Shading via GPU and body radiometry

docs/optics.md

@@ -313,17 +313,75 @@ Picking the exposure time is the same trade a photographer makes. A longer
 exposure saturates the sunlit target. A shorter one leaves the side of the
 target lit only by Earthshine lost in noise once noise is modeled (M3).
 
+## Earth, Moon and Sun
+
+Code: `bodies.rs`, `gpu/bodies.rs`, `shaders/bodies.wgsl`.
+
+The three bodies are not drawn as triangle meshes. For every pixel, the
+shader sends a ray from the camera through the pixel's center and solves
+for where it meets each body's exact shape. The nearest hit wins. This
+gives an exact edge at any zoom, at the cost of a few arithmetic operations
+per pixel. A mesh would show its facets along the limb, the edge of the
+disk, which is the feature horizon-based navigation measures.
+
+- **Earth** is the WGS84 ellipsoid: 6378.137 km equatorial radius,
+  6356.752 km polar. The 21 km difference matters at fine pixel scales. A
+  camera with 5.5 urad pixels at 200,000 km sees the north limb 19 pixels
+  away from where a spherical Earth would put it. A test checks the limb
+  against the exact tangent to the ellipsoid to within a pixel.
+- **The Moon** is a sphere of 1737.4 km radius. From Earth's distance it
+  is about 0.52 degrees across, 82 pixels in the example camera.
+- **The Sun** is a sphere of 695,700 km radius: 0.53 degrees across, about
+  85 pixels in the example camera. Its disk has the solar radiance from the
+  folding section above, and it is drawn only where no nearer body covers
+  it. So Earth eclipses it naturally.
+
+### Shading
+
+Earth and the Moon are Lambertian, with one albedo each, set by
+`Appearance`: 0.3 for Earth and 0.12 for the Moon, flat across wavelength.
+Each point's radiance is rho cos(i) S_k / (pi d^2), with i the angle between
+the surface normal and the Sun. The night side has i past 90 degrees and is
+black. The Sun's distance d is taken from each body's center, since the
+difference across a body is a few parts in 10^5.
+
+This gets the overall brightness and the phase (how much of the disk is
+lit) right. It misses some things that are visible in real images:
+
+- Earth's oceans, land and clouds differ in brightness by a factor of
+  several. An albedo map comes in M2.
+- The full Moon looks almost uniformly bright out to its edge. A Lambertian
+  sphere instead darkens toward the edge, because the light there arrives
+  and leaves at grazing angles. Lunar soil scatters light back toward its
+  source much more strongly than Lambert predicts, and a dedicated lunar
+  reflectance model (M4) fixes that. The Moon's maria (the dark plains of
+  old basalt lava, the "seas" seen with the naked eye) and its bright
+  highlands also differ in albedo by about a factor of two (M2 albedo
+  map).
+- Earth's atmosphere softens the limb and adds a thin bright band around it
+  (M4). Here Earth's edge is a sharp line.
+
+### Depth from the bodies
+
+The pass also writes each hit's depth, near / z, as described in the
+geometry section. The target spacecraft, drawn after the bodies, uses the
+same depth buffer. So a target in front of Earth covers it, and a target
+behind Earth's limb is hidden.
+
 ## Not modeled yet
 
 | Effect | Where |
 |---|---|
 | Light from Earth and the Moon illuminating the target (Earthshine, Moonshine) | M2 |
+| Earth's shadow on the Moon (lunar eclipses) | M2 |
+| Earthshine on the Moon's night side | M4 |
 | Shadows the target casts on itself | M2 |
 | The Sun as a disk that is darker toward its edge (limb darkening) | M2 |
 | Lens distortion | M3 |
 | Blur from diffraction and lens imperfections (point spread function) | M3 |
 | Noise: photon shot noise, read noise, dark current, pixel-to-pixel variation | M3 |
 | Saturation spilling into neighbors (blooming) | M3 |
-| Non-Lambertian materials (BRDFs), glints | M4 |
+| Non-Lambertian materials (BRDFs), glints, lunar backscatter | M4 |
+| Earth and Moon albedo maps | M2 |
 | Earth's atmosphere: scattering, the bright limb | M4 |
 | Motion blur, rolling shutter, stray light | M6 |