/// <summary>
/// Integrates a given function within the given integral.
/// </summary>
/// <param name="f">The function to integrate.</param>
/// <param name="a">The lower limit.</param>
/// <param name="b">The higher limit.</param>
/// <returns>
/// The integral of <paramref name="function"/> over the interval from <paramref name="a"/> to <paramref name="b"/>
/// </returns>
public double Integrate(Sharp3D.Math.Core.MathFunctions.UnaryFunction<double> f, double a, double b)
{
if (a > b) return -Integrate(f, b, a);
double sum = 0;
double stepSize = (b - a) / _stepCount;
double stepSizeDiv3 = stepSize / 3;
for (int i = 0; i < _stepCount; i = i + 2)
{
sum += (f(a + i * stepSize) + 4 * f(a + (i + 1) * stepSize) + f(a + (i + 2) * stepSize)) * stepSizeDiv3;
}
return sum;
}
/// <summary>
/// Integrates a given function within the given integral.
/// </summary>
/// <param name="f">The function to integrate.</param>
/// <param name="a">The lower limit.</param>
/// <param name="b">The higher limit.</param>
/// <returns>
/// The integral of <paramref name="function"/> over the interval from <paramref name="a"/> to <paramref name="b"/>
/// </returns>
public float Integrate(Sharp3D.Math.Core.MathFunctions.UnaryFunction<float> f, float a, float b)
{
if (a > b) return -Integrate(f, b, a);
float sum = 0;
float stepSize = (float)((b - a) / _stepCount);
float stepSizeDiv3 = stepSize / 3.0f;
for (int i = 0; i < _stepCount; i = i + 2)
{
sum += (f(a + i * stepSize) + 4.0f * f(a + (i + 1) * stepSize) + f(a + (i + 2) * stepSize)) * stepSizeDiv3;
}
return sum;
}
public override void Transform(Sharp3D.Math.Core.Transform2D transform)
{
}
/// <summary>
/// Integrates a given function within the given integral.
/// </summary>
/// <param name="f">The function to integrate.</param>
/// <param name="a">The lower limit.</param>
/// <param name="b">The higher limit.</param>
/// <returns>
/// The integral of <paramref name="function"/> over the interval from <paramref name="a"/> to <paramref name="b"/>
/// </returns>
public double Integrate(Sharp3D.Math.Core.MathFunctions.UnaryFunction<double> f, double a, double b)
{
// Check the _romD field is initialized correctly.
if ((_romD == null) || (_romD.GetLength(1) == _order))
{
_romD = new double[1, _order];
}
if (a > b) return Integrate(f, b, a);
double h = (b-a);
_romD[0,0] = 0.5*h*(f(a) + f(b));
for (int i = 2, ipower = 1; i <= _order; i++, ipower *= 2, h /= 2)
{
// Approximation using the trapezoid rule.
double sum = 0;
for (int j = 1; j <= ipower; j++)
{
sum += f(a + h*(j-0.5));
}
// Richardson extrapolation
_romD[1,0] = 0.5 * (_romD[0,0] + (h*sum));
for (int k = 1, kpower = 4; k < i; k++, kpower *= 4)
{
_romD[1,k] = (kpower*_romD[1, k-1] - _romD[0,k-1]) / (kpower-1);
}
// Save the extrapolated values for the next iteration
for (int j = 0; j < i; j++)
{
_romD[0, j] = _romD[1, j];
}
}
return _romD[0,_order-1];
}
/// <summary>
/// Integrates a given function within the given integral.
/// </summary>
/// <param name="f">The function to integrate.</param>
/// <param name="a">The lower limit.</param>
/// <param name="b">The higher limit.</param>
/// <returns>
/// The integral of <paramref name="function"/> over the interval from <paramref name="a"/> to <paramref name="b"/>
/// </returns>
public double Integrate(Sharp3D.Math.Core.MathFunctions.UnaryFunction<double> f, double a, double b)
{
if (a == b)
return 0;
if (a > b)
return -Integrate(f, b, a);
// Start with the crudest estimate
int n = 1;
double estimate = ((f(a) + f(b)) * (b - a)) / 2.0;
double newEstimate = 0;
int i = 1;
do
{
switch (_method)
{
case Method.Default:
newEstimate = defaultIteration(f, a, b, estimate, n);
n *= 2;
break;
case Method.MidPoint:
newEstimate = midPointIteration(f, a, b, estimate, n);
n *= 3;
break;
}
// Check accuracy
if (System.Math.Abs(newEstimate - estimate) <= _accuracy)
return newEstimate;
estimate = newEstimate;
i++;
}
while (i < _maxSteps);
throw new MathException("Max number of iterations reached.");
}
public override Sharp3D.Math.Core.Vector3D getUpVector(Sharp3D.Math.Core.Vector3D at)
{
return base.getUpVector(at);
}
