public Coordinate3D ProjectOnto(Coordinate3D coord)
{
var uNormal = GetUnitNormalVector();
return(coord - uNormal.Scale((coord - MidPoint).DotProduct(uNormal)));
}
public void GenerateEmpricialDensityGrid(long numsamples, List <Tuple <ICoordinate, bool> > lableddata, double jitterscale = 1E-7)
{
producer = Task.Run(() =>
{
var pairs = new List <Tuple <ICoordinate, ICoordinate> >();
for (var i = 0; i < lableddata.Count - 1; i++)
{
for (var j = i + 1; j < lableddata.Count; j++)
{
if (lableddata[i].Item2 != lableddata[j].Item2)
{
pairs.Add(new Tuple <ICoordinate, ICoordinate>(lableddata[i].Item1, lableddata[j].Item1));
}
}
}
//add bottom boundary
var problemDim = lableddata.First().Item1.GetDimensionality();
switch (problemDim)
{
case 2:
pairs.Add(new Tuple <ICoordinate, ICoordinate>(new Coordinate(0, 0), new Coordinate(jitterscale, -20)));
break;
case 3:
pairs.Add(new Tuple <ICoordinate, ICoordinate>(new Coordinate3D(0, 0, 0), new Coordinate3D(jitterscale, jitterscale, -20)));
break;
}
Parallel.For(0, numsamples, (i) =>
{
var inducers = pairs.OrderBy(v => StaticConfigParams.rnd.NextDouble()).Take(problemDim).ToList();
ICoordinate intersectionCoord, first_coord, second_coord, third_coord, jitteredPivot = null;
switch (problemDim)
{
case 2:
var firstbisectorLine = Line.Bisector((Coordinate)inducers[0].Item1, (Coordinate)inducers[0].Item2, isCounted: false);
var secondbisectorLine = Line.Bisector((Coordinate)inducers[1].Item1, (Coordinate)inducers[1].Item2, isCounted: false);
intersectionCoord = firstbisectorLine.Intersection(secondbisectorLine);
//empirical gradient
var first_posdir = firstbisectorLine.EvaluateAtX(intersectionCoord.GetDimension(0) + jitterscale);
var first_negdir = firstbisectorLine.EvaluateAtX(intersectionCoord.GetDimension(0) - jitterscale);
var second_posdir = secondbisectorLine.EvaluateAtX(intersectionCoord.GetDimension(0) + jitterscale);
var second_negdir = secondbisectorLine.EvaluateAtX(intersectionCoord.GetDimension(0) - jitterscale);
//Find local minima directions.
first_coord = first_posdir > first_negdir ?
new Coordinate(intersectionCoord.GetDimension(0) + jitterscale, first_posdir) :
new Coordinate(intersectionCoord.GetDimension(0) - jitterscale, first_negdir);
second_coord = second_posdir > second_negdir ?
new Coordinate(intersectionCoord.GetDimension(0) + jitterscale, second_posdir) :
new Coordinate(intersectionCoord.GetDimension(0) - jitterscale, second_negdir);
//averaging ensures we are in the exact cell who's bottom-most coordinate is the intersection coord.
jitteredPivot = new Coordinate(first_coord.GetDimension(0) + second_coord.GetDimension(0) / 2.0, first_coord.GetDimension(1) + second_coord.GetDimension(1) / 2.0);
/*
* // Note: I abandoned the Random sampled jitter strategy since this simpler strategy ensures a 1-1 mapping between an intersectionCoord and a cell (up to scale).
* var jitteredPivot = new Coordinate(
* intersectionCoord.X + GeometryHelpers.SampleGaussian(StaticConfigParams.rnd, 0.0, jitterscale),
* intersectionCoord.Y + GeometryHelpers.SampleGaussian(StaticConfigParams.rnd, 0.0, jitterscale));
*/
break;
case 3:
var firstbisectorPlane = Plane.Bisector((Coordinate3D)inducers[0].Item1, (Coordinate3D)inducers[0].Item2);
var secondbisectorPlane = Plane.Bisector((Coordinate3D)inducers[1].Item1, (Coordinate3D)inducers[1].Item2);
var thirdbisectorPlane = Plane.Bisector((Coordinate3D)inducers[2].Item1, (Coordinate3D)inducers[2].Item2);
//We find the intersection of three planes by solving a system of linear equations.
double[,] matrix =
{
{ firstbisectorPlane.Normal.X, firstbisectorPlane.Normal.Y, firstbisectorPlane.Normal.Z },
{ secondbisectorPlane.Normal.X, secondbisectorPlane.Normal.Y, secondbisectorPlane.Normal.Z },
{ thirdbisectorPlane.Normal.X, thirdbisectorPlane.Normal.Y, thirdbisectorPlane.Normal.Z }
};
double[,] rightSide = { { -firstbisectorPlane.D }, { -secondbisectorPlane.D }, { -thirdbisectorPlane.D } };
var x = Matrix.Solve(matrix, rightSide, leastSquares: true);
intersectionCoord = new Coordinate3D(x[0, 0], x[1, 0], x[2, 0]);
//empirical gradients dy
first_coord = (Coordinate3D)intersectionCoord + firstbisectorPlane.Normal.Scale(jitterscale);
second_coord = (Coordinate3D)intersectionCoord + secondbisectorPlane.Normal.Scale(jitterscale);
third_coord = (Coordinate3D)intersectionCoord + thirdbisectorPlane.Normal.Scale(jitterscale);
jitteredPivot = new Coordinate3D((first_coord.GetDimension(0) + second_coord.GetDimension(0) + third_coord.GetDimension(0)) / 3.0,
(first_coord.GetDimension(1) + second_coord.GetDimension(1) + third_coord.GetDimension(1)) / 3.0,
(first_coord.GetDimension(2) + second_coord.GetDimension(2) + third_coord.GetDimension(2)) / 3.0);
break;
}
pivots.Add(jitteredPivot);
});
pivots.CompleteAdding();
});
}
public double D; //plane given as aX+bY+cZ=d where a,b,c is the Normal
public Plane(double a, double b, double c, double d)
{
Normal = new Coordinate3D(a, b, c);
D = d;
}
