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using System;
using System.Collections.Generic;
using System.Text;
namespace libTerrain
{
partial class Channel
{
// Navier Stokes Algorithms ported from
// "Real-Time Fluid Dynamics for Games" by Jos Stam.
// presented at GDC 2003.
// Poorly ported from C++. (I gave up making it properly native somewhere after nsSetBnd)
private static int nsIX(int i, int j, int N)
{
return ((i) + (N + 2) * (j));
}
private static void nsSwap(ref double x0, ref double x)
{
double tmp = x0;
x0 = x;
x = tmp;
}
private static void nsSwap(ref double[] x0, ref double[] x)
{
double[] tmp = x0;
x0 = x;
x = tmp;
}
private void nsAddSource(int N, ref double[] x, ref double[] s, double dt)
{
int i;
int size = (N + 2) * (N + 2);
for (i = 0; i < size; i++)
{
x[i] += dt * s[i];
}
}
private void nsSetBnd(int N, int b, ref double[] x)
{
int i;
for (i = 0; i <= N; i++)
{
x[nsIX(0, i, N)] = b == 1 ? -x[nsIX(1, i, N)] : x[nsIX(1, i, N)];
x[nsIX(0, N + 1, N)] = b == 1 ? -x[nsIX(N, i, N)] : x[nsIX(N, i, N)];
x[nsIX(i, 0, N)] = b == 2 ? -x[nsIX(i, 1, N)] : x[nsIX(i, 1, N)];
x[nsIX(i, N + 1, N)] = b == 2 ? -x[nsIX(i, N, N)] : x[nsIX(i, N, N)];
}
x[nsIX(0, 0, N)] = 0.5f * (x[nsIX(1, 0, N)] + x[nsIX(0, 1, N)]);
x[nsIX(0, N + 1, N)] = 0.5f * (x[nsIX(1, N + 1, N)] + x[nsIX(0, N, N)]);
x[nsIX(N + 1, 0, N)] = 0.5f * (x[nsIX(N, 0, N)] + x[nsIX(N + 1, 1, N)]);
x[nsIX(N + 1, N + 1, N)] = 0.5f * (x[nsIX(N, N + 1, N)] + x[nsIX(N + 1, N, N)]);
}
private void nsLinSolve(int N, int b, ref double[] x, ref double[] x0, double a, double c)
{
int i, j;
for (i = 1; i <= N; i++)
{
for (j = 1; j <= N; j++)
{
x[nsIX(i, j, N)] = (x0[nsIX(i, j, N)] + a *
(x[nsIX(i - 1, j, N)] +
x[nsIX(i + 1, j, N)] +
x[nsIX(i, j - 1, N)] + x[nsIX(i, j + 1, N)])
) / c;
}
}
nsSetBnd(N, b, ref x);
}
private void nsDiffuse(int N, int b, ref double[] x, ref double[] x0, double diff, double dt)
{
double a = dt * diff * N * N;
nsLinSolve(N, b, ref x, ref x0, a, 1 + 4 * a);
}
private void nsAdvect(int N, int b, ref double[] d, ref double[] d0, ref double[] u, ref double[] v, double dt)
{
int i, j, i0, j0, i1, j1;
double x, y, s0, t0, s1, t1, dt0;
dt0 = dt * N;
for (i = 1; i <= N; i++)
{
for (j = 1; j <= N; j++)
{
x = i - dt0 * u[nsIX(i, j, N)];
y = j - dt0 * v[nsIX(i, j, N)];
if (x < 0.5)
x = 0.5;
if (x > N + 0.5)
x = N + 0.5;
i0 = (int)x;
i1 = i0 + 1;
if (y < 0.5)
y = 0.5;
if (y > N + 0.5)
y = N + 0.5;
j0 = (int)y;
j1 = j0 + 1;
s1 = x - i0;
s0 = 1 - s1;
t1 = y - j0;
t0 = 1 - t1;
d[nsIX(i, j, N)] = s0 * (t0 * d0[nsIX(i0, j0, N)] + t1 * d0[nsIX(i0, j1, N)]) +
s1 * (t0 * d0[nsIX(i1, j0, N)] + t1 * d0[nsIX(i1, j1, N)]);
}
}
nsSetBnd(N, b, ref d);
}
public void nsProject(int N, ref double[] u, ref double[] v, ref double[] p, ref double[] div)
{
int i, j;
for (i = 1; i <= N; i++)
{
for (j = 1; j <= N; j++)
{
div[nsIX(i, j, N)] = -0.5 * (u[nsIX(i + 1, j, N)] - u[nsIX(i - 1, j, N)] + v[nsIX(i, j + 1, N)] - v[nsIX(i, j - 1, N)]) / N;
p[nsIX(i, j, N)] = 0;
}
}
nsSetBnd(N, 0, ref div);
nsSetBnd(N, 0, ref p);
nsLinSolve(N, 0, ref p, ref div, 1, 4);
for (i = 1; i <= N; i++)
{
for (j = 1; j <= N; j++)
{
u[nsIX(i, j, N)] -= 0.5 * N * (p[nsIX(i + 1, j, N)] - p[nsIX(i - 1, j, N)]);
v[nsIX(i, j, N)] -= 0.5 * N * (p[nsIX(i, j + 1, N)] - p[nsIX(i, j - 1, N)]);
}
}
nsSetBnd(N, 1, ref u);
nsSetBnd(N, 2, ref v);
}
private void nsDensStep(int N, ref double[] x, ref double[] x0, ref double[] u, ref double[] v, double diff, double dt)
{
nsAddSource(N, ref x, ref x0, dt);
nsSwap(ref x0, ref x);
nsDiffuse(N, 0, ref x, ref x0, diff, dt);
nsSwap(ref x0, ref x);
nsAdvect(N, 0, ref x, ref x0, ref u, ref v, dt);
}
private void nsVelStep(int N, ref double[] u, ref double[] v, ref double[] u0, ref double[] v0, double visc, double dt)
{
nsAddSource(N, ref u, ref u0, dt);
nsAddSource(N, ref v, ref v0, dt);
nsSwap(ref u0, ref u);
nsDiffuse(N, 1, ref u, ref u0, visc, dt);
nsSwap(ref v0, ref v);
nsDiffuse(N, 2, ref v, ref v0, visc, dt);
nsProject(N, ref u, ref v, ref u0, ref v0);
nsSwap(ref u0, ref u);
nsSwap(ref v0, ref v);
nsAdvect(N, 1, ref u, ref u0, ref u0, ref v0, dt);
nsAdvect(N, 2, ref v, ref v0, ref u0, ref v0, dt);
nsProject(N, ref u, ref v, ref u0, ref v0);
}
private void nsBufferToDoubles(ref double[] dens, int N, ref double[,] doubles)
{
int i;
int j;
for (i = 1; i <= N; i++)
{
for (j = 1; j <= N; j++)
{
doubles[i - 1, j - 1] = dens[nsIX(i, j, N)];
}
}
}
private void nsDoublesToBuffer(double[,] doubles, int N, ref double[] dens)
{
int i;
int j;
for (i = 1; i <= N; i++)
{
for (j = 1; j <= N; j++)
{
dens[nsIX(i, j, N)] = doubles[i - 1, j - 1];
}
}
}
private void nsSimulate(int N, int rounds, double dt, double diff, double visc)
{
int size = (N * 2) * (N * 2);
double[] u = new double[size]; // Force, X axis
double[] v = new double[size]; // Force, Y axis
double[] u_prev = new double[size];
double[] v_prev = new double[size];
double[] dens = new double[size];
double[] dens_prev = new double[size];
nsDoublesToBuffer(this.map, N, ref dens);
nsDoublesToBuffer(this.map, N, ref dens_prev);
for (int i = 0; i < rounds; i++)
{
u_prev = u;
v_prev = v;
dens_prev = dens;
nsVelStep(N, ref u, ref v, ref u_prev, ref v_prev, visc, dt);
nsDensStep(N, ref dens, ref dens_prev, ref u, ref v, diff, dt);
}
nsBufferToDoubles(ref dens, N, ref this.map);
}
///
/// Performs computational fluid dynamics on a channel
///
/// The number of steps to perform (Recommended: 20)
/// Delta Time - The time between steps (Recommended: 0.1)
/// Fluid diffusion rate (Recommended: 0.0)
/// Fluid viscosity (Recommended: 0.0)
public void navierStokes(int rounds, double dt, double diff, double visc)
{
nsSimulate(this.h, rounds, dt, diff, visc);
}
public void navierStokes(int rounds, double dt, double diff, double visc, ref double[,] uret, ref double[,] vret)
{
int N = this.h;
int size = (N * 2) * (N * 2);
double[] u = new double[size]; // Force, X axis
double[] v = new double[size]; // Force, Y axis
double[] u_prev = new double[size];
double[] v_prev = new double[size];
double[] dens = new double[size];
double[] dens_prev = new double[size];
nsDoublesToBuffer(this.map, N, ref dens);
nsDoublesToBuffer(this.map, N, ref dens_prev);
for (int i = 0; i < rounds; i++)
{
u_prev = u;
v_prev = v;
dens_prev = dens;
nsVelStep(N, ref u, ref v, ref u_prev, ref v_prev, visc, dt);
nsDensStep(N, ref dens, ref dens_prev, ref u, ref v, diff, dt);
}
nsBufferToDoubles(ref u, N, ref uret);
nsBufferToDoubles(ref v, N, ref vret);
nsBufferToDoubles(ref dens, N, ref this.map);
}
}
}