// Functions assumes ellipsoid scaled coordinates
public static Double ComputeMagnitude(Vector3 point, Vector3 sphereCenter)
{
var magnitudeSquared = Cartesian3D.MagnitudeSquared(point);
var magnitude = Math.Sqrt(magnitudeSquared);
var direction = Cartesian3D.MultiplyByScalar(point, 1 / magnitude);
magnitudeSquared = Math.Max(1.0, magnitudeSquared);
magnitude = Math.Max(1.0, magnitude);
var cosAlpha = DotProduct(direction, sphereCenter);
var sinAlpha = Cartesian3D.Magnitude(CrossProduct(direction, sphereCenter));
var cosBeta = 1.0 / magnitude;
var sinBeta = Math.Sqrt(magnitudeSquared - 1.0) * cosBeta;
return(1.0 / (cosAlpha * cosBeta - sinAlpha * sinBeta));
}
// Based on Ritter's algorithm
public void FromPoints(Vector3[] points) // ECFC
{
nbPositions = points.Length;
if (nbPositions < 2)
{
throw new Exception("Your list of points must contain at least 2 points");
}
Vector3 pt;
for (int i = 0; i < nbPositions; i++)
{
var point = points[i];
// Store the points containing the smallest and largest component used for the naive approach
if (point.X < minPointX.X)
{
minPointX = point;
}
if (point.Y < minPointY.Y)
{
minPointY = point;
}
if (point.Z < minPointZ.Z)
{
minPointZ = point;
}
if (point.X > maxPointX.X)
{
maxPointX = point;
}
if (point.Y > maxPointY.Y)
{
maxPointY = point;
}
if (point.Z > maxPointZ.Z)
{
maxPointZ = point;
}
}
// Squared distance between each component min and max
var xSpan = Cartesian3D.MagnitudeSquared(Cartesian3D.Subtract(maxPointX, minPointX));
var ySpan = Cartesian3D.MagnitudeSquared(Cartesian3D.Subtract(maxPointY, minPointY));
var zSpan = Cartesian3D.MagnitudeSquared(Cartesian3D.Subtract(maxPointZ, minPointZ));
var diameter1 = minPointX;
var diameter2 = maxPointX;
var maxSpan = xSpan;
if (ySpan > maxSpan)
{
maxSpan = ySpan;
diameter1 = minPointY;
diameter2 = maxPointY;
}
if (zSpan > maxSpan)
{
maxSpan = zSpan;
diameter1 = minPointZ;
diameter2 = maxPointZ;
}
var ritterCenter = new Vector3()
{
X = (diameter1.X + diameter2.X) * 0.5,
Y = (diameter1.Y + diameter2.Y) * 0.5,
Z = (diameter1.Z + diameter2.Z) * 0.5
};
var radiusSquared = Cartesian3D.MagnitudeSquared(Cartesian3D.Subtract(diameter2, ritterCenter));
var ritterRadius = Math.Sqrt(radiusSquared);
// Initial center and radius (naive) get min and max box
var minBoxPt = new Vector3()
{
X = minPointX.X,
Y = minPointY.Y,
Z = minPointZ.Z
};
var maxBoxPt = new Vector3()
{
X = maxPointX.X,
Y = maxPointY.Y,
Z = maxPointZ.Z
};
var naiveCenter = Cartesian3D.MultiplyByScalar(Cartesian3D.Add(minBoxPt, maxBoxPt), 0.5);
var naiveRadius = 0.0;
for (int i = 0; i < nbPositions; i++)
// foreach (var i in xrange(0, nbPositions))
{
var currentP = points[i];
// Find the furthest point from the naive center to calculate the naive radius.
var r = Cartesian3D.Magnitude(Cartesian3D.Subtract(currentP, naiveCenter));
if (r > naiveRadius)
{
naiveRadius = r;
}
// Make adjustments to the Ritter Sphere to include all points.
var oldCenterToPointSquared = Cartesian3D.MagnitudeSquared(Cartesian3D.Subtract(currentP, ritterCenter));
if (oldCenterToPointSquared > radiusSquared)
{
var oldCenterToPoint = Math.Sqrt(oldCenterToPointSquared);
ritterRadius = (ritterRadius + oldCenterToPoint) * 0.5;
// Calculate center of new Ritter sphere
var oldToNew = oldCenterToPoint - ritterRadius;
ritterCenter = new Vector3()
{
X = (ritterRadius * ritterCenter.X + oldToNew * currentP.X) / oldCenterToPoint,
Y = (ritterRadius * ritterCenter.Y + oldToNew * currentP.Y) / oldCenterToPoint,
Z = (ritterRadius * ritterCenter.Z + oldToNew * currentP.Z) / oldCenterToPoint
};
}
}
// Keep the naive sphere if smaller
if (naiveRadius < ritterRadius)
{
Radius = (float)ritterRadius;
Center = ritterCenter;
}
else
{
Radius = (float)naiveRadius;
Center = naiveCenter;
}
}