public void BaseFunctionException()
{
// Setup scattered interpolation with radial basis functions.
RadialBasisRegressionF rbr = new RadialBasisRegressionF();
rbr.BasisFunction = null;
}
public void TestException()
{
float[] xValues = new float[] { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };
float[] yValues = new float[] { 0, 4, 5, 3, 1, 2, 3, 7, 8, 9 };
// Setup scattered interpolation with radial basis functions.
RadialBasisRegressionF rbr = new RadialBasisRegressionF();
rbr.BasisFunction = (x, i) => MathHelper.Gaussian(x, 1, 0, 100); // Use Gaussian function as basis function.
for (int i = 0; i < xValues.Length; i++)
rbr.Add(new Pair<VectorF, VectorF>(new VectorF(1, xValues[i]), new VectorF(1, yValues[i])));
rbr.Setup();
rbr.Compute(new VectorF(1, 0));
}
public void TestException()
{
float[] xValues = new float[] { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };
float[] yValues = new float[] { 0, 4, 5, 3, 1, 2, 3, 7, 8, 9 };
// Setup scattered interpolation with radial basis functions.
RadialBasisRegressionF rbr = new RadialBasisRegressionF();
rbr.BasisFunction = (x, i) => MathHelper.Gaussian(x, 1, 0, 100); // Use Gaussian function as basis function.
for (int i = 0; i < xValues.Length; i++)
{
rbr.Add(new Pair <VectorF, VectorF>(new VectorF(1, xValues[i]), new VectorF(1, yValues[i])));
}
rbr.Setup();
rbr.Compute(new VectorF(1, 0));
}
public void Test1()
{
float[] xValues = new float[] { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };
float[] yValues = new float[] { 0, 4, 5, 3, 1, 2, 3, 7, 8, 9 };
// Setup scattered interpolation with radial basis functions.
RadialBasisRegressionF rbr = new RadialBasisRegressionF();
rbr.BasisFunction = (x, i) => MathHelper.Gaussian(x, 1, 0, 0.5f); // Use Gaussian function as basis function.
//rbr.BaseFunction = delegate(float x) { return x; }; // Use identity functions as basis function.
for (int i = 0; i < xValues.Length; i++)
rbr.Add(new Pair<VectorF, VectorF>(new VectorF(1, xValues[i]), new VectorF(1, yValues[i])));
rbr.Setup();
Assert.IsTrue(Numeric.AreEqual(yValues[0], rbr.Compute(new VectorF(1, 0))[0]));
Assert.IsTrue(Numeric.AreEqual(yValues[2], rbr.Compute(new VectorF(1, 2))[0]));
Assert.IsTrue(Numeric.AreEqual(yValues[3], rbr.Compute(new VectorF(1, 3))[0]));
Assert.IsTrue(Numeric.AreEqual(yValues[4], rbr.Compute(new VectorF(1, 4))[0]));
Assert.IsTrue(Numeric.AreEqual(yValues[8], rbr.Compute(new VectorF(1, 8))[0]));
}
public void Test1()
{
float[] xValues = new float[] { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };
float[] yValues = new float[] { 0, 4, 5, 3, 1, 2, 3, 7, 8, 9 };
// Setup scattered interpolation with radial basis functions.
RadialBasisRegressionF rbr = new RadialBasisRegressionF();
rbr.BasisFunction = (x, i) => MathHelper.Gaussian(x, 1, 0, 0.5f); // Use Gaussian function as basis function.
//rbr.BaseFunction = delegate(float x) { return x; }; // Use identity functions as basis function.
for (int i = 0; i < xValues.Length; i++)
{
rbr.Add(new Pair <VectorF, VectorF>(new VectorF(1, xValues[i]), new VectorF(1, yValues[i])));
}
rbr.Setup();
Assert.IsTrue(Numeric.AreEqual(yValues[0], rbr.Compute(new VectorF(1, 0))[0]));
Assert.IsTrue(Numeric.AreEqual(yValues[2], rbr.Compute(new VectorF(1, 2))[0]));
Assert.IsTrue(Numeric.AreEqual(yValues[3], rbr.Compute(new VectorF(1, 3))[0]));
Assert.IsTrue(Numeric.AreEqual(yValues[4], rbr.Compute(new VectorF(1, 4))[0]));
Assert.IsTrue(Numeric.AreEqual(yValues[8], rbr.Compute(new VectorF(1, 8))[0]));
}
private void DoScatteredInterpolation()
{
// Create random points for a height field.
// The height field is in the x/z plane. Height is along the y axis.
var points = new List <Vector3>();
for (int i = 0; i < 9; i++)
{
float x = i * 10;
float y = RandomHelper.Random.NextFloat(0, 20);
float z = RandomHelper.Random.NextInteger(0, 44) * 2;
points.Add(new Vector3(x, y, z));
}
// Now we setup scattered interpolation.
// The RadialBasisRegression class does one form of scattered interpolation:
// Multiple regression analysis with radial basis functions.
RadialBasisRegressionF rbf = new RadialBasisRegressionF();
// We must define a basis function which will be used to determine the influence
// of each input data pair. The Gaussian bell curve is a good candidate for most
// applications.
// We set the standard deviation to 10. Choosing a higher standard deviation makes
// the Gaussian bell curve wider and increases the influence of the data points.
// If we choose a lower standard deviation, we limit the influence of the data points.
rbf.BasisFunction = (x, i) => MathHelper.Gaussian(x, 1, 0, 10);
// Feed the data points into the scattered interpolation instance.
foreach (var point in points)
{
// For each random point we add a data pair (X, Y), where X is a 2D position
// in the height field, and Y is the observed height.
VectorF X = new VectorF(new[] { point.X, point.Z });
VectorF Y = new VectorF(new[] { point.Y });
var dataPair = new Pair <VectorF, VectorF>(X, Y);
rbf.Add(dataPair);
}
// These were all data points. Now, we perform some precomputations.
rbf.Setup();
// Finally, we create a height field.
var heightField = new float[100, 100];
for (int x = 0; x < 100; x++)
{
for (int z = 0; z < 100; z++)
{
// The scattered interpolation instance can compute a height for
// any 2D input vector.
float y = rbf.Compute(new VectorF(new float[] { x, z }))[0];
heightField[x, z] = y;
}
}
var debugRenderer = GraphicsScreen.DebugRenderer;
debugRenderer.Clear();
// Draw the random data points.
const float scale = 0.04f;
Vector3 offset = new Vector3(-2, 0, -2);
foreach (var point in points)
{
debugRenderer.DrawPoint(scale * point + offset, Color.Black, false);
}
// Draw the height field.
const int stepSize = 2;
for (int x = 0; x < 100; x += stepSize)
{
for (int z = 0; z < 100; z += stepSize)
{
float y0 = heightField[x, z];
if (x + stepSize < 100)
{
float y1 = heightField[x + stepSize, z];
debugRenderer.DrawLine(
scale * new Vector3(x, y0, z) + offset,
scale * new Vector3(x + stepSize, y1, z) + offset,
Color.Black,
false);
}
if (z + stepSize < 100)
{
float y2 = heightField[x, z + stepSize];
debugRenderer.DrawLine(
scale * new Vector3(x, y0, z) + offset,
scale * new Vector3(x, y2, z + stepSize) + offset,
Color.Black,
false);
}
}
}
}
public void BaseFunctionException()
{
// Setup scattered interpolation with radial basis functions.
RadialBasisRegressionF rbr = new RadialBasisRegressionF();
rbr.BasisFunction = null;
}
