public static double SurfaceArea3D(Functionxy fxyz, Function f, Function g, Function h, Function i, double a, double b, int m, int n)// needs finishing.
{
Integral3 intMethod = GaussianRuleIntetration3();
//return TripleIntegration((double x, double y, double z) =>
//Math.Sqrt(1 + Math.Pow(PartialDifferentiationx(fxyz, x, y), 2) + Math.Pow(PartialDifferentiationy(fxyz, x, y), 2) + Math.Pow(PartialDifferentiationz(fxyz, x, z), 2) + Math.Pow(PartialDifferentiationz(fxyz, y, z), 2)), f, g, i, a, b, m, n, intMethod, intMethod);
return(0);
}
/// <summary>
/// 4-point Gaussian rule integration of the function f, over n subintervals in the interval (a,b).
/// </summary>
public static Integral3 GaussianRuleIntetration3()
{
Integral3 integral = (f, a, b, c, n) =>
{
var weight = new double[4];
weight[2] = 0.652145154862546;
weight[1] = weight[2];
weight[3] = 0.347854845137454;
weight[0] = weight[3];
var point = new double[4];
point[3] = 0.861136311594053;
point[0] = -point[3];
point[2] = 0.339981043584856;
point[1] = -point[2];
double sum = 0;
var h = (b - a) / n;
var h1 = (c - b) / n;
var h2 = (c - a) / n;
for (var i = 0; i < n; i++)
{
double s = 0;
var xl = a + i * h;
var xr = xl + h;
var xm = (xr - xl) / 2;
var xd = (xr + xl) / 2;
var yl = b + i * h1;
var yr = yl + h1;
var ym = (yr - yl) / 2;
var yd = (yr + yl) / 2;
var zl = c + i * h2;
var zr = zl + h2;
var zm = (zr - zl) / 2;
var zd = (zr + zl) / 2;
for (var j = 0; j < 4; j++)
{
s = s + weight[j] * f(xm * point[j] + xd, ym * point[j] + yd, zm * point[j] + zd) * xm;
}
sum = sum + s;
}
return(sum);
};
return(integral);
}
/// <summary>
/// 3D integration of a function of 3 variables. (( f(x,y,z) dxdydz )).
/// </summary>
/// <param name="fxyz">The fxyz.</param>
/// <param name="g">The function g(x).</param>
/// <param name="h">The function h(y).</param>
/// <param name="i">The function i(z).</param>
/// <param name="a">A.</param>
/// <param name="b">The b.</param>
/// <param name="m">The m.</param>
/// <param name="n">The n.</param>
/// <param name="inInt">The in int.</param>
/// <param name="outInt">The out int.</param>
/// <remarks>Inner integral dx, from x=g(y) to x=h(y), over m subintervals, using algorithm inInt.
/// Outer integral dy, from y=a to y=b, over n subintervals, using algorithm outInt.
/// Third integral dz, from z....</remarks>
public static double TripleIntegration(Functionxyz fxyz, Function g, Function h, Function i, double a, double b, double c, int m, int n, Integral3 inInt, Integral3 outInt)// needs finishing
{
//return outInt((double u) => inInt((double x, double y, double z) => fxyz(x, y, z), g(u), h(u), i(u), m), a, b, c, n);
return(0);
}
