How can I simulate objects floating on water without a physics engine?

Question

In my game the water movement is done in a shader using Gerstner equations. The water movement looks realistic enough for a school project but I encounter serious problem when I wanted to do sailing on waves (similar to this). I managed to do collision with land by calculating quad's vertices and normals beneath ship, however same method can not be applied to water because XZ are displaced and Y is calculated in a shader :(

1. How to approach this problem ?

2. Is it possible to retrieve transformed grid from shader?

3. Unfortunately no external physics libraries can be used.

Answer 1

1. How to approach this problem?

Move the simulation of the wave height to the CPU. Depending on which works better for you and your logic/performance needs, you can move the entire simulation to the CPU and simply send the computed coordinates to the GPU (avoiding duplicate work) or you can do a simpler approximation of the computation on the CPU.

2.Is it possible to retrieve transformed grid from shader?

Not easily. Shaders aren't really designed for that. You can do various things to make the GPU do general purpose computation and read the results back on the CPU, and various GPGPU ("general purpose GPU") libraries and tools exist to wrap and abstract all that complexity, such as OpenCL. However, in this particular case it's unlikely to be that useful for you.

3.Unfortunately no external physics libraries can be used

That's fine, you should not need them, you've already done the majority of work you need.