public static Vector2 IntegrateRK4(Vector2 position, float step, UniformGrid2DVector2 vectorField)
{
Vector2 v1 = vectorField.Interpolate(position);
Vector2 v2 = vectorField.Interpolate(position + 0.5f * step * v1);
Vector2 v3 = vectorField.Interpolate(position + 0.5f * step * v2);
Vector2 v4 = vectorField.Interpolate(position + step * v3);
float inverse6 = 1.0f / 6.0f;
float inverse3 = 1.0f / 3.0f;
return(position + step * (inverse6 * v1 + inverse3 * v2 + inverse3 * v3 + inverse6 * v4));
}
private void CalculateGradient()
{
// For each grid point in the terrain grid, do convolution using Sobel operator.
// Values for points that are out of range are treated as the center value.
// Initialize grid as a uniform grid of 2D vectors with the same size and number of points as the terrain grid.
gradientGrid = new UniformGrid2DVector2(terrainGrid.minPoint, terrainGrid.maxPoint, terrainGrid.numPointsX, terrainGrid.numPointsY);
for (int j = 0; j < terrainGrid.numPointsY; ++j)
{
for (int i = 0; i < terrainGrid.numPointsX; ++i)
{
// Extract the scalars.
float[,] scalars = new float[3, 3];
for (int b = 0; b < 3; ++b)
{
// Indicates whether to subtract 1, add 0 or add 1 to the j index.
int jTerm = b - 1;
for (int a = 0; a < 3; ++a)
{
// Indicates whether to subtract 1, add 0 or add 1 to the i index.
int iTerm = a - 1;
// Try to access the scalar at the index. If at an edge of the grid, exception is thrown and scalar set to NaN.
try {
scalars[a, b] = terrainGrid[i + iTerm, j + jTerm];
} catch (IndexOutOfRangeException) {
scalars[a, b] = float.NaN;
}
}
}
// Correct the NaN scalars.
CorrectScalars(scalars);
// The x-kernel takes the form:
// 1, 0, -1
// 2, 0, -2
// 1, 0, -1
// The z-kernel takes the form:
// -1, -2, -1
// 0, 0, 0
// 1, 2, 1
float partialX = scalars[0, 0] - scalars[2, 0] + 2 * scalars[0, 1] - 2 * scalars[2, 1] + scalars[0, 2] - scalars[2, 2];
float partialZ = scalars[0, 0] + 2 * scalars[1, 0] + scalars[2, 0] - scalars[0, 2] - 2 * scalars[1, 2] - scalars[2, 2];
gradientGrid[i, j] = new Vector2(partialX, partialZ);
}
}
}
public static Vector3 IntegrateRK4(Vector3 position, float step, UniformGrid2DVector2 vectorField)
{
return(HV2ToV3(IntegrateRK4(V3ToHV2(position), step, vectorField)));
}