Ocean 2: standing in the sea

Now we look at the water from a boat. For each pixel we shoot a ray from the camera and need to know where it meets the wave surface.

You know ray marching from the 3D lessons, but a height field allows a cheaper trick. Start at the point where the ray crosses a flat water level, then repeat: how far above the surface am I? q.y - waveH(q.xz). Move along the ray by about that much. When the waves are gentle this settles on the surface in a couple of dozen steps (a relaxed step, we only move 70% of the way so we never overshoot).

float t = min((ro.y - 0.3) / -rd.y, 80.0);   // where the ray meets a flat level
for (int i = 0; i < 24; i++)
{
    float3 q = ro + rd * t;
    t += (q.y - waveH(q.xz)) * 0.7;           // walk towards the real surface
}
float3 pos = ro + rd * t;

Lighting needs the normal. A height field makes that easy: measure the height a tiny bit to the left and right, and a tiny bit in front and behind. The slope gives the normal: (hL - hR, 2e, hD - hU), normalized.

Rays that point up never meet the water. They get a flat sky color for now.