public static float CircleY(Vector vec)
{
float r = (float)Math.Sqrt(vec[0] * vec[0] + vec[1] * vec[1]) + 0.00001f;
//if (r == 0 || Math.Abs(2- r) < 0)
// return 0;
return (vec[0] + 0.00001f) / r * (float)Math.Exp(-Math.Abs(r - RADIUS)) * 20; //vec[0] / r * (1 - (1- r)*(1 - r)) * 20;
}
public static float BowlY(Vector vec)
{
float r = (float)Math.Sqrt(vec[0] * vec[0] + vec[1] * vec[1]) + 0.00001f;
//if (r == 0 || Math.Abs(2- r)<0)
// return 0;
return (vec[0] + 0.00001f) / r * 20f;
}
public SquareMatrix(Vector[] columns)
{
#if DEBUG
foreach (Vector col in columns)
Debug.Assert(columns.Length == col.Length); // Only sqare matrices allowed.
#endif
Columns = columns;
}
public SquareMatrix(SquareMatrix m)
{
#if DEBUG
foreach (Vector col in m.Columns)
Debug.Assert(m.Columns.Length == col.Length); // Only sqare matrices allowed.
#endif
Columns = new Vector[m.Columns.Length];
for (int c = 0; c < Columns.Length; ++c)
Columns[c] = new Vector(m.Columns[c]);
}
public virtual Vector Sample(VectorField field, Vector position)
{
// Query relevant edges and their weights. Result varies with different grid types.
int numCells = NumAdjacentPoints();
float[] weights;
int[] indices = FindAdjacentIndices(position, out weights);
Debug.Assert(indices.Length == weights.Length);
Vector result = new Vector(0, field.NumVectorDimensions);
// Add the other weightes grid points.
for (int dim = 0; dim < indices.Length; ++dim)
{
Vector add = field.Sample(indices[dim]);
if(add[0] == field.InvalidValue)
{
return new Vector(field.InvalidValue??float.MaxValue, field.NumVectorDimensions);
}
result += add * weights[dim];
}
return result;
}
public override bool InGrid(Vector position)
{
Debug.Assert(position.Length == Size.Length, "Trying to access " + Size.Length + "D field with " + position.Length + "D index.");
//int dims = _timeOrigin == null ? Size.Length : Size.Length - 1;
//Vector relPos = position - Origin.ToVec(dims);
//for (int dim = 0; dim < dims; ++dim)
//{
// if (relPos[dim] < 0 || relPos[dim] > Size[dim] - 1)
// return false;
//}
//if (_timeOrigin != null && (position.T < _timeOrigin || position.T > _timeOrigin + Size.T - 1))
// return false;
for (int dim = 0; dim < Size.Length; ++dim)
if (position[dim] < Origin[dim] || position[dim] >= Origin[dim] + Size[dim])
return false;
return true;
}
/// <summary> /// Returns all cell points necessary to interpolate a value at the position. /// </summary> /// <param name="position">The position in either world or grid space.</param> /// <param name="weights">The weights used for linear interpolation.</param> /// <returns>Scalar indices for acessing the grid.</returns> public abstract int[] FindAdjacentIndices(Vector position, out float[] weights);
// private float? _timeOrigin;
// private bool _timeDependent = false;
//public override float? TimeOrigin
//{
// get
// {
// return _timeOrigin;
// }
// set
// {
// //Debug.Assert((_timeDependent) == (value != null), "Please don't mess with time!");
// _timeOrigin = value;// ?? 0;
// Origin.T = value ?? Origin.T;
// }
//}
/// <summary>
/// Create a new rectlinear grid descriptor.
/// </summary>
/// <param name="size">Number of cells in each dimension.</param>
/// <param name="cellSize">Size of one cell, only used for rendering.</param>
public RectlinearGrid(Index size, Vector origin = null, float? timeOrigin = null)
{
Size = new Index(size);
Origin = origin ?? new Vector(0, size.Length);
TimeDependant = timeOrigin != null;
Origin.T = timeOrigin ?? Origin.T;
//_timeDependent = (timeOrigin != null);
//TimeOrigin = timeOrigin;
}
/// <summary>
/// Returns the adjacent grid point indices.
/// Indices in ascending order.
/// </summary>
/// <param name="pos"></param>
/// <param name="indices"></param>
/// <param name="weights"></param>
public override int[] FindAdjacentIndices(Vector pos, out float[] weights)
{
int numPoints = NumAdjacentPoints();
int[] indices = new int[numPoints];
weights = new float[numPoints];
Vector position = new Vector(pos);
Debug.Assert(InGrid(position) || ((Vector)Size + Origin - pos).Min() == 0);
Index gridPos = Index.Min((Index)(position - Origin), Size - new Index(1, Size.Length));
Vector relativePos = position - Origin - (Vector)gridPos;
// Convert to int.
int offsetScale = 1;
int index = 0;
// Have last dimension running fastest. Compute 1D index.
for (int dim = 0; dim < Size.Length; ++dim)
{
index += offsetScale * gridPos[dim];
offsetScale *= Size[dim];
}
// Linear interpolation in N dimensions.
for (int point = 0; point < numPoints; ++point)
{
int stepDim = 1;
int pointIndex = index;
float pointWeight = 1.0f;
// Compute the one dimensional index of each point.
for (int dim = 0; dim < Size.Length; ++dim)
{
// Is the dimth bit set?
if ((point & (1 << dim)) > 0)
{
// Extremum case: The value is on the outmost border. Clip that position.
if (gridPos[dim] < Size[dim] - 1)
pointIndex += stepDim;
pointWeight *= relativePos[dim];
}
else
{
pointWeight *= (1 - relativePos[dim]);
}
stepDim *= Size[dim];
}
// Accumulated all dimensions. Save value to output arrays.
indices[point] = pointIndex;
weights[point] = pointWeight;
}
return indices;
}
public override Vector Sample(Vector position)
{
Vector result = Grid.Sample(this, position);
// Work against the small numerical deviations here.
Debug.Assert(Math.Abs(result.T - 1) < 0.1f);
result[NumVectorDimensions - 1] = 1;
return result;
}
public Vector(Vector copy)
{
_data = (float[])copy.Data.Clone();
}
public override float Sample(Vector position)
{
Debug.Assert(_operationsAllowed, "The field data is not scaled to its grid yet.");
float time = position.T - Grid.TimeOrigin??0;
Vector samplePos = position;
Debug.Assert(time >= 0 && time < _slices.Length);
Vector slicePos = new Vector(samplePos.Length - 1);
Array.Copy(samplePos.Data, slicePos.Data, slicePos.Length);
float valueT = _slices[(int)time].Sample(slicePos);
float valueTNext = _slices[Math.Min((int)time + 1, NumTimeSlices-1)].Sample(slicePos);
float t = time - (int)time;
return (1 - t) * valueT + t * valueTNext;
}
public static Vector operator *(Vector a, Vector b)
{
Debug.Assert(a.Length == b.Length);
Vector prod = new Vector(a);
for (int dim = 0; dim < a.Length; ++dim)
prod[dim] *= b[dim];
return prod;
}
public static Vector operator /(Vector a, Vector b)
{
Debug.Assert(a.Length == b.Length);
Vector quot = new Vector(a);
for (int dim = 0; dim < a.Length; ++dim)
quot[dim] /= b[dim];
return quot;
}
public virtual float Sample(ScalarField field, Vector position)
{
// Query relevant edges and their weights. Reault varies with different grid types.
int numCells = NumAdjacentPoints();
float[] weights;
int[] indices = FindAdjacentIndices(position, out weights);
Debug.Assert(indices.Length == weights.Length);
// Start with the first grid point.
float result = field[indices[0]];
if (result == field.InvalidValue)
return (float)field.InvalidValue;
result *= weights[0];
// Add the other weightes grid points.
for (int dim = 1; dim < indices.Length; ++dim)
{
if (field[indices[dim]] == field.InvalidValue)
return (float)field.InvalidValue;
result += weights[dim] * field[indices[dim]];
}
return result;
}
public static Vector operator -(Vector a)
{
Vector neg = new Vector(a);
for (int dim = 0; dim < a.Length; ++dim)
neg[dim] = -neg[dim];
return neg;
}
public static Vector operator -(Vector a, Vector b)
{
Debug.Assert(a.Length == b.Length);
Vector diff = new Vector(a);
for (int dim = 0; dim < a.Length; ++dim)
diff[dim] -= b[dim];
return diff;
}
public static Vector operator +(Vector a, Vector b)
{
Debug.Assert(a.Length == b.Length);
Vector sum = new Vector(a);
for (int dim = 0; dim < a.Length; ++dim)
sum[dim] += b[dim];
return sum;
}
public abstract bool InGrid(Vector pos);
public override bool IsValid(Vector pos)
{
return ScalarsAsSFU[0].TimeSlices[0].Grid.InGrid(pos) && Scalars[0].IsValid(pos);
}
public static Vector operator /(Vector a, float b)
{
Vector quot = new Vector(a);
for (int dim = 0; dim < a.Length; ++dim)
quot[dim] /= b;
return quot;
}
public static Vector operator *(Vector a, float b)
{
Vector prod = new Vector(a);
for(int dim = 0; dim < a.Length; ++dim)
prod[dim] *= b;
return prod;
}
public override bool IsValid(Vector pos)
{
float[] weights;
int[] neighbors = _slices[0].Grid.FindAdjacentIndices(pos, out weights);
foreach (int neighbor in neighbors)
if (this[neighbor] == InvalidValue)
return false;
return true;
}
public static float Dot(Vector a, Vector b)
{
return (a * b).Sum();
}
public override Vector SampleDerivative(Vector position)
{
Debug.Assert(_operationsAllowed, "The field data is not scaled to its grid yet.");
float time = position.T;
// Get spacial sample position in grid space.
Vector samplePos = position;
Debug.Assert(time >= 0 && time < _slices.Length);
Vector slicePos = new Vector(samplePos.Length - 1);
Array.Copy(samplePos.Data, slicePos.Data, slicePos.Length);
// Sample data in current and next time slice.
Vector valueT = _slices[(int)time].SampleDerivative(slicePos);
Vector valueTNext = _slices[Math.Min((int)time + 1, NumTimeSlices - 1)].SampleDerivative(slicePos);
float t = time - (int)time;
Vector spaceGrad = (1 - t) * valueT + t * valueTNext;
// Add derivative in last dimension - always 0.
Vector gradient = new Vector(spaceGrad.Length + 1);
Array.Copy(spaceGrad.Data, gradient.Data, spaceGrad.Length);
gradient[spaceGrad.Length] = 1;
return gradient;
}
public Vector Abs()
{
Vector abs = new Vector(this);
for (int dim = 0; dim < Length; ++dim)
abs[dim] = Math.Abs(abs[dim]);
return abs;
}
/// <summary>
/// Access field by scalar index.
/// </summary>
public override Vector Sample(int index)
{
Debug.Assert(index >= 0 && index < Size.Product(), "Index out of bounds: " + index + " not within [0, " + Size.Product() + ").");
Vector vec = new Vector(NumVectorDimensions);
for (int dim = 0; dim < _scalarsUnsteady.Length; ++dim)
vec[dim] = Scalars[dim][index];
// Unsteady!
vec[NumVectorDimensions - 1] = 1;
return vec;
}
public Vector Normalized()
{
Vector norm = new Vector(this);
norm.Normalize();
return norm;
}
public virtual void ScaleToGrid(Vector scale)
{
Debug.Assert(Scalars.Length == scale.Length);
for (int dim = 0; dim < Scalars.Length; ++dim)
{
ScalarFieldUnsteady field = _scalarsUnsteady[dim];
field.ScaleToGrid(scale[dim]);
}
SpreadInvalidValue();
}
/// <summary>
/// Convert first N elements to a VecN. If less, fill with zeros.
/// </summary>
public Vector ToVec(int N)
{
Vector result = new Vector(0,N);
for (int dim = 0; dim < Math.Min(Length, N); ++dim)
result[dim] = this[dim];
return result;
}