public static PlanarAxis ComputeProjectTo2DArguments(IList <Vec3> positions)
{
var box = OrientedBoundingBox.FromPoints(positions);
var halfAxis = box.HalfAxis;
var xAxis = halfAxis.GetColumn(0);
var scratchXAxis = xAxis;
var yAxis = halfAxis.GetColumn(1);
var scratchYAxis = yAxis;
var zAxis = halfAxis.GetColumn(2);
var scratchZAxis = zAxis;
var xMag = xAxis.GetLength();
var yMag = yAxis.GetLength();
var zMag = zAxis.GetLength();
var min = new[] { xMag, yMag, zMag }.Min();
// If all the points are on a line return undefined because we can't draw a polygon
if ((xMag == 0 && (yMag == 0 || zMag == 0)) || (yMag == 0 && zMag == 0))
{
return(null);
}
var planeAxis1 = new Vec3();
var planeAxis2 = new Vec3();
if (min == yMag || min == zMag)
{
planeAxis1 = xAxis;
}
if (min == xMag)
{
planeAxis1 = yAxis;
}
else if (min == zMag)
{
planeAxis2 = yAxis;
}
if (min == xMag || min == yMag)
{
planeAxis2 = zAxis;
}
return(new PlanarAxis
{
Center = box.Center,
Axis1 = planeAxis1,
Axis2 = planeAxis2
});
}
public static OrientedBoundingBox FromPoints(IList <Vec3> positions)
{
var result = new OrientedBoundingBox();
var length = positions.Count;
var meanPoint = positions[0];
for (var i = 1; i < length; i++)
{
meanPoint = Vec3.Add(meanPoint, positions[i]);
}
var invLength = 1.0 / length;
meanPoint = meanPoint.MultiplyBy(invLength);
var exx = 0.0;
var exy = 0.0;
var exz = 0.0;
var eyy = 0.0;
var eyz = 0.0;
var ezz = 0.0;
for (var i = 0; i < length; i++)
{
var p = positions[i].Substract(meanPoint);
exx += p.X * p.X;
exy += p.X * p.Y;
exz += p.X * p.Z;
eyy += p.Y * p.Y;
eyz += p.Y * p.Z;
ezz += p.Z * p.Z;
}
exx *= invLength;
exy *= invLength;
exz *= invLength;
eyy *= invLength;
eyz *= invLength;
ezz *= invLength;
var covarianceMatrix = new Matrix3(exx, exy, exz, exy, eyy, eyz, exz, eyz, ezz);
var eigenDecomposition = covarianceMatrix.ComputeEigenDecomposition();
var diagMatrix = eigenDecomposition.Item1;
var unitaryMatrix = eigenDecomposition.Item2;
var rotation = unitaryMatrix.Clone();
var v1 = rotation.GetColumn(0);
var v2 = rotation.GetColumn(1);
var v3 = rotation.GetColumn(2);
var u1 = double.MinValue; //-Number.MAX_VALUE;
var u2 = double.MinValue; //-Number.MAX_VALUE;
var u3 = double.MinValue; //-Number.MAX_VALUE;
var l1 = double.MaxValue; //Number.MAX_VALUE;
var l2 = double.MaxValue; //Number.MAX_VALUE;
var l3 = double.MaxValue; //Number.MAX_VALUE;
for (var i = 0; i < length; i++)
{
var p = positions[i];
u1 = new[] { Vec3.Dot(v1, p), u1 }.Max();
u2 = new[] { Vec3.Dot(v2, p), u2 }.Max();
u3 = new[] { Vec3.Dot(v3, p), u3 }.Max();
l1 = new[] { Vec3.Dot(v1, p), l1 }.Min();
l2 = new[] { Vec3.Dot(v2, p), l2 }.Min();
l3 = new[] { Vec3.Dot(v3, p), l3 }.Min();
}
v1 = v1.MultiplyBy(0.5 * (l1 + u1));
v2 = v2.MultiplyBy(0.5 * (l2 + u2));
v3 = v3.MultiplyBy(0.5 * (l3 + u3));
var center = Vec3.Add(v1, v2);
center = Vec3.Add(center, v3);
var scale = new Vec3(u1 - l1, u2 - l2, u3 - l3);
scale = scale.MultiplyBy(0.5);
rotation = rotation.MultiplyByScale(scale);
return(new OrientedBoundingBox
{
Center = center,
HalfAxis = rotation
});
}