25 * System.Math.PI * 2) * System.Math.Sin(v * VFactor),
System.Math.Sin((u) * UFactor + 0.25 * System.Math.PI * 2) * System.Math.Sin(v * VFactor),
-System.Math.Cos(v * VFactor)) * ZHeight(u, v)));
}
return(Base.Absolut(new xyz(x, y, z)));
}
/// <summary>
/// paramtisizes the a prism for the to parameters u and v which are given in the interval [0, 1]
/// </summary>
/// <param name="u">first parameter</param>
/// <param name="v">second parameter</param>
/// <returns>prismcoordinate</returns>
public override xyz Value(double u, double v)
{
int Id = (int)(u * Array.Count);
if (Id == Array.Count)
{
Id--;
}
double _ZHeight = ZHeight(u, v);
xy N = new xy(0, 0);
if (_ZHeight > 0)
{
N = Normal(u * Array.Count) * _ZHeight;
}
return(Base.Absolut((Array.Value(u * Array.Count) + N).toXYZ() + new xyz(0, 0, v * VFactor)));
}
/// <summary>
/// overrides the <see cref="Value(double, double)"/> method of a <see cref="Surface"/>.
/// </summary>
/// <param name="u">first u-parameter</param>
/// <param name="v">second v-parameter</param>
/// <returns>coordinate of the extruded object</returns>
public override xyz Value(double u, double v)
{
double Lam = -1;
xyz Q = new xyz(0, 0, 0);
xy P = Curve.Value(u);
xyz K = StandardBase.BaseO + StandardBase.BaseX * P.x + StandardBase.BaseY * P.y;
if (Height < 0)
{
xyz Pkt = new xyz(0, 0, 0);
xyz Pkt2 = new xyz(0, 0, 0);
DownPlane.Cross(new LineType(K, Direction), out Lam, out Pkt);
UpPlane.Cross(new LineType(K, Direction), out Lam, out Pkt2);
xyz N = Base.Absolut(Pkt + (Pkt2 - Pkt) * v);
if (ZHeight(u, v) > 0)
{
return(Base.Absolut(Pkt + (Pkt2 - Pkt) * v + Normal(u, v) * ZHeight(u, v)));
}
else
{
return(Base.Absolut(Pkt + (Pkt2 - Pkt) * v));
}
}
else
{
LineType L = new LineType(K, Direction);
Plane PL = new Plane(Base.BaseO, Base.BaseZ);
Q = new xyz(0, 0, 0);
PL.Cross(L, out Lam, out Q);
if (ZHeight(u, v) > 0)
{
return(Q + Direction.normalized() * (Height * v) + Normal(u, v) * ZHeight(u, v));
}
else
{
return(Q + Direction.normalized() * (Height * v));
}
}
}
/// <summary>
/// implements the <see cref="INurbs3d.getCtrlPoints"/> method.
/// </summary>
/// <returns></returns>
public override xyz[,] getCtrlPoints()
{
if (BoundedCurves != null)
{
Env = BoundedCurves[0].MaxRect;
}
else
{
Env = new RectangleF(new PointF(0, 0), new SizeF((float)Radius, (float)Height));
}
double Max = Env.Y + Env.Height;
double Min = Env.Y;
double BaseRadius = Radius;
double TopR = Radius - Height * System.Math.Tan(HalfAngle);
TopR = Radius - (VFactor * (System.Math.Tan(HalfAngle)));
BaseRadius = Radius - (VFactor * (System.Math.Tan(HalfAngle) * (Min)));
xyz[,] CP = new xyz[, ]
{
{ new xyz(BaseRadius, 0, Min), new xyz(TopR, 0, Max) },
{ new xyz(BaseRadius, BaseRadius, Min), new xyz(TopR, TopR, Max) },
{ new xyz(0, BaseRadius, Min), new xyz(0, TopR, Max) },
{ new xyz(-BaseRadius, BaseRadius, Min), new xyz(-TopR, TopR, Max) },
{ new xyz(-BaseRadius, 0, Min), new xyz(-TopR, 0, Max) },
{ new xyz(-BaseRadius, -BaseRadius, Min), new xyz(-TopR, -TopR, Max) },
{ new xyz(0, -BaseRadius, Min), new xyz(0, -TopR, Max) },
{ new xyz(BaseRadius, -BaseRadius, Min), new xyz(TopR, -TopR, Max) },
{ new xyz(BaseRadius, 0, Min), new xyz(TopR, 0, Max) },
};
for (int i = 0; i < CP.GetLength(0); i++)
{
for (int j = 0; j < CP.GetLength(1); j++)
{
CP[i, j] = Base.Absolut(CP[i, j]);
}
}
return(CP);
}
/// <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);
}
/// <summary>
/// Calulates the v-derivation of a bezierfunction for the two parameters u and v which are given in the interval [0, 1]
/// </summary>
/// <param name="u">first parameter</param>
/// <param name="v">second parameter</param>
/// <returns>v-derivation</returns>
public override xyz vDerivation(double u, double v)
{
return(Base.Absolut(Utils.BezierSurfaceDeriveV(ControlPoints, u, v)) - Base.BaseO);
}
/// <summary>
/// Overrides the <see cref="Curve3D.Derivation"/>-method.
/// </summary>
/// <param name="t"></param>
/// <returns></returns>
public override xyz Derivation(double t)
{
return(Base.Absolut(Arc.Derivation(t).toXYZ()) - Base.BaseO);
}
/// <summary>
/// implements the <see cref="INurbs3d.getUKnots"/> method.
/// </summary>
/// <returns></returns>
public override xyz[,] getCtrlPoints()
{
double IRSqrt = InnerRadius;// / System.Math.Sqrt(2);
xyz[,] CP = new xyz[, ]
{
{
new xyz(OuterRadius + InnerRadius, 0, 0),
new xyz(OuterRadius + InnerRadius, 0, InnerRadius),
new xyz(OuterRadius, 0, InnerRadius),
new xyz(OuterRadius - InnerRadius, 0, InnerRadius),
new xyz(OuterRadius - InnerRadius, 0, 0),
new xyz(OuterRadius - InnerRadius, 0, -InnerRadius),
new xyz(OuterRadius, 0, -InnerRadius),
new xyz(OuterRadius + InnerRadius, 0, -InnerRadius),
new xyz(OuterRadius + InnerRadius, 0, 0),
},
{
new xyz(OuterRadius + InnerRadius, OuterRadius + InnerRadius, 0),
new xyz(OuterRadius + InnerRadius, OuterRadius + InnerRadius, InnerRadius),
new xyz(OuterRadius, OuterRadius, InnerRadius),
new xyz(OuterRadius - InnerRadius, OuterRadius - InnerRadius, InnerRadius),
new xyz(OuterRadius - InnerRadius, OuterRadius - InnerRadius, 0),
new xyz(OuterRadius - InnerRadius, OuterRadius - InnerRadius, -InnerRadius),
new xyz(OuterRadius, OuterRadius, -InnerRadius),
new xyz(OuterRadius + InnerRadius, OuterRadius + InnerRadius, -InnerRadius),
new xyz(OuterRadius + InnerRadius, OuterRadius + InnerRadius, 0),
},
{
new xyz(0, OuterRadius + InnerRadius, 0),
new xyz(0, OuterRadius + InnerRadius, InnerRadius),
new xyz(0, OuterRadius, InnerRadius),
new xyz(0, OuterRadius - InnerRadius, InnerRadius),
new xyz(0, OuterRadius - InnerRadius, 0),
new xyz(0, OuterRadius - InnerRadius, -InnerRadius),
new xyz(0, OuterRadius, -InnerRadius),
new xyz(0, OuterRadius + InnerRadius, -InnerRadius),
new xyz(0, OuterRadius + InnerRadius, 0),
},
{
new xyz(-(OuterRadius + InnerRadius), OuterRadius + InnerRadius, 0),
new xyz(-(OuterRadius + InnerRadius), OuterRadius + InnerRadius, InnerRadius),
new xyz(-OuterRadius, OuterRadius, InnerRadius),
new xyz(-(OuterRadius - InnerRadius), OuterRadius - InnerRadius, InnerRadius),
new xyz(-(OuterRadius - InnerRadius), OuterRadius - InnerRadius, 0),
new xyz(-(OuterRadius - InnerRadius), OuterRadius - InnerRadius, -InnerRadius),
new xyz(-OuterRadius, OuterRadius, -InnerRadius),
new xyz(-(OuterRadius + InnerRadius), OuterRadius + InnerRadius, -InnerRadius),
new xyz(-(OuterRadius + InnerRadius), OuterRadius + InnerRadius, 0),
},
{
new xyz(-(OuterRadius + InnerRadius), 0, 0),
new xyz(-(OuterRadius + InnerRadius), 0, InnerRadius),
new xyz(-OuterRadius, 0, InnerRadius),
new xyz(-(OuterRadius - InnerRadius), 0, InnerRadius),
new xyz(-(OuterRadius - InnerRadius), 0, 0),
new xyz(-(OuterRadius - InnerRadius), 0, -InnerRadius),
new xyz(-OuterRadius, 0, -InnerRadius),
new xyz(-(OuterRadius + InnerRadius), 0, -InnerRadius),
new xyz(-(OuterRadius + InnerRadius), 0, 0),
},
{
new xyz(-(OuterRadius + InnerRadius), -(OuterRadius + InnerRadius), 0),
new xyz(-(OuterRadius + InnerRadius), -(OuterRadius + InnerRadius), InnerRadius),
new xyz(-OuterRadius, -(OuterRadius), InnerRadius),
new xyz(-(OuterRadius - InnerRadius), -(OuterRadius - InnerRadius), InnerRadius),
new xyz(-(OuterRadius - InnerRadius), -(OuterRadius - InnerRadius), 0),
new xyz(-(OuterRadius - InnerRadius), -(OuterRadius - InnerRadius), -InnerRadius),
new xyz(-OuterRadius, -OuterRadius, -InnerRadius),
new xyz(-(OuterRadius + InnerRadius), -(OuterRadius + InnerRadius), -InnerRadius),
new xyz(-(OuterRadius + InnerRadius), -(OuterRadius + InnerRadius), 0),
},
{
new xyz(0, -(OuterRadius + InnerRadius), 0),
new xyz(0, -(OuterRadius + InnerRadius), InnerRadius),
new xyz(0, -OuterRadius, InnerRadius),
new xyz(0, -(OuterRadius - InnerRadius), InnerRadius),
new xyz(0, -(OuterRadius - InnerRadius), 0), new xyz(0, -(OuterRadius - InnerRadius), -InnerRadius),
new xyz(0, -OuterRadius, -InnerRadius),
new xyz(0, -(OuterRadius + InnerRadius), -InnerRadius),
new xyz(0, -(OuterRadius + InnerRadius), 0),
},
{
new xyz(OuterRadius + InnerRadius, -(OuterRadius + InnerRadius), 0),
new xyz(OuterRadius + InnerRadius, -(OuterRadius + InnerRadius), InnerRadius),
new xyz(OuterRadius, -OuterRadius, InnerRadius),
new xyz(OuterRadius - InnerRadius, -(OuterRadius - InnerRadius), InnerRadius),
new xyz(OuterRadius - InnerRadius, -(OuterRadius - InnerRadius), 0),
new xyz(OuterRadius - InnerRadius, -(OuterRadius - InnerRadius), -InnerRadius),
new xyz(OuterRadius, -OuterRadius, -InnerRadius),
new xyz(OuterRadius + InnerRadius, -(OuterRadius + InnerRadius), -InnerRadius),
new xyz(OuterRadius + InnerRadius, -(OuterRadius + InnerRadius), 0),
},
{
new xyz(OuterRadius + InnerRadius, 0, 0),
new xyz(OuterRadius + InnerRadius, 0, InnerRadius),
new xyz(OuterRadius, 0, InnerRadius),
new xyz(OuterRadius - InnerRadius, 0, InnerRadius),
new xyz(OuterRadius - InnerRadius, 0, 0),
new xyz(OuterRadius - InnerRadius, 0, -InnerRadius),
new xyz(OuterRadius, 0, -InnerRadius),
new xyz(OuterRadius + InnerRadius, 0, -InnerRadius),
new xyz(OuterRadius + InnerRadius, 0, 0),
},
};
for (int i = 0; i < CP.GetLength(0); i++)
{
for (int j = 0; j < CP.GetLength(1); j++)
{
CP[i, j] = Base.Absolut(CP[i, j]);
}
}
return(CP);
}
/// <summary>
/// Overrides the vDerivation function and implements the cone calulations.
/// </summary>
/// <param name="u">Specifies the u parameter int [0,1]</param>
/// <param name="v">Specifies the v parameter int [0,1]</param>
/// <returns>returns a xyz Point</returns>
public override xyz vDerivation(double u, double v)
{
return(Base.Absolut(new xyz(0, 0, 1)) - Base.BaseO);
}
/// <summary>
/// Calculates the partial uDerivation
/// </summary>
/// <param name="u">first parameter</param>
/// <param name="v">second parameter</param>
/// <returns>value of the partial uDerivation</returns>
public override xyz uDerivation(double u, double v)
{
return(Base.Absolut(Curve.Derivation(u).toXYZ()));
}
//ControlPoints.length = Knots.Length - Order;
//ControlPoint.Lenght = Knonot.Length- Order - 1
/// <summary>
/// Calculates the values for a nurbs, at the parameters u and v.
/// </summary>
/// <param name="u">Specifies the u parameter.</param>
/// <param name="v">Specifies the v parameter.</param>
/// <returns>Value of a nurbs at u,v.</returns>
public override xyz Value(double u, double v)
{
try
{
xyz Result = new xyz(0, 0, 0);
if ((UKnots == null) || (VKnots == null))
{
return(Result);
}
double[] UCoeff = Utils.CoeffSpline(UKnots, ControlPoints.GetLength(0), UDegree, UPeriodicity, u);
double[] VCoeff = Utils.CoeffSpline(VKnots, ControlPoints.GetLength(1), VDegree, VPeriodicity, v);
int UCount = ControlPoints.GetLength(0);
int VCount = ControlPoints.GetLength(1);
{
double W1 = 0;
{
int VCoeffIndex = 0;
int uCoeffIndex = 0;
for (int i = 0; i < UCount; i++)
{
VCoeffIndex = 0;
for (int j = 0; j < VCount; j++)
{
W1 = W1 + Weights[i, j] * UCoeff[uCoeffIndex] * VCoeff[VCoeffIndex];// *VCoeffDerived[j].Value;
VCoeffIndex++;
}
uCoeffIndex++;
}
}
int uCoeffI = 0;
int VCoeffI = 0;
for (int i = 0; i < UCount; i++)
{
VCoeffI = 0;
for (int k = 0; k < VCount; k++)
{
Result = Result + ControlPoints[i, k] * (UCoeff[uCoeffI] * VCoeff[VCoeffI]
* Weights[i, k] / W1);
VCoeffI++;
}
uCoeffI++;
}
}
return(Base.Absolut(Result));
}
catch (Exception)
{
if ((ControlPoints.GetLength(0) + UDegree + 1) != UKnots.Length)
{
System.Windows.Forms.MessageBox.Show("the definition of the UKnots is wrong. It must be UKnots.Length=ControlPoints.GetLength(0) + UDegree + 1");
}
else
if ((ControlPoints.GetLength(1) + VDegree + 1) != VKnots.Length)
{
System.Windows.Forms.MessageBox.Show("the definition of the VKnots is wrong. It must be VKnots.Length=ControlPoints.GetLength(1) + VDegree + 1");
}
return(Base.BaseO);
}
}
/// <summary>
/// Calculates the partial v derivation of the <see cref="BSplineSurface"/>.
/// </summary>
/// <param name="u">Parameter u.</param>
/// <param name="v">Parameter v.</param>
/// <returns>The partial v derivation.</returns>
public override xyz vDerivation(double u, double v)
{
try
{
xyz Result = new xyz(0, 0, 0);
double[] UCoeff = Utils.CoeffSpline(UKnots, ControlPoints.GetLength(0), UDegree, UPeriodicity, v);
double[] VCoeff = Utils.CoeffSpline(VKnots, ControlPoints.GetLength(1), VDegree, VPeriodicity, u);
Utils.SplineExValue[] VCoeffDerived = Utils.CoeffSplineEx(VKnots, ControlPoints.GetLength(1), VDegree, VPeriodicity, u);
int FirstUCoeffNonZero = 0;
for (int i = 0; i < UCoeff.Length; i++)
{
if (UCoeff[i] != 0)
{
FirstUCoeffNonZero = i;
break;
}
}
int FirstVCoeffNonZero = 0;
for (int i = 0; i < VCoeffDerived.Length; i++)
{
if (VCoeffDerived[i].Value != 0)
{
FirstVCoeffNonZero = i;
break;
}
}
int UntilU = Math.Min(FirstUCoeffNonZero + UDegree, UCoeff.Length - 1);
int UntilV = Math.Min(FirstVCoeffNonZero + VDegree, VCoeffDerived.Length - 1);
// Derivation without Weigths
for (int i = FirstUCoeffNonZero; i <= UntilU; i++)
{
for (int k = FirstVCoeffNonZero; k <= UntilV; k++)
{
Result = Result + ControlPoints[i, k] * (VCoeffDerived[k].Derivation * UCoeff[i]);
}
}
// Derivation width Weigth
// noch machen
return(Base.Absolut(Result) - Base.BaseO);
}
catch (Exception)
{
if ((ControlPoints.GetLength(0) + UDegree + 1) != UKnots.Length)
{
System.Windows.Forms.MessageBox.Show("the definition of the UKnots is wrong.");
}
else
if ((ControlPoints.GetLength(1) + VDegree + 1) != VKnots.Length)
{
System.Windows.Forms.MessageBox.Show("the definition of the VKnots is wrong.");
}
System.Windows.Forms.Application.Exit();
return(new xyz(0, 0, 0));
}
}
/// <summary>
/// Calculates the value of the <see cref="BSplineSurface"/>.
/// </summary>
/// <param name="u">Parameter u.</param>
/// <param name="v">Parameter v.</param>
/// <returns>The Evaluation of the bspline.</returns>
public override xyz Value(double u, double v)
{
try
{
if (UKnots == null)
{
UKnots = Utils.StandardKnots(ControlPoints.GetLength(0), UDegree);
}
if (VKnots == null)
{
VKnots = Utils.StandardKnots(ControlPoints.GetLength(1), VDegree);
}
Rectangled R = DefinitionDomain;
xyz Result = new xyz(0, 0, 0);
int UCount = ControlPoints.GetLength(0);
int VCount = ControlPoints.GetLength(1);
double[] UCoeff = Utils.CoeffSpline(UKnots, UCount, UDegree, UPeriodicity, v);
double[] VCoeff = Utils.CoeffSpline(VKnots, VCount, VDegree, VPeriodicity, u);
int FirstUCoeffNonZero = 0;
for (int i = 0; i < UCoeff.Length; i++)
{
if (UCoeff[i] != 0)
{
FirstUCoeffNonZero = i;
break;
}
}
int FirstVCoeffNonZero = 0;
for (int i = 0; i < VCoeff.Length; i++)
{
if (VCoeff[i] != 0)
{
FirstVCoeffNonZero = i;
break;
}
}
int UntilU = Math.Min(FirstUCoeffNonZero + UDegree, UCoeff.Length - 1);
int UntilV = Math.Min(FirstVCoeffNonZero + VDegree, VCoeff.Length - 1);
for (int i = 0; i < UCoeff.Length; i++)
{
for (int k = 0; k < VCoeff.Length; k++)
{
Result = Result + ControlPoints[i, k] * (UCoeff[i] * VCoeff[k]);
}
}
if (ZHeight(u, v) != 0)
{
return(Base.Absolut(Result + Normal(u, v) * ZHeight(u, v)));
}
else
{
return(Base.Absolut(Result));
}
}
catch (Exception)
{
if ((ControlPoints.GetLength(0) + UDegree + 1) != UKnots.Length)
{
System.Windows.Forms.MessageBox.Show("the definition of the UKnots is wrong. . It must be UKnots.Length=ControlPoints.GetLength(0) + UDegree + 1");
}
else
if ((ControlPoints.GetLength(1) + VDegree + 1) != VKnots.Length)
{
System.Windows.Forms.MessageBox.Show("the definition of the VKnots is wrong. It must be VKnots.Length=ControlPoints.GetLength(1) + VDegree + 1");
}
return(new xyz(0, 0, 0));
}
}
/// <summary>
/// Overrides the<see cref="Surface.Value(double, double)"/> method.
/// </summary>
/// <param name="u">Specifies the u parameter int [0,1]</param>
/// <param name="v">Specifies the v parameter int [0,1]</param>
/// <returns>returns a xyz Point</returns>
public override xyz Value(double u, double v)
{
return(Base.Absolut(new xyz(u * UFactor, v * VFactor, ZHeight(u, v))));
}
/// <summary>
/// Overrides the value function and implement the circle function. For a full Circle you have to take the parameter from 0 to 1.
/// 1 is equivalent to 2*PI.
/// </summary>
/// <param name="t">a Parameter</param>
/// <returns></returns>
public override xyz Value(double t)
{
return(Base.Absolut(Arc.Value(t).toXYZ()));
}