/// <summary>
/// Computes the change of area when mapping a direction from the hemisphere around the camera
/// to the image. Given by our transformation to spherical coordinates, followed by the scaling to the
/// desired resolution.
/// </summary>
/// <param name="pos">Position in world space of a point towards which the direction points</param>
/// <returns>
/// Jacobian determinant that describes how much larger an area on the image plane is than
/// the corresponding solid angle.
/// </returns>
public override float SolidAngleToPixelJacobian(Vector3 pos)
{
var dir = Vector3.Normalize(pos - position);
dir = Shading.ShadingSpace.WorldToShading(upVector, dir);
float theta = SampleWarp.CartesianToSpherical(dir).Y;
return(1 / (2 * MathF.PI * MathF.PI * MathF.Sin(theta)) * width * height);
}
Vector3 WorldToFilm(Vector3 pos)
{
Debug.Assert(width != 0 && height != 0);
var dir = pos - position;
float distance = dir.Length();
dir = Shading.ShadingSpace.WorldToShading(upVector, dir / distance);
var spherical = SampleWarp.CartesianToSpherical(dir);
return(new(
width * spherical.X / (2 * MathF.PI),
height *spherical.Y / MathF.PI,
distance
));
}
public void SphericalInverse()
{
// Y axis
var spherical = SampleWarp.CartesianToSpherical(Vector3.UnitY);
var dir = SampleWarp.SphericalToCartesian(spherical);
Assert.Equal(0, dir.X, 4);
Assert.Equal(1, dir.Y, 4);
Assert.Equal(0, dir.Z, 4);
spherical = SampleWarp.CartesianToSpherical(-Vector3.UnitY);
dir = SampleWarp.SphericalToCartesian(spherical);
Assert.Equal(0, dir.X, 4);
Assert.Equal(-1, dir.Y, 4);
Assert.Equal(0, dir.Z, 4);
// x axis
spherical = SampleWarp.CartesianToSpherical(Vector3.UnitX);
dir = SampleWarp.SphericalToCartesian(spherical);
Assert.Equal(1, dir.X, 4);
Assert.Equal(0, dir.Y, 4);
Assert.Equal(0, dir.Z, 4);
spherical = SampleWarp.CartesianToSpherical(-Vector3.UnitX);
dir = SampleWarp.SphericalToCartesian(spherical);
Assert.Equal(-1, dir.X, 4);
Assert.Equal(0, dir.Y, 4);
Assert.Equal(0, dir.Z, 4);
// z axis
spherical = SampleWarp.CartesianToSpherical(Vector3.UnitZ);
dir = SampleWarp.SphericalToCartesian(spherical);
Assert.Equal(0, dir.X, 4);
Assert.Equal(0, dir.Y, 4);
Assert.Equal(1, dir.Z, 4);
spherical = SampleWarp.CartesianToSpherical(-Vector3.UnitZ);
dir = SampleWarp.SphericalToCartesian(spherical);
Assert.Equal(0, dir.X, 4);
Assert.Equal(0, dir.Y, 4);
Assert.Equal(-1, dir.Z, 4);
}
