/// <summary>
/// Gets the 2D coordinates as seen from a calculated plane.
/// </summary>
/// <param name="cc">3D coordinates to convert.</param>
/// <returns>The converted 2D coordinates.</returns>
private Cartesian2dCoordinate GetFromProjection(Cartesian3dCoordinate cc)
{
// Project the coordinates on the reference
ParametricLine projectionLine = this.Plane.GetPerpendicular(cc);
Cartesian3dCoordinate planeCoordinate = this.Plane.GetIntersection(projectionLine);
Cartesian3dCoordinate ccOnX = planeCoordinate.TransposeFromReferential(this.Plane.Normal);
return(GetFromFront(ccOnX));
}
/// <summary>
/// Gets the intersection point coordinate between the current plane and the speicifed line.
/// </summary>
/// <param name="l">Line that should cross the plane at the seeked intersection point.</param>
/// <returns>The cartesian coordinates of the intersection point between the line and the Plane.</returns>
/// <remarks>
/// Formula :
///
/// A(x1 + at) + B(y1 + bt) + C(z1 + ct) + D = 0
///
/// Then giving t :
///
/// -(Ax1 + By1 + Cz1 + D)
/// t = ------------------------
/// Aa + Bb + Cc
///
/// Coordinates are then :
///
/// a(Ax1 + By1 + Cz1 + D) b(Ax1 + By1 + Cz1 + D) c(Ax1 + By1 + Cz1 + D)
/// x = x1 - ------------------------ y = y1 - ------------------------ z = z1 - ------------------------
/// Aa + Bb + Cc Aa + Bb + Cc Aa + Bb + Cc
///
/// </remarks>
public Cartesian3dCoordinate GetIntersection(ParametricLine l)
{
if (l.IsParallelTo(this))
{
throw new InvalidOperationException("Cannot Get Intersection between a Plane and a parallel line.");
}
double divisor = GetSumOfAbcProduct(l);
double planePart = ((this.A * l.X) + (this.B * l.Y) + (this.C * l.Z) + this.D) / divisor;
return(new Cartesian3dCoordinate(
l.X - (l.A * planePart),
l.Y - (l.B * planePart),
l.Z - (l.C * planePart)
));
}
/// <summary> /// Gets the sum of products of the A, B and C factor of the plane and parametric line formula. /// </summary> /// <param name="l">Parametric line with which we calculate the product.</param> /// <returns>Result of the sum of the product of the A, B and C factor of the plane and parametric line formula.</returns> private double GetSumOfAbcProduct(ParametricLine l) => (this.A * l.A) + (this.B * l.B) + (this.C * l.C);
