} // Add
#endregion
#region Multiply by a scalar
/// <summary>
/// Multiply a spherical harmonic by a constant scale factor
/// </summary>
public static SphericalHarmonicL1 Multiply(SphericalHarmonicL1 x, float scale)
{
return(new SphericalHarmonicL1
{
weighting = x.weighting * scale,
c0 = { X = x.c0.X * scale, Y = x.c0.Y * scale, Z = x.c0.Z * scale },
c1 = { X = x.c1.X * scale, Y = x.c1.Y * scale, Z = x.c1.Z * scale },
c2 = { X = x.c2.X * scale, Y = x.c2.Y * scale, Z = x.c2.Z * scale },
c3 = { X = x.c3.X * scale, Y = x.c3.Y * scale, Z = x.c3.Z * scale }
});
} // Multiply
} // ExtractSphericalHarmonicForCubeFace
#endregion
#region Add
/// <summary>
/// Add two spherical harmonics together.
/// </summary>
public static SphericalHarmonicL1 Add(SphericalHarmonicL1 x, SphericalHarmonicL1 y)
{
return(new SphericalHarmonicL1
{
weighting = x.weighting + y.weighting,
c0 = { X = x.c0.X + y.c0.X, Y = x.c0.Y + y.c0.Y, Z = x.c0.Z + y.c0.Z },
c1 = { X = x.c1.X + y.c1.X, Y = x.c1.Y + y.c1.Y, Z = x.c1.Z + y.c1.Z },
c2 = { X = x.c2.X + y.c2.X, Y = x.c2.Y + y.c2.Y, Z = x.c2.Z + y.c2.Z },
c3 = { X = x.c3.X + y.c3.X, Y = x.c3.Y + y.c3.Y, Z = x.c3.Z + y.c3.Z }
});
} // Add
} // Multiply
#endregion
#region Lerp
/// <summary>
/// Linear interpolate (Lerp) between two spherical harmonics based on a interpolation factor.
/// </summary>
/// <param name="factor">Determines the interpolation point. When factor is 1.0, the output will be x, when factor is 0.0, the output will be y</param>
public static SphericalHarmonicL1 Lerp(SphericalHarmonicL1 x, SphericalHarmonicL1 y, float factor)
{
float xs = factor;
float ys = 1.0f - factor;
return(new SphericalHarmonicL1
{
weighting = x.weighting * xs + y.weighting * ys,
c0 = { X = xs * x.c0.X + ys * y.c0.X, Y = xs * x.c0.Y + ys * y.c0.Y, Z = xs * x.c0.Z + ys * y.c0.Z },
c1 = { X = xs * x.c1.X + ys * y.c1.X, Y = xs * x.c1.Y + ys * y.c1.Y, Z = xs * x.c1.Z + ys * y.c1.Z },
c2 = { X = xs * x.c2.X + ys * y.c2.X, Y = xs * x.c2.Y + ys * y.c2.Y, Z = xs * x.c2.Z + ys * y.c2.Z },
c3 = { X = xs * x.c3.X + ys * y.c3.X, Y = xs * x.c3.Y + ys * y.c3.Y, Z = xs * x.c3.Z + ys * y.c3.Z },
});
} // Lerp
} // SampleDirection
#endregion
#region Generate Spherical Harmonic from CubeMap
/// <summary>
/// Generate a spherical harmonic from the faces of a cubemap, treating each pixel as a light source and averaging the result.
/// </summary>
public static SphericalHarmonicL1 GenerateSphericalHarmonicFromCubeMap(TextureCube cubeMap)
{
SphericalHarmonicL1 sh = new SphericalHarmonicL1();
// Extract the 6 faces of the cubemap.
for (int face = 0; face < 6; face++)
{
CubeMapFace faceId = (CubeMapFace)face;
// Get the transformation for this face,
Matrix cubeFaceMatrix;
switch (faceId)
{
case CubeMapFace.PositiveX:
cubeFaceMatrix = Matrix.CreateLookAt(Vector3.Zero, new Vector3(1, 0, 0), new Vector3(0, 1, 0));
break;
case CubeMapFace.NegativeX:
cubeFaceMatrix = Matrix.CreateLookAt(Vector3.Zero, new Vector3(-1, 0, 0), new Vector3(0, 1, 0));
break;
case CubeMapFace.PositiveY:
cubeFaceMatrix = Matrix.CreateLookAt(Vector3.Zero, new Vector3(0, 1, 0), new Vector3(0, 0, 1));
break;
case CubeMapFace.NegativeY:
cubeFaceMatrix = Matrix.CreateLookAt(Vector3.Zero, new Vector3(0, -1, 0), new Vector3(0, 0, -1));
break;
case CubeMapFace.PositiveZ:
cubeFaceMatrix = Matrix.CreateLookAt(Vector3.Zero, new Vector3(0, 0, -1), new Vector3(0, 1, 0));
break;
case CubeMapFace.NegativeZ:
cubeFaceMatrix = Matrix.CreateLookAt(Vector3.Zero, new Vector3(0, 0, 1), new Vector3(0, 1, 0));
break;
default:
throw new ArgumentOutOfRangeException();
}
Color[] colorArray = new Color[cubeMap.Size * cubeMap.Size];
cubeMap.Resource.GetData <Color>(faceId, colorArray);
// Extract the spherical harmonic for this face and accumulate it.
sh += ExtractSphericalHarmonicForCubeFace(cubeFaceMatrix, colorArray, cubeMap.Size, cubeMap.IsRgbm, cubeMap.RgbmMaxRange);
}
//average out over the sphere
return(sh.GetWeightedAverageLightInputFromSphere());
} // GenerateSphericalHarmonicFromCubeMap
} // GetWeightedAverageLightInputFromSphere
private static SphericalHarmonicL1 ExtractSphericalHarmonicForCubeFace(Matrix faceTransform, Color[] colorDataRgb, int faceSize, bool isRgbm, float rgbmMaxRange)
{
SphericalHarmonicL1 sh = new SphericalHarmonicL1();
// For each pixel in the face, generate it's SH contribution.
// Treat each pixel in the cube as a light source, which gets added to the SH.
// This is used to generate an indirect lighting SH for the scene.
float directionStep = 2.0f / (faceSize - 1.0f);
int pixelIndex = 0;
float dirY = 1.0f;
for (int y = 0; y < faceSize; y++)
{
SphericalHarmonicL1 lineSh = new SphericalHarmonicL1();
float dirX = -1.0f;
for (int x = 0; x < faceSize; x++)
{
//the direction to the pixel in the cube
Vector3 direction = new Vector3(dirX, dirY, 1);
Vector3.TransformNormal(ref direction, ref faceTransform, out direction);
//length of the direction vector
float length = direction.Length();
//approximate area of the pixel (pixels close to the cube edges appear smaller when projected)
float weight = 1.0f / length;
//normalise:
direction.X *= weight;
direction.Y *= weight;
direction.Z *= weight;
Vector3 rgbFloat;
if (isRgbm)
{
Color rgbm = colorDataRgb[pixelIndex++];
rgbFloat = RgbmHelper.RgbmGammaToFloatLinear(rgbm, rgbmMaxRange);
}
else
{
Color rgb = colorDataRgb[pixelIndex++];
rgbFloat = new Vector3(GammaLinearSpaceHelper.GammaToLinear(rgb).X, GammaLinearSpaceHelper.GammaToLinear(rgb).Y, GammaLinearSpaceHelper.GammaToLinear(rgb).Z);
}
//Add it to the SH
lineSh.AddLight(rgbFloat, direction, weight);
dirX += directionStep;
}
//average the SH
if (lineSh.weighting > 0)
{
lineSh *= 1 / lineSh.weighting;
}
// Add the line to the full SH
// (SH is generated line by line to ease problems with floating point accuracy loss)
sh += lineSh;
dirY -= directionStep;
}
if (sh.weighting > 0)
{
sh *= 1 / sh.weighting;
}
return(sh);
} // ExtractSphericalHarmonicForCubeFace
