/// <summary>
/// The offset interpolate.
/// </summary>
/// <param name="Value1">The Value1.</param>
/// <param name="Value2">The Value2.</param>
/// <param name="Offset">The Offset.</param>
/// <param name="Weight">The Weight.</param>
/// <returns>The <see cref="Point2D"/>.</returns>
public static Point2D OffsetInterpolate(Point2D Value1, Point2D Value2, double Offset, double Weight)
{
var UnitVectorAB = new Vector2D(Value1, Value2);
var PerpendicularAB = new Vector2D(PerpendicularClockwiseVectorTests.PerpendicularClockwise(UnitVectorAB.I, UnitVectorAB.J)) * 0.5d * Offset;
return(new Point2D(InterpolateLinear2DTests.LinearInterpolate2D(Weight, Value1.X, Value1.Y, Value2.X, Value2.Y)) * (Size2D)PerpendicularAB);
}
/// <summary>
/// Calculate the geometry of points offset at a specified distance. aka Double Line.
/// </summary>
/// <param name="pointA">First reference point.</param>
/// <param name="pointB">First inclusive point.</param>
/// <param name="pointC">Second inclusive point.</param>
/// <param name="pointD">Second reference point.</param>
/// <param name="offsetDistance">Offset Distance</param>
/// <returns></returns>
/// <acknowledgment>
/// Suppose you have 4 points; A, B C, and D. With Lines AB, BC, and CD.<BR/>
///<BR/>
/// B1 BC1 C1<BR/>
/// |\¯B¯¯¯¯¯BC¯¯¯C¯¯¯/|<BR/>
/// | \--------------/ |<BR/>
/// | |\____________/| |<BR/>
/// | | |B2 BC2 C2| | |<BR/>
/// AB| | | | | |CD<BR/>
/// AB1| | |AB2 CD2| | |CD1<BR/>
/// | | | | | |<BR/>
/// | | | | | |<BR/>
/// A1 A A2 D2 D D1<BR/>
///
/// </acknowledgment>
public static Point2D[] CenteredOffsetLinePoints(Point2D pointA, Point2D pointB, Point2D pointC, Point2D pointD, double offsetDistance)
{
// To get the vectors of the angles at each corner B and C, Normalize the Unit Delta Vectors along AB, BC, and CD.
var UnitVectorAB = pointB - pointA;
UnitVectorAB = new Vector2D(Normalize2DVectorTests.Normalize(UnitVectorAB.I, UnitVectorAB.J));
var UnitVectorBC = pointC - pointB;
UnitVectorBC = new Vector2D(Normalize2DVectorTests.Normalize(UnitVectorBC.I, UnitVectorBC.J));
var UnitVectorCD = pointD - pointC;
UnitVectorCD = new Vector2D(Normalize2DVectorTests.Normalize(UnitVectorCD.I, UnitVectorCD.J));
// Find the Perpendicular of the outside vectors
var PerpendicularAB = new Vector2D(PerpendicularClockwiseVectorTests.PerpendicularClockwise(UnitVectorAB.I, UnitVectorAB.J));
var PerpendicularCD = new Vector2D(PerpendicularClockwiseVectorTests.PerpendicularClockwise(UnitVectorCD.I, UnitVectorCD.J));
// Normalized Vectors pointing out from B and C.
var OutUnitVectorB = UnitVectorAB - UnitVectorBC;
OutUnitVectorB = new Vector2D(Normalize2DVectorTests.Normalize(OutUnitVectorB.I, OutUnitVectorB.J));
var OutUnitVectorC = UnitVectorCD - UnitVectorBC;
OutUnitVectorC = new Vector2D(Normalize2DVectorTests.Normalize(OutUnitVectorC.I, OutUnitVectorC.J));
// The distance out from B is the radius / Cos(theta) where theta is the angle
// from the perpendicular of BC of the UnitVector. The cosine can also be
// calculated by doing the dot product of Unit(Perpendicular(AB)) and
// UnitVector.
var BPointScale = DotProduct2Vector2DTests.DotProduct2D(PerpendicularAB.I, PerpendicularAB.J, OutUnitVectorB.I, OutUnitVectorB.J) * offsetDistance;
var CPointScale = DotProduct2Vector2DTests.DotProduct2D(PerpendicularCD.I, PerpendicularCD.J, OutUnitVectorC.I, OutUnitVectorC.J) * offsetDistance;
OutUnitVectorB *= CPointScale;
OutUnitVectorC *= BPointScale;
// Corners of the parallelogram to draw
var Out = new Point2D[] {
pointC + OutUnitVectorC,
pointB + OutUnitVectorB,
pointB - OutUnitVectorB,
pointC - OutUnitVectorC,
pointC + OutUnitVectorC
};
return(Out);
}