/// <summary>
/// Transforms a <see cref="M34d"/> to a <see cref="M33d"/> by deleting the
/// specified row and column. Internally the <see cref="M34d"/> is tarnsformed
/// to a <see cref="M44d"/> to delete the row and column.
/// </summary>
/// <param name="deleted_row">Row to delete.</param>
/// <param name="deleted_column">Column to delete.</param>
/// <returns>A <see cref="M33d"/>.</returns>
public M33d Minor(int deleted_row, int deleted_column)
{
M44d temp = (M44d)this;
M33d result = new M33d();
int checked_row = 0;
for (int actual_row = 0; actual_row < 4; actual_row++)
{
int checked_column = 0;
if (actual_row != deleted_row)
{
for (int actual_column = 0; actual_column < 4; actual_column++)
{
if (actual_column != deleted_column)
{
result[checked_row, checked_column] = temp[actual_row, actual_column];
checked_column++;
}
}
checked_row++;
}
}
return(result);
}
static M33d CreateConversionMatrix()
{
// for spectral to xyz conversion see: http://www.brucelindbloom.com/index.html?Eqn_Spect_to_XYZ.html
var specS0Vec = new Vector <double>(SpecS0_380_780_10nm);
var specS1Vec = new Vector <double>(SpecS1_380_780_10nm);
var specS2Vec = new Vector <double>(SpecS2_380_780_10nm);
var cieXVec = new Vector <double>(Ciexyz31X_380_780_10nm);
var cieYVec = new Vector <double>(Ciexyz31Y_380_780_10nm);
var cieZVec = new Vector <double>(Ciexyz31Z_380_780_10nm);
var specM = new M33d
(
cieXVec.DotProduct(specS0Vec), cieXVec.DotProduct(specS1Vec), cieXVec.DotProduct(specS2Vec),
cieYVec.DotProduct(specS0Vec), cieYVec.DotProduct(specS1Vec), cieYVec.DotProduct(specS2Vec),
cieZVec.DotProduct(specS0Vec), cieZVec.DotProduct(specS1Vec), cieZVec.DotProduct(specS2Vec)
);
var cieN = 1.0 / cieYVec.Data.Sum(); // cie response curve integral normalization
// sun spectral radiance (S0, S1, S2) is expressed in micro-meters =>
// convert to wavelengthes in nm (unit of color matching functions) -> scale by 1/1000
// the cie response functions are in 10nm steps -> scale by 10
var specN = 1.0 / 1000 * 10; // spectrum unit converions (1 micro meter to 10 nano meter)
var norm = cieN * specN; // normalization of color space conversion matrix
return(specM * norm);
}
/// <summary>
/// Calculates the inverse matrix using Householder transformations
/// </summary>
public static M33d QrInverse(this M33d mat)
{
var qr = new Matrix <double>((double[])mat, 3, 3);
var diag = qr.QrFactorize();
return((M33d)(qr.QrInverse(diag).Data));
}
public static M33d Multiply(Rot2d rot, M33d mat)
{
double a = (double)System.Math.Cos(rot.Angle);
double b = (double)System.Math.Sin(rot.Angle);
return(new M33d(a * mat.M00 +
b * mat.M10,
a * mat.M01 +
b * mat.M11,
a * mat.M02 +
b * mat.M12,
-b * mat.M00 +
a * mat.M10,
-b * mat.M01 +
a * mat.M11,
-b * mat.M02 +
a * mat.M12,
mat.M20,
mat.M21,
mat.M22));
}
public static Trafo2d Parse(string s)
{
var x = s.NestedBracketSplitLevelOne().ToArray();
return(new Trafo2d(
M33d.Parse(x[0]),
M33d.Parse(x[1])
));
}
/// <summary>
/// Returns true if the ray hits the other ray before the parameter
/// value contained in the supplied hit. Detailed information about
/// the hit is returned in the supplied hit.
/// </summary>
public bool HitsRay(
Ray3d ray,
double tmin, double tmax,
ref RayHit3d hit
)
{
V3d d = Origin - ray.Origin;
V3d u = Direction;
V3d v = ray.Direction;
V3d n = u.Cross(v);
if (Fun.IsTiny(d.Length))
{
return(true);
}
else if (Fun.IsTiny(u.Cross(v).Length))
{
return(false);
}
else
{
//-t0*u + t1*v + t2*n == d
//M = {-u,v,n}
//M*{t0,t1,t2}T == d
//{t0,t1,t2}T == M^-1 * d
M33d M = new M33d();
M.C0 = -u;
M.C1 = v;
M.C2 = n;
if (M.Invertible)
{
V3d t = M.Inverse * d;
if (Fun.IsTiny(t.Z))
{
ProcessHits(t.X, double.MaxValue, tmin, tmax, ref hit);
return(true);
}
else
{
return(false);
}
}
else
{
return(false);
}
}
}
/// <summary>
/// Multiplacation of a <see cref="Scale3d"/> with a <see cref="M33d"/>.
/// </summary>
public static M33d Multiply(Scale3d scale, M33d mat)
{
return(new M33d(scale.X * mat.M00,
scale.X * mat.M01,
scale.X * mat.M02,
scale.Y * mat.M10,
scale.Y * mat.M11,
scale.Y * mat.M12,
scale.Z * mat.M20,
scale.Z * mat.M21,
scale.Z * mat.M22));
}
public readonly V3d Translation; // cam 2 world was chosen, so that it can be easily read
// while debugging
public CameraExtrinsics(M33d cam2worldRotation, V3d cam2worldTranslation)
{
var zero = cam2worldRotation * cam2worldRotation.Transposed - M33d.Identity;
if (zero.NormMax > 1e6)
{
throw new ArgumentException("supplied matrix is not a rotation");
}
if (cam2worldRotation.Determinant < 0.0)
{
throw new ArgumentException("supplied rotation is improper (mirroring)");
}
Rotation = cam2worldRotation;
Translation = cam2worldTranslation;
}
/// <summary>
/// Transforms XYZ coord on one reference ellipsoid to XYZ coords on another
/// ref ellipsoid. The ellipsoids-difference is defined in a geometric datum
/// which is passes as the second argument.
/// </summary>
public static V3d HelmertsTransformXyzToXyz(V3d xyz, GeoDatum datum)
{
// transformation matrix
var T = new M33d(1.0, datum.rZrad, -datum.rYrad,
-datum.rZrad, 1.0, datum.rXrad,
datum.rYrad, -datum.rXrad, 1.0);
// delta in ellipsoid center positions
var dP = new V3d(datum.dX, datum.dY, datum.dZ);
// scale factor
var mu = new Scale3d(datum.dS * 0.000001 + 1.0);
var result = dP + (mu * T) * xyz;
return(result);
}
/// <summary>
/// </summary>
public static M33d operator *(Euclidean3d r3, Rot2d r2)
{
M33d m33 = (M33d)r3;
M22d m22 = (M22d)r2;
return(new M33d(
m33.M00 * m22.M00 + m33.M01 * m22.M10,
m33.M00 * m22.M01 + m33.M01 * m22.M11,
m33.M02,
m33.M10 * m22.M00 + m33.M11 * m22.M10,
m33.M10 * m22.M01 + m33.M11 * m22.M11,
m33.M12,
m33.M20 * m22.M00 + m33.M21 * m22.M10,
m33.M20 * m22.M01 + m33.M21 * m22.M11,
m33.M22
));
}
/// <summary>
/// Updates position until stopDragging completes.
/// </summary>
public static async Task <IBehavior> DragRelative(this IBehavior self,
V2d initialPosition, IEvent <V2d> moves, IAwaitable stopDragging, CancellationToken ct
)
{
var obj = self as IBehaviorTransform2d;
if (obj == null)
{
throw new InvalidOperationException("DragRelative requires IBehaviorTransform2d.");
}
var lastPos = initialPosition;
await stopDragging.RepeatUntilCompleted(
async delegate
{
var p = await moves.Next.WithCancellation(ct);
obj.Transform(M33d.Translation(p - lastPos));
lastPos = p;
});
return(self);
}
/// <summary>
/// A <see cref="M44d"/> is transformed to <see cref="M33d"/> by deleting specified row and column
/// </summary>
public M33d Minor(int rowToDelete, int columnToDelete)
{
M33d result = new M33d();
int checked_row = 0;
for (int actual_row = 0; actual_row < 4; actual_row++)
{
int checked_column = 0;
if (actual_row != rowToDelete)
{
for (int actual_column = 0; actual_column < 4; actual_column++)
{
if (actual_column != columnToDelete)
{
result[checked_row, checked_column] = this[actual_row, actual_column];
checked_column++;
}
}
checked_row++;
}
}
return(result);
}
public static M34d Multiply(M33d m, Euclidean3d r)
{
return(M34d.Multiply(m, (M34d)r));
}
public static M33d NormalizedImagePosToPixelEdgeMat(V2d imgSizeInPixel)
{
return(M33d.Scale(imgSizeInPixel - 1));
}
/// <summary>
/// Returns a Matrix to
/// convert from pixel-center position to normalized image position [0,1][0,1].
/// (The inverse of toPixelCenter.)
/// </summary>
public static M33d PixelCenterToNormalizedImgMat(V2d imgSizeInPixel)
{
return(M33d.Scale(V2d.II / imgSizeInPixel) * M33d.Translation(V2dHalf));
}
/// <summary>
/// Returns a Matrix to
/// convert from normalized image position [0,1][0,1] to pixel-center position
/// (The inverse of toNormalizedImgPos.)
/// </summary>
public static M33d NormalizedImagePosToPixelCenterMat(V2d imgSizeInPixel)
{
return(M33d.Translation(-V2dHalf) * M33d.Scale(imgSizeInPixel));
}
public static M33d PixelEdgeToNormalizedImgMat(V2d imgSizeInPixel)
{
return(M33d.Scale(V2d.II / (imgSizeInPixel - 1)));
}
public static V3d[] Transformed(this V3d[] points, M33d matrix)
{
return(points.Map(p => matrix.Transform(p)));
}
/// <summary>
/// Returns new array containing transformed points.
/// </summary>
public static V2d[] TransformedDir(this V2d[] pointArray, M33d m)
{
return(new V2d[pointArray.LongLength].SetByIndexLong(i => m.TransformDir(pointArray[i])));
}
public Trafo2d(Trafo2d trafo)
{
Forward = trafo.Forward;
Backward = trafo.Backward;
}
public static CameraExtrinsics FromWorld2Camera(M33d rotation, V3d translation) => new CameraExtrinsics(rotation.Transposed, -rotation.TransposedTransform(translation));
/// <summary> /// Returns new polygon with point transformed. /// </summary> public static IImmutablePolygon <V2d> TransformPoint(this IImmutablePolygon <V2d> self, int index, M33d trafo) => self.SetPoint(index, trafo.TransformPos(self.Points[index]));
/// <summary>
/// Creates a rigid transformation from a rotation matrix <paramref name="rot"/> and a (subsequent) translation <paramref name="trans"/>.
/// </summary>
public Euclidean3d(M33d rot, V3d trans, double epsilon = 1e-12)
{
Rot = Rot3d.FromM33d(rot, epsilon);
Trans = trans;
}
public static Trafo2d Scale(double s)
{
return(new Trafo2d(M33d.Scale(s),
M33d.Scale(1 / s)));
}
public static Trafo2d Rotation(double angleInRadians)
{
return(new Trafo2d(M33d.Rotation(angleInRadians),
M33d.Rotation(-angleInRadians)));
}
public static Trafo2d Scale(V2d sv)
{
return(new Trafo2d(M33d.Scale(sv),
M33d.Scale(1 / sv)));
}
public static Trafo2d Translation(double dx, double dy)
{
return(new Trafo2d(M33d.Translation(dx, dy),
M33d.Translation(-dx, -dy)));
}
public static Trafo2d Translation(V2d v)
{
return(new Trafo2d(M33d.Translation(v),
M33d.Translation(-v)));
}
public static Trafo2d Scale(double sx, double sy)
{
return(new Trafo2d(M33d.Scale(sx, sy),
M33d.Scale(1 / sx, 1 / sy)));
}
public Trafo2d(M33d forward, M33d backward)
{
Forward = forward;
Backward = backward;
}