/// <summary>
/// Moves, scales, and/or rotates the current entity given a 3x3 transformation matrix and a translation vector.
/// </summary>
/// <param name="transformation">Transformation matrix.</param>
/// <param name="translation">Translation vector.</param>
/// <remarks>Matrix3 adopts the convention of using column vectors to represent a transformation matrix.</remarks>
public override void TransformBy(Matrix3 transformation, Vector3 translation)
{
// NOTE: this is a generic implementation of the ellipse transformation,
// for non rotated ellipses and/or uniform scaling the code can be simplified
// rectangle that circumscribe the ellipse
double semiMajorAxis = this.MajorAxis * 0.5;
double semiMinorAxis = this.MinorAxis * 0.5;
Vector2 p1 = new Vector2(-semiMajorAxis, semiMinorAxis);
Vector2 p2 = new Vector2(semiMajorAxis, semiMinorAxis);
Vector2 p3 = new Vector2(-semiMajorAxis, -semiMinorAxis);
Vector2 p4 = new Vector2(semiMajorAxis, -semiMinorAxis);
List <Vector2> ocsPoints = MathHelper.Transform(new[] { p1, p2, p3, p4 }, this.Rotation * MathHelper.DegToRad, CoordinateSystem.Object, CoordinateSystem.World);
Vector3 p1Prime = new Vector3(ocsPoints[0].X, ocsPoints[0].Y, 0.0);
Vector3 p2Prime = new Vector3(ocsPoints[1].X, ocsPoints[1].Y, 0.0);
Vector3 p3Prime = new Vector3(ocsPoints[2].X, ocsPoints[2].Y, 0.0);
Vector3 p4Prime = new Vector3(ocsPoints[3].X, ocsPoints[3].Y, 0.0);
List <Vector3> wcsPoints = MathHelper.Transform(new[] { p1Prime, p2Prime, p3Prime, p4Prime }, this.Normal, CoordinateSystem.Object, CoordinateSystem.World);
for (int i = 0; i < wcsPoints.Count; i++)
{
wcsPoints[i] += this.Center;
wcsPoints[i] = transformation * wcsPoints[i];
wcsPoints[i] += translation;
}
Vector3 newNormal = transformation * this.Normal;
if (Vector3.Equals(Vector3.Zero, newNormal))
{
newNormal = this.Normal;
}
List <Vector3> rectPoints = MathHelper.Transform(wcsPoints, newNormal, CoordinateSystem.World, CoordinateSystem.Object);
// corners of the transformed rectangle that circumscribe the new ellipse
Vector2 pointA = new Vector2(rectPoints[0].X, rectPoints[0].Y);
Vector2 pointB = new Vector2(rectPoints[1].X, rectPoints[1].Y);
Vector2 pointC = new Vector2(rectPoints[2].X, rectPoints[2].Y);
Vector2 pointD = new Vector2(rectPoints[3].X, rectPoints[3].Y);
// the new ellipse is tangent at the mid points
Vector2 pointM = Vector2.MidPoint(pointA, pointB);
Vector2 pointN = Vector2.MidPoint(pointC, pointD);
Vector2 pointH = Vector2.MidPoint(pointA, pointC);
Vector2 pointK = Vector2.MidPoint(pointB, pointD);
// we need to find a fifth point
Vector2 origin = Vector2.MidPoint(pointH, pointK);
Vector2 pointX = Vector2.MidPoint(pointH, origin); // a point along the OH segment
// intersection line AC and line parallel to BC through pointX
Vector2 pointY = MathHelper.FindIntersection(pointA, pointC - pointA, pointX, pointC - pointB);
if (Vector2.IsNaN(pointY))
{
Debug.Assert(false, "The transformation cannot be applied.");
return;
}
// find the fifth point in the ellipse
Vector2 pointZ = MathHelper.FindIntersection(pointM, pointX - pointM, pointN, pointY - pointN);
if (Vector2.IsNaN(pointZ))
{
Debug.Assert(false, "The transformation cannot be applied.");
return;
}
Vector3 oldNormal = this.Normal;
double oldRotation = this.Rotation * MathHelper.DegToRad;
if (ConicThroughFivePoints.EllipseProperties(pointM, pointN, pointH, pointK, pointZ, out Vector2 _, out double newSemiMajorAxis, out double newSemiMinorAxis, out double newRotation))
{
double axis1 = 2 * newSemiMajorAxis;
axis1 = MathHelper.IsZero(axis1) ? MathHelper.Epsilon : axis1;
double axis2 = 2 * newSemiMinorAxis;
axis2 = MathHelper.IsZero(axis2) ? MathHelper.Epsilon : axis2;
this.Center = transformation * this.Center + translation;
this.MajorAxis = axis1;
this.MinorAxis = axis2;
this.Rotation = newRotation * MathHelper.RadToDeg;
this.Normal = newNormal;
}
/// <summary>
/// Moves, scales, and/or rotates the current entity given a 3x3 transformation matrix and a translation vector.
/// </summary>
/// <param name="transformation">Transformation matrix.</param>
/// <param name="translation">Translation vector.</param>
/// <remarks>Matrix3 adopts the convention of using column vectors to represent a transformation matrix.</remarks>
public override void TransformBy(Matrix3 transformation, Vector3 translation)
{
// NOTE: this is a generic implementation of the ellipse transformation,
// for non rotated ellipses and/or uniform scaling the code can be simplified
// rectangle that circumscribe the ellipse
double semiMajorAxis = this.MajorAxis * 0.5;
double semiMinorAxis = this.MinorAxis * 0.5;
Vector2 p1 = new Vector2(-semiMajorAxis, semiMinorAxis);
Vector2 p2 = new Vector2(semiMajorAxis, semiMinorAxis);
Vector2 p3 = new Vector2(-semiMajorAxis, -semiMinorAxis);
Vector2 p4 = new Vector2(semiMajorAxis, -semiMinorAxis);
List <Vector2> ocsPoints = MathHelper.Transform(new[] { p1, p2, p3, p4 }, this.Rotation * MathHelper.DegToRad, CoordinateSystem.Object, CoordinateSystem.World);
Vector3 p1Prime = new Vector3(ocsPoints[0].X, ocsPoints[0].Y, 0.0);
Vector3 p2Prime = new Vector3(ocsPoints[1].X, ocsPoints[1].Y, 0.0);
Vector3 p3Prime = new Vector3(ocsPoints[2].X, ocsPoints[2].Y, 0.0);
Vector3 p4Prime = new Vector3(ocsPoints[3].X, ocsPoints[3].Y, 0.0);
List <Vector3> wcsPoints = MathHelper.Transform(new[] { p1Prime, p2Prime, p3Prime, p4Prime }, this.Normal, CoordinateSystem.Object, CoordinateSystem.World);
for (int i = 0; i < wcsPoints.Count; i++)
{
wcsPoints[i] += this.Center;
wcsPoints[i] = transformation * wcsPoints[i];
wcsPoints[i] += translation;
}
Vector3 newNormal = transformation * this.Normal;
if (Vector3.Equals(Vector3.Zero, newNormal))
{
newNormal = this.Normal;
}
List <Vector3> rectPoints = MathHelper.Transform(wcsPoints, newNormal, CoordinateSystem.World, CoordinateSystem.Object);
// corners of the transformed rectangle that circumscribe the new ellipse
Vector2 pointA = new Vector2(rectPoints[0].X, rectPoints[0].Y);
Vector2 pointB = new Vector2(rectPoints[1].X, rectPoints[1].Y);
Vector2 pointC = new Vector2(rectPoints[2].X, rectPoints[2].Y);
Vector2 pointD = new Vector2(rectPoints[3].X, rectPoints[3].Y);
// the new ellipse is tangent at the mid points
Vector2 pointM = Vector2.MidPoint(pointA, pointB);
Vector2 pointN = Vector2.MidPoint(pointC, pointD);
Vector2 pointH = Vector2.MidPoint(pointA, pointC);
Vector2 pointK = Vector2.MidPoint(pointB, pointD);
// we need to find a fifth point
Vector2 origin = Vector2.MidPoint(pointH, pointK);
Vector2 pointX = Vector2.MidPoint(pointH, origin); // a point along the OH segment
// intersection line AC and line parallel to BC through pointX
Vector2 pointY = MathHelper.FindIntersection(pointA, pointC - pointA, pointX, pointC - pointB);
if (Vector2.IsNaN(pointY))
{
Debug.Assert(false, "The transformation cannot be applied.");
return;
}
// find the fifth point in the ellipse
Vector2 pointZ = MathHelper.FindIntersection(pointM, pointX - pointM, pointN, pointY - pointN);
if (Vector2.IsNaN(pointZ))
{
Debug.Assert(false, "The transformation cannot be applied.");
return;
}
Vector3 oldNormal = this.Normal;
double oldRotation = this.Rotation;
Vector2 newCenter;
double newSemiMajorAxis;
double newSemiMinorAxis;
double newRotation;
if (ConicThroughFivePoints.EllipseProperties(pointM, pointN, pointH, pointK, pointZ, out newCenter, out newSemiMajorAxis, out newSemiMinorAxis, out newRotation))
{
double axis1 = 2 * newSemiMajorAxis;
axis1 = MathHelper.IsZero(axis1) ? MathHelper.Epsilon : axis1;
double axis2 = 2 * newSemiMinorAxis;
axis2 = MathHelper.IsZero(axis2) ? MathHelper.Epsilon : axis2;
this.Center = transformation * this.Center + translation;
this.MajorAxis = axis1;
this.MinorAxis = axis2;
this.Rotation = newRotation * MathHelper.RadToDeg;
this.Normal = newNormal;
}
else
{
Debug.Assert(false, "The transformation cannot be applied.");
return;
}
if (this.IsFullEllipse)
{
return;
}
//if not full ellipse calculate start and end angles
Vector2 start = this.PolarCoordinateRelativeToCenter(this.StartAngle);
Vector2 end = this.PolarCoordinateRelativeToCenter(this.EndAngle);
if (!MathHelper.IsZero(oldRotation))
{
double beta = oldRotation * MathHelper.DegToRad;
double sinBeta = Math.Sin(beta);
double cosBeta = Math.Cos(beta);
start = new Vector2(start.X * cosBeta - start.Y * sinBeta, start.X * sinBeta + start.Y * cosBeta);
end = new Vector2(end.X * cosBeta - end.Y * sinBeta, end.X * sinBeta + end.Y * cosBeta);
}
Vector3 pStart = new Vector3(start.X, start.Y, 0.0);
Vector3 pEnd = new Vector3(end.X, end.Y, 0.0);
List <Vector3> wcsAnglePoints = MathHelper.Transform(new[] { pStart, pEnd }, oldNormal, CoordinateSystem.Object, CoordinateSystem.World);
for (int i = 0; i < wcsAnglePoints.Count; i++)
{
wcsPoints[i] += this.Center;
wcsAnglePoints[i] = transformation * wcsAnglePoints[i];
wcsPoints[i] += translation;
}
List <Vector3> ocsAnglePoints = MathHelper.Transform(wcsAnglePoints, newNormal, CoordinateSystem.World, CoordinateSystem.Object);
Vector2 newStart = new Vector2(ocsAnglePoints[0].X, ocsAnglePoints[0].Y);
Vector2 newEnd = new Vector2(ocsAnglePoints[1].X, ocsAnglePoints[1].Y);
double invert = Math.Sign(transformation.M11 * transformation.M22 * transformation.M33) < 0 ? 180.0 : 0.0;
this.StartAngle = invert + Vector2.Angle(newStart) * MathHelper.RadToDeg - this.Rotation;
this.EndAngle = invert + Vector2.Angle(newEnd) * MathHelper.RadToDeg - this.Rotation;
}
