/// <summary>
///
/// </summary>
/// <param name="result"></param>
/// <param name="parallel"></param>
public static void GetLaplacian(this GridField2d <double> field, double[] 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;
(var dx, var dy) = field.Scale;
dx = 1.0 / (dx * dx);
dy = 1.0 / (dy * dy);
(int di, int dj) = field.GetBoundaryOffsets();
(int i, int j) = field.IndicesAt(from);
for (int index = from; index < to; index++, i++)
{
if (i == nx)
{
j++; i = 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 t = vals[index] * 2.0;
result[index] = (tx0 + tx1 - t) * dx + (ty0 + ty1 - t) * dy;
}
}
}
/// <summary>
///
/// </summary>
public static void GetCurl(this GridField2d <Vec2d> field, double[] 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;
(var tx, var ty) = (0.5 / field.Scale);
(int di, int dj) = field.GetBoundaryOffsets();
(int i, int j) = field.IndicesAt(from);
for (int index = from; index < to; index++, i++)
{
if (i == nx)
{
j++; i = 0;
}
Vec2d tx0 = (i == 0) ? vals[index + di] : vals[index - 1];
Vec2d tx1 = (i == nx - 1) ? vals[index - di] : vals[index + 1];
Vec2d ty0 = (j == 0) ? vals[index + dj] : vals[index - nx];
Vec2d ty1 = (j == ny - 1) ? vals[index - dj] : vals[index + nx];
result[index] = (tx1.Y - tx0.Y) * tx - (ty1.X - ty0.X) * ty;
}
}
}
/// <summary>
///
/// </summary>
/// <param name="result"></param>
/// <param name="parallel"></param>
public static void GetGradient(this GridField2d <double> field, Vec2d[] 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;
(var dx, var dy) = (0.5 / field.Scale);
(int di, int dj) = field.GetBoundaryOffsets();
(int i, int j) = field.IndicesAt(from);
for (int index = from; index < to; index++, i++)
{
if (i == nx)
{
j++; i = 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];
result[index] = new Vec2d((tx1 - tx0) * dx, (ty1 - ty0) * dy);
}
}
}
/// <summary>
/// Calculates L1 (Manhattan) geodesic distance via Dijksta's algorithm as detailed in
/// http://www.numerical-tours.com/matlab/fastmarching_0_implementing/
/// </summary>
/// <param name="cost"></param>
/// <param name="sources"></param>
/// <param name="result"></param>
public static void GeodesicDistanceL1(GridField2d<double> field, double[] cost, IEnumerable<int> sources, IEnumerable<int> exclude = null)
{
// TODO handle additonal wrap modes
var dists = field.Values;
int nx = field.CountX;
int ny = field.CountY;
(double dx, double dy) = Vec2d.Abs(field.Scale);
var queue = new PriorityQueue<double, int>();
dists.Set(double.PositiveInfinity);
// enqueue sources
foreach (int i in sources)
{
dists[i] = 0.0;
queue.Insert(0.0, i);
}
// exclude
if (exclude != null)
{
foreach (int i in exclude)
dists[i] = 0.0;
}
// breadth first search from sources
while (queue.Count > 0)
{
(var d0, int i0) = queue.RemoveMin();
if (dists[i0] < d0) continue; // skip if lower value has been assigned
(int x0, int y0) = field.IndicesAt(i0);
// -x
if (x0 > 0)
TryUpdate(d0 + dx * cost[i0 - 1], i0 - 1);
// +x
if (x0 < nx - 1)
TryUpdate(d0 + dx * cost[i0 + 1], i0 + 1);
// -y
if (y0 > 0)
TryUpdate(d0 + dy * cost[i0 - nx], i0 - nx);
// +y
if (y0 < ny - 1)
TryUpdate(d0 + dy * cost[i0 + nx], i0 + nx);
// add to queue if less than current min
void TryUpdate(double distance, int index)
{
if (distance < dists[index])
{
dists[index] = distance;
queue.Insert(distance, index);
}
}
}
}
/// <summary>
/// Calculates L1 (Manhattan) geodesic distance via Dijksta's algorithm as detailed in
/// http://www.numerical-tours.com/matlab/fastmarching_0_implementing/
/// </summary>
/// <param name="cost"></param>
/// <param name="sources"></param>
/// <param name="field"></param>
public static void GeodesicDistanceL1(GridField2d<double> field, IEnumerable<int> sources, IEnumerable<int> exclude = null)
{
// TODO handle additonal wrap modes
var dists = field.Values;
int nx = field.CountX;
int ny = field.CountY;
(double dx, double dy) = Vec2d.Abs(field.Scale);
var queue = new Queue<int>();
dists.Set(double.PositiveInfinity);
// enqueue sources
foreach (int i in sources)
{
dists[i] = 0.0;
queue.Enqueue(i);
}
// exclude
if (exclude != null)
{
foreach (int i in exclude)
dists[i] = 0.0;
}
// breadth first search from sources
while (queue.Count > 0)
{
int i0 = queue.Dequeue();
var d0 = dists[i0];
(int x0, int y0) = field.IndicesAt(i0);
// -x
if (x0 > 0)
TryUpdate(d0 + dx, i0 - 1);
// +x
if (x0 < nx - 1)
TryUpdate(d0 + dx, i0 + 1);
// -y
if (y0 > 0)
TryUpdate(d0 + dy, i0 - nx);
// +y
if (y0 < ny - 1)
TryUpdate(d0 + dy, i0 + nx);
// add to queue if less than current min
void TryUpdate(double distance, int index)
{
if (distance < dists[index])
{
dists[index] = distance;
queue.Enqueue(index);
}
}
}
}
/// <summary>
///
/// </summary>
/// <param name="field"></param>
/// <param name="cost"></param>
/// <param name="sources"></param>
/// <param name="exclude"></param>
public static void GeodesicDistanceL2(GridField2d<double> field, double[] cost, IEnumerable<int> sources, IEnumerable<int> exclude = null)
{
// TODO handle additonal wrap modes
var dists = field.Values;
var nx = field.CountX;
var ny = field.CountY;
(var dx, var dy) = Vec2d.Abs(field.Scale);
var eikonal = new Eikonal2d(dx, dy);
var queue = new PriorityQueue<double, int>();
dists.Set(double.PositiveInfinity);
// enqueue sources
foreach (int i in sources)
{
dists[i] = 0.0;
queue.Insert(0.0, i);
}
// exclude
if (exclude != null)
{
foreach (var i in exclude)
dists[i] = 0.0;
}
// breadth first search from sources
while (queue.Count > 0)
{
(double d0, int i0) = queue.RemoveMin();
if (dists[i0] < d0) continue; // skip if lower value has been assigned
(int x0, int y0) = field.IndicesAt(i0);
if (x0 > 0) X(i0 - 1);
if (x0 < nx - 1) X(i0 + 1);
if (y0 > 0) Y(i0 - nx);
if (y0 < ny - 1) Y(i0 + nx);
// process x neighbor
void X(int index)
{
var d1 = dists[index];
if (d1 < d0) return; // no backtracking
double d2;
double minY = GetMinY(index); // will return infinity if neither neighbor has been visited
if (minY > double.MaxValue || !eikonal.Evaluate(d0, minY, cost[index], out d2))
d2 = d0 + dx * cost[index];
// add to queue if less than current min
if (d2 < d1)
{
dists[index] = d2;
queue.Insert(d2, index);
}
}
// process y neighbor
void Y(int index)
{
var d1 = dists[index];
if (d1 < d0) return; // no backtracking
double d2;
double minX = GetMinX(index); // will return infinity if neither neighbor has been visited
if (minX > double.MaxValue || !eikonal.Evaluate(minX, d0, cost[index], out d2))
d2 = d0 + dy * cost[index];
// add to queue if less than current min
if (d2 < d1)
{
dists[index] = d2;
queue.Insert(d2, index);
}
}
// returns the minimum adjacent value in the x
double GetMinX(int index)
{
if (x0 == 0) return dists[index + 1];
else if (x0 == nx - 1) return dists[index - 1];
return Math.Min(dists[index - 1], dists[index + 1]);
}
// returns the minimum adjacent value in the y
double GetMinY(int index)
{
if (y0 == 0) return dists[index + nx];
else if (y0 == ny - 1) return dists[index - nx];
return Math.Min(dists[index - nx], dists[index + nx]);
}
}
}
/*
* /// <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(HeVertexScalarField field, double[] deltas, double rate, bool parallel = false)
* {
* var vals = field.Values;
* var verts = field.Vertices;
*
* Action<Tuple<int, int>> func = range =>
* {
* for (int i = range.Item1; i < range.Item2; i++)
* {
* double sum = 0.0;
* int n = 0;
*
* foreach (var he in verts[i].IncomingHalfedges)
* {
* sum += vals[he.Start.Index];
* n++;
* }
*
* deltas[i] += (sum / n - vals[i]) * rate;
* }
* };
*
* if (parallel)
* Parallel.ForEach(Partitioner.Create(0, field.Count), func);
* else
* func(Tuple.Create(0, field.Count));
* }
*
*
* /// <summary>
* /// Adds the Laplacian of the field to the deltas array.
* /// The Laplacian is calculated with a user-defined weighting scheme.
* /// http://www.cs.princeton.edu/courses/archive/fall10/cos526/papers/sorkine05.pdf
* /// http://www.igl.ethz.ch/projects/Laplacian-mesh-processing/Laplacian-mesh-optimization/lmo.pdf
* /// </summary>
* /// <param name="field"></param>
* /// <param name="deltas"></param>
* /// <param name="rate"></param>
* /// <param name="hedgeWeights"></param>
* /// <param name="parallel"></param>
* public static void Diffuse(HeVertexScalarField field, double[] deltas, double rate, IReadOnlyList<double> hedgeWeights, bool parallel = false)
* {
* var vals = field.Values;
* var verts = field.Vertices;
*
* Action<Tuple<int, int>> func = range =>
* {
* for (int i = range.Item1; i < range.Item2; i++)
* {
* double value = vals[i];
* double sum = 0.0;
*
* foreach (var he in verts[i].OutgoingHalfedges)
* sum += (vals[he.End.Index] - value) * hedgeWeights[he.Index];
*
* deltas[i] += sum * rate;
* }
* };
*
* if (parallel)
* Parallel.ForEach(Partitioner.Create(0, field.Count), func);
* else
* func(Tuple.Create(0, field.Count));
* }
*/
/// <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(GridField2d <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;
(double dx, double dy) = field.Scale;
dx = 1.0 / Math.Abs(dx);
dy = 1.0 / Math.Abs(dy);
(int di, int dj) = field.GetBoundaryOffsets();
(int i, int j) = field.IndicesAt(from);
for (int index = from; index < to; index++, i++)
{
if (i == nx)
{
j++; i = 0;
}
double value = vals[index];
double sum = 0.0;
double m, md;
//-x
m = ((i == 0) ? vals[index + di] : vals[index - 1]) - value;
m *= dx;
md = Math.Abs(m) - slope;
if (md > 0.0)
{
sum += Math.Sign(m) * md;
}
//+x
m = ((i == nx - 1) ? vals[index - di] : vals[index + 1]) - value;
m *= dx;
md = Math.Abs(m) - slope;
if (md > 0.0)
{
sum += Math.Sign(m) * md;
}
//-y
m = ((j == 0) ? vals[index + dj] : vals[index - nx]) - value;
m *= dy;
md = Math.Abs(m) - slope;
if (md > 0.0)
{
sum += Math.Sign(m) * md;
}
//+y
m = ((j == ny - 1) ? vals[index - dj] : vals[index + nx]) - value;
m *= dy;
md = Math.Abs(m) - slope;
if (md > 0.0)
{
sum += Math.Sign(m) * md;
}
deltas[index] += sum * rate;
}
}
}