/// <summary>
/// Creates an AffineTransformation defined by a pair of control vectors. A
/// control vector consists of a source point and a destination point, which is
/// the image of the source point under the desired transformation. The
/// computed transformation is a combination of one or more of a uniform scale,
/// a rotation, and a translation (i.e. there is no shear component and no
/// reflection)
/// </summary>
/// <param name="src0"></param>
/// <param name="src1"></param>
/// <param name="dest0"></param>
/// <param name="dest1"></param>
/// <returns>The computed transformation</returns>
/// <returns><c>null</c> if the control vectors do not determine a well-defined transformation</returns>
public static AffineTransformation CreateFromControlVectors(Coordinate src0,
Coordinate src1, Coordinate dest0, Coordinate dest1)
{
var rotPt = new Coordinate(dest1.X - dest0.X, dest1.Y - dest0.Y);
double ang = AngleUtility.AngleBetweenOriented(src1, src0, rotPt);
double srcDist = src1.Distance(src0);
double destDist = dest1.Distance(dest0);
if (srcDist == 0.0)
{
return(null);
}
double scale = destDist / srcDist;
var trans = AffineTransformation.TranslationInstance(
-src0.X, -src0.Y);
trans.Rotate(ang);
trans.Scale(scale, scale);
trans.Translate(dest0.X, dest0.Y);
return(trans);
}
/// <summary>
/// Creates an AffineTransformation defined by a mapping between two baselines.
/// The computed transformation consists of:
/// <list type="bullet">
/// <item><description>a translation from the start point of the source baseline to the start point of the destination baseline,</description></item>
/// <item><description>a rotation through the angle between the baselines about the destination start point,</description></item>
/// <item><description>and a scaling equal to the ratio of the baseline lengths.</description></item>
/// </list>
/// If the source baseline has zero length, an identity transformation is returned.
/// </summary>
/// <param name="src0">The start point of the source baseline</param>
/// <param name="src1">The end point of the source baseline</param>
/// <param name="dest0">The start point of the destination baseline</param>
/// <param name="dest1">The end point of the destination baseline</param>
/// <returns></returns>
public static AffineTransformation CreateFromBaseLines(
Coordinate src0, Coordinate src1,
Coordinate dest0, Coordinate dest1)
{
var rotPt = new Coordinate(src0.X + dest1.X - dest0.X, src0.Y + dest1.Y - dest0.Y);
double ang = AngleUtility.AngleBetweenOriented(src1, src0, rotPt);
double srcDist = src1.Distance(src0);
double destDist = dest1.Distance(dest0);
// return identity if transformation would be degenerate
if (srcDist == 0.0)
{
return(new AffineTransformation());
}
double scale = destDist / srcDist;
var trans = AffineTransformation.TranslationInstance(
-src0.X, -src0.Y);
trans.Rotate(ang);
trans.Scale(scale, scale);
trans.Translate(dest0.X, dest0.Y);
return(trans);
}
/// <summary>
/// Creates an AffineTransformation defined by a single control vector. A
/// control vector consists of a source point and a destination point, which is
/// the image of the source point under the desired transformation. This
/// produces a translation.
/// </summary>
/// <param name="src0">The start point of the control vector</param>
/// <param name="dest0">The end point of the control vector</param>
/// <returns>The computed transformation</returns>
public static AffineTransformation CreateFromControlVectors(Coordinate src0,
Coordinate dest0)
{
double dx = dest0.X - src0.X;
double dy = dest0.Y - src0.Y;
return(AffineTransformation.TranslationInstance(dx, dy));
}
