public void Rotate(Chessboard3DReprezentation boardRepresentation, CameraSpacePoint[] csp)
{
var firstVector = boardRepresentation.FieldVector1;
var secondVector = boardRepresentation.FieldVector2;
var cornerPoint = boardRepresentation.CornerOfChessboard;
firstVector = MyVector3DStruct.Normalize(firstVector);
secondVector = MyVector3DStruct.Normalize(secondVector);
var a = MyVector3DStruct.CrossProduct(ref firstVector, ref secondVector);
var b = MyVector3DStruct.CrossProduct(ref secondVector, ref firstVector);
var xVec = new MyVector3DStruct();
var yVec = new MyVector3DStruct();
var zVec = new MyVector3DStruct();
// get new base based on two known vectors and their cross product
if ((a.z > 0 && b.z < 0)) // originally (a.z > 0 && b.z < 0)
{
zVec = a; // a
yVec = MyVector3DStruct.Normalize(MyVector3DStruct.CrossProduct(ref xVec, ref zVec));
}
else if ((a.z < 0 && b.z > 0)) // originally (a.z < 0 && b.z > 0)
{
zVec = b; // b
yVec = MyVector3DStruct.Normalize(MyVector3DStruct.CrossProduct(ref xVec, ref zVec));
}
else
{
throw new InvalidOperationException();
}
// normalize base
xVec = MyVector3DStruct.Normalize(firstVector);
yVec = MyVector3DStruct.Normalize(secondVector);
zVec = MyVector3DStruct.Normalize(zVec);
// get inverse mapping to base
double[,] matrix =
{
{ xVec.x, yVec.x, zVec.x },
{ xVec.y, yVec.y, zVec.y },
{ xVec.z, yVec.z, zVec.z }
};
var inverseMatrix = matrix.Inverse();
// move all points
for (int i = 0; i < csp.Length; i++)
{
// translation to corner point
var nx = (float)(csp[i].X - cornerPoint.x);
var ny = (float)(csp[i].Y - cornerPoint.y);
var nz = (float)(csp[i].Z - cornerPoint.z);
// rotation around it to given base
csp[i].X = (float)(inverseMatrix[0, 0] * nx + inverseMatrix[0, 1] * ny + inverseMatrix[0, 2] * nz);
csp[i].Y = (float)(inverseMatrix[1, 0] * nx + inverseMatrix[1, 1] * ny + inverseMatrix[1, 2] * nz);
csp[i].Z = (float)(inverseMatrix[2, 0] * nx + inverseMatrix[2, 1] * ny + inverseMatrix[2, 2] * nz);
}
}
/// <summary>
/// Finds most suitable chessboard fitting real points
/// </summary>
public static Chessboard3DReprezentation ChessboardFittingAlgorithm(List <Point2D> contractedPoints, ChessboardTrackingCompleteData chessboardData)
{
const int takeXNearestNeighbors = 7;
var contractedPoints3D = ConvertIntersectionsTo3D(contractedPoints, chessboardData);
var contractedPoints3DasStruct = contractedPoints3D.Select(x => new MyVector3DStruct(x.X, x.Y, x.Z)).ToArray();
double lowestError = double.MaxValue;
Chessboard3DReprezentation boardRepresentation = null;
Parallel.ForEach(contractedPoints3DasStruct, csp =>
{
// take _ nearest neighbors
var neighbors = contractedPoints3DasStruct.OrderBy((MyVector3DStruct x) => MyVector3DStruct.Distance(ref x, ref csp)).Take(takeXNearestNeighbors).ToArray();
// take all pairs of neighbors
for (int i = 0; i < neighbors.Length; i++)
{
for (int j = i + 1; j < neighbors.Length; j++)
{
var first = neighbors[i];
var second = neighbors[j];
var firstPoint = new MyVector3DStruct(first.x, first.y, first.z);
var secondPoint = new MyVector3DStruct(second.x, second.y, second.z);
// st. point + 2 vectors
var initialPoint = new MyVector3DStruct(csp.x, csp.y, csp.z);
var firstVector = MyVector3DStruct.Difference(ref firstPoint, ref initialPoint);
var secondVector = MyVector3DStruct.Difference(ref secondPoint, ref initialPoint);
// perpendicularity check
double angleBetweenVectors = MyVector3DStruct.AngleInDeg(ref firstVector, ref secondVector);
if (!(angleBetweenVectors < 91.4 && angleBetweenVectors > 88.6))
{
break;
}
// length check
double ratio = firstVector.Magnitude() / secondVector.Magnitude();
if (!(ratio > 0.85f && ratio < 1.15f))
{
break;
}
// ensure right mutual position of first and second vector - otherwise switch them
if (MyVector3DStruct.CrossProduct(ref firstVector, ref secondVector).z < 0)
{
var temp = firstVector;
firstVector = secondVector;
secondVector = temp;
}
// length normalization of vectors
double averageLength = (firstVector.Magnitude() + secondVector.Magnitude()) / 2;
firstVector = MyVector3DStruct.MultiplyByNumber(MyVector3DStruct.Normalize(ref firstVector), averageLength);
secondVector = MyVector3DStruct.MultiplyByNumber(MyVector3DStruct.Normalize(ref secondVector), averageLength);
var negatedFirstVector = MyVector3DStruct.Negate(ref firstVector);
var negatedSecondVector = MyVector3DStruct.Negate(ref secondVector);
// locate all possible starting points
for (int f = 0; f < 9; f++)
{
for (int s = 0; s < 9; s++)
{
var startingPoint =
MyVector3DStruct.Addition(
MyVector3DStruct.Addition(
MyVector3DStruct.MultiplyByNumber(negatedFirstVector, f),
MyVector3DStruct.MultiplyByNumber(negatedSecondVector, s)
)
, initialPoint
);
// generate all possible chessboards for given starting point and compute their error
double currentError = 0;
for (int ff = 0; ff < 9; ff++)
{
for (int ss = 0; ss < 9; ss++)
{
var currentPoint = MyVector3DStruct.Addition(
startingPoint,
MyVector3DStruct.Addition(
MyVector3DStruct.MultiplyByNumber(firstVector, ff),
MyVector3DStruct.MultiplyByNumber(secondVector, ss)
)
);
var closestPointDistance = contractedPoints3DasStruct.Min(x =>
MyVector3DStruct.Distance(ref currentPoint,
new MyVector3DStruct(x.x, x.y, x.z)));
// clipping of max error per point
var clippingDistance = chessboardData.UserParameters.ClippedDistanecInChessboardFittingMetric / 1000f;
closestPointDistance = closestPointDistance > clippingDistance ? clippingDistance : closestPointDistance;
if (chessboardData.UserParameters.IsDistanceMetricInChessboardFittingExperimental)
{
closestPointDistance = closestPointDistance * closestPointDistance;
}
currentError += closestPointDistance;
}
}
if (currentError < lowestError)
{
lowestError = currentError;
boardRepresentation = new Chessboard3DReprezentation(startingPoint, firstVector, secondVector);
}
}
}
}
}
});
return(boardRepresentation);
}