private void GenerateDataByte()
{
if (InterpolationSpline == null)
{
InterpolationSpline = Interpolation.CreateRational(new double[] { 0, 0.5, 1 }, new double[] { 1, FallOff, 0 });
}
mDataByte = new byte[Width * Height];
PointF midPoint = new PointF(Width / 2.0f, Height / 2.0f);
for (uint i = 0; i < Width; ++i)
{
for (uint j = 0; j < Height; ++j)
{
byte value = 0;
PointF curPos = new PointF(i, j);
double distance = Math.Sqrt(Math.Pow(curPos.X - midPoint.X, 2) + Math.Pow(curPos.Y - midPoint.Y, 2));
if (distance < InnerRadius)
{
double coeff = InterpolationSpline.Interpolate(distance / InnerRadius);
if (coeff < 0)
{
coeff = 0;
}
int curValue = (int)(mRandom.Next(0, 255) * coeff);
value = (byte)curValue;
}
mDataByte[j * Height + i] = value;
}
}
}
public SplineControl()
{
InitializeComponent();
mSplineInterpolation = Interpolation.CreateRational(new double[] { 0, mMidPoint.X, 1 }, new double[] { 1, mMidPoint.Y, 0 });
Paint += new PaintEventHandler(paintControl);
MouseDown += new MouseEventHandler(mousePressed);
MouseUp += new MouseEventHandler(mouseReleased);
MouseMove += new MouseEventHandler(mouseMoved);
}
void mouseMoved(object sender, MouseEventArgs e)
{
if (IsLeftDown)
{
int x = Math.Min(Math.Max(1, e.X), Width - 1);
int y = Math.Min(Math.Max(1, e.Y), Height - 1);
mMidPoint = new PointF(x / (float)Width, (Height - y) / (float)Height);
mSplineInterpolation = Interpolation.CreateRational(new double[] { 0, mMidPoint.X, 1 }, new double[] { 1, mMidPoint.Y, 0 });
Invalidate();
if (SplineChanged != null)
{
SplineChanged();
}
}
}
public void TestInterpolationMethod_RationalWithPoles()
{
double[] t = new double[] { 0, 1, 3, 4, 5 };
double[] x = new double[] { 0, 3, 1000, -1000, 3 };
RationalInterpolation method = new RationalInterpolation();
method.Init(t, x);
for (int i = 0; i < t.Length; i++)
{
Assert.That(method.Interpolate(t[i]), Is.EqualTo(x[i]), "Exact Point " + i.ToString());
}
// Maple: "with(CurveFitting);"
// Maple: "evalf(subs({x=0.1},RationalInterpolation([[0,0],[1,3],[3,1000],[4,-1000], [5,3]], x)),20);"
Assert.That(method.Interpolate(0.1), NumericIs.AlmostEqualTo(.19389203383553566255, 1e-14), "A 0.1");
Assert.That(method.Interpolate(0.4), NumericIs.AlmostEqualTo(.88132900698869875369, 1e-14), "A 0.4");
Assert.That(method.Interpolate(1.1), NumericIs.AlmostEqualTo(3.5057665681580626913, 1e-15), "A 1.1");
Assert.That(method.Interpolate(3.01), NumericIs.AlmostEqualTo(1548.7666642693586902, 1e-13), "A 3.01");
Assert.That(method.Interpolate(3.02), NumericIs.AlmostEqualTo(3362.2564334253633516, 1e-13), "A 3.02");
Assert.That(method.Interpolate(3.03), NumericIs.AlmostEqualTo(-22332.603641443806014, 1e-12), "A 3.03");
Assert.That(method.Interpolate(3.1), NumericIs.AlmostEqualTo(-440.30323769822443789, 1e-14), "A 3.1");
Assert.That(method.Interpolate(3.2), NumericIs.AlmostEqualTo(-202.42421196280566349, 1e-14), "A 3.2");
Assert.That(method.Interpolate(4.5), NumericIs.AlmostEqualTo(21.208249625210155439, 1e-14), "A 4.5");
Assert.That(method.Interpolate(10.0), NumericIs.AlmostEqualTo(-4.8936986959784751517, 1e-13), "A 10.0");
Assert.That(method.Interpolate(-10.0), NumericIs.AlmostEqualTo(-3.6017584308603731307, 1e-13), "A -10.0");
// Test Linear Case
for (int k = 2; k < 6; k++)
{
double[] linx, liny, linxtest, linytest;
BuildLinearCase(2, k, out linx, out liny, out linxtest, out linytest);
IInterpolationMethod linearMethod = Interpolation.CreateRational(linx, liny);
for (int i = 0; i < linxtest.Length; i++)
{
// very weak test, but rational with poles is incredibly bad in the linear case
Assert.That(linearMethod.Interpolate(linxtest[i]), Is.Not.NaN, String.Format("Linear k={0} i={1}", k, i));
}
}
}
