/// <summary>
///
/// </summary>
public static void GetCurl(this GridField3d <Vec3d> field, Vec3d[] result, bool parallel = false)
{
// implementation reference
// http://www.math.harvard.edu/archive/21a_spring_09/PDF/13-05-curl-and-divergence.pdf
if (parallel)
{
Parallel.ForEach(Partitioner.Create(0, field.Count), range => Body(range.Item1, range.Item2));
}
else
{
Body(0, field.Count);
}
void Body(int from, int to)
{
var vals = field.Values;
int nx = field.CountX;
int ny = field.CountY;
int nz = field.CountZ;
int nxy = nx * ny;
(var dx, var dy, var dz) = (0.5 / field.Scale);
(int di, int dj, int dk) = field.GetBoundaryOffsets();
(int i, int j, int k) = field.IndicesAt(from);
for (int index = from; index < to; index++, i++)
{
if (i == nx)
{
j++; i = 0;
}
if (j == ny)
{
k++; j = 0;
}
Vec3d tx0 = (i == 0) ? vals[index + di] : vals[index - 1];
Vec3d tx1 = (i == nx - 1) ? vals[index - di] : vals[index + 1];
Vec3d ty0 = (j == 0) ? vals[index + dj] : vals[index - nx];
Vec3d ty1 = (j == ny - 1) ? vals[index - dj] : vals[index + nx];
Vec3d tz0 = (k == 0) ? vals[index + dk] : vals[index - nxy];
Vec3d tz1 = (k == nz - 1) ? vals[index - dk] : vals[index + nxy];
result[index] = new Vec3d(
(ty1.Z - ty0.Z) * dy - (tz1.Y - tz0.Y) * dz,
(tz1.X - tz0.X) * dz - (tx1.Z - tx0.Z) * dx,
(tx1.Y - tx0.Y) * dx - (ty1.X - ty0.X) * dy);
}
}
}
/// <summary>
/// Adds the Laplacian of the field to the deltas array.
/// http://en.wikipedia.org/wiki/Discrete_Laplace_operator
/// </summary>
/// <param name="field"></param>
/// <param name="deltas"></param>
/// <param name="rate"></param>
/// <param name="parallel"></param>
public static void Diffuse(GridField3d <double> field, double[] deltas, double rate, bool parallel = false)
{
if (parallel)
{
Parallel.ForEach(Partitioner.Create(0, field.Count), range => Body(range.Item1, range.Item2));
}
else
{
Body(0, field.Count);
}
void Body(int from, int to)
{
var vals = field.Values;
int nx = field.CountX;
int ny = field.CountY;
int nz = field.CountZ;
int nxy = field.CountXY;
(double dx, double dy, double dz) = field.Scale;
dx = 1.0 / (dx * dx);
dy = 1.0 / (dy * dy);
dz = 1.0 / (dz * dz);
(int di, int dj, int dk) = field.GetBoundaryOffsets();
(int i, int j, int k) = field.IndicesAt(from);
for (int index = from; index < to; index++, i++)
{
if (i == nx)
{
j++; i = 0;
}
if (j == ny)
{
k++; j = 0;
}
double tx0 = (i == 0) ? vals[index + di] : vals[index - 1];
double tx1 = (i == nx - 1) ? vals[index - di] : vals[index + 1];
double ty0 = (j == 0) ? vals[index + dj] : vals[index - nx];
double ty1 = (j == ny - 1) ? vals[index - dj] : vals[index + nx];
double tz0 = (k == 0) ? vals[index + dk] : vals[index - nxy];
double tz1 = (k == nz - 1) ? vals[index - dk] : vals[index + nxy];
double t = vals[index] * 2.0;
deltas[index] += ((tx0 + tx1 - t) * dx + (ty0 + ty1 - t) * dy + (tz0 + tz1 - t) * dz) * rate;
}
}
}
/// <summary>
///
/// </summary>
public static void GetLaplacian(this GridField3d <Vec3d> field, Vec3d[] result, bool parallel = false)
{
if (parallel)
{
Parallel.ForEach(Partitioner.Create(0, field.Count), range => Body(range.Item1, range.Item2));
}
else
{
Body(0, field.Count);
}
void Body(int from, int to)
{
var vals = field.Values;
int nx = field.CountX;
int ny = field.CountY;
int nz = field.CountZ;
int nxy = nx * ny;
(var dx, var dy, var dz) = field.Scale;
dx = 1.0 / (dx * dx);
dy = 1.0 / (dy * dy);
dz = 1.0 / (dz * dz);
(int di, int dj, int dk) = field.GetBoundaryOffsets();
(int i, int j, int k) = field.IndicesAt(from);
for (int index = from; index < to; index++, i++)
{
if (i == nx)
{
j++; i = 0;
}
if (j == ny)
{
k++; j = 0;
}
Vec3d tx0 = (i == 0) ? vals[index + di] : vals[index - 1];
Vec3d tx1 = (i == nx - 1) ? vals[index - di] : vals[index + 1];
Vec3d ty0 = (j == 0) ? vals[index + dj] : vals[index - nx];
Vec3d ty1 = (j == ny - 1) ? vals[index - dj] : vals[index + nx];
Vec3d tz0 = (k == 0) ? vals[index + dk] : vals[index - nxy];
Vec3d tz1 = (k == nz - 1) ? vals[index - dk] : vals[index + nxy];
Vec3d t = vals[index] * 2.0;
result[index] = (tx0 + tx1 - t) * dx + (ty0 + ty1 - t) * dy + (tz0 + tz1 - t) * dz;
}
}
}
/// <summary>
///
/// </summary>
/// <param name="result"></param>
/// <param name="parallel"></param>
public static void GetGradient(this GridField3d <double> field, Vec3d[] result, bool parallel = false)
{
if (parallel)
{
Parallel.ForEach(Partitioner.Create(0, field.Count), range => Body(range.Item1, range.Item2));
}
else
{
Body(0, field.Count);
}
void Body(int from, int to)
{
var vals = field.Values;
int nx = field.CountX;
int ny = field.CountY;
int nz = field.CountZ;
int nxy = nx * ny;
(var dx, var dy, var dz) = (0.5 / field.Scale);
(int di, int dj, int dk) = field.GetBoundaryOffsets();
(int i, int j, int k) = field.IndicesAt(from);
for (int index = from; index < to; index++, i++)
{
if (i == nx)
{
j++; i = 0;
}
if (j == ny)
{
k++; j = 0;
}
double tx0 = (i == 0) ? vals[index + di] : vals[index - 1];
double tx1 = (i == nx - 1) ? vals[index - di] : vals[index + 1];
double ty0 = (j == 0) ? vals[index + dj] : vals[index - nx];
double ty1 = (j == ny - 1) ? vals[index - dj] : vals[index + nx];
double tz0 = (k == 0) ? vals[index + dk] : vals[index - nxy];
double tz1 = (k == nz - 1) ? vals[index - dk] : vals[index + nxy];
result[index] = new Vec3d((tx1 - tx0) * dx, (ty1 - ty0) * dy, (tz1 - tz0) * dz);
}
}
}
/// <summary>
/// http://micsymposium.org/mics_2011_proceedings/mics2011_submission_30.pdf
/// </summary>
/// <param name="field"></param>
/// <param name="deltas"></param>
/// <param name="slope"></param>
/// <param name="rate"></param>
/// <param name="parallel"></param>
public static void ErodeThermal(GridField3d <double> field, double[] deltas, double slope, double rate, bool parallel = false)
{
if (parallel)
{
Parallel.ForEach(Partitioner.Create(0, field.Count), range => Body(range.Item1, range.Item2));
}
else
{
Body(0, field.Count);
}
void Body(int from, int to)
{
var vals = field.Values;
int nx = field.CountX;
int ny = field.CountY;
int nz = field.CountZ;
int nxy = field.CountXY;
(double dx, double dy, double dz) = field.Scale;
dx = 1.0 / Math.Abs(dx);
dy = 1.0 / Math.Abs(dy);
dz = 1.0 / Math.Abs(dz);
(int di, int dj, int dk) = field.GetBoundaryOffsets();
(int i, int j, int k) = field.IndicesAt(from);
for (int index = from; index < to; index++, i++)
{
if (i == nx)
{
j++; i = 0;
}
if (j == ny)
{
k++; j = 0;
}
double value = vals[index];
double sum = 0.0;
double m, md;
//-x
m = ((i == 0) ? vals[index + di] : vals[index - 1]) - value;
md = Math.Abs(m * dx) - slope;
if (md > 0.0)
{
sum += Math.Sign(m) * md;
}
//+x
m = ((i == nx - 1) ? vals[index - di] : vals[index + 1]) - value;
md = Math.Abs(m * dx) - slope;
if (md > 0.0)
{
sum += Math.Sign(m) * md;
}
//-y
m = ((j == 0) ? vals[index + dj] : vals[index - nx]) - value;
md = Math.Abs(m * dy) - slope;
if (md > 0.0)
{
sum += Math.Sign(m) * md;
}
//+y
m = ((j == ny - 1) ? vals[index - dj] : vals[index + nx]) - value;
md = Math.Abs(m * dy) - slope;
if (md > 0.0)
{
sum += Math.Sign(m) * md;
}
//-z
m = (k == 0) ? vals[index + dk] - value : vals[index - nxy] - value;
md = Math.Abs(m * dz) - slope;
if (md > 0.0)
{
sum += Math.Sign(m) * md;
}
//+z
m = ((k == nz - 1) ? vals[index - dk] : vals[index + nxy]) - value;
md = Math.Abs(m * dz) - slope;
if (md > 0.0)
{
sum += Math.Sign(m) * md;
}
deltas[index] += sum * rate;
}
}
}