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The process for transforming a C++ class that is not compatible with CUDA into one that is involves a number of steps:

1. Identify the parts of the class that are not compatible with CUDA, such as any non-POD types, virtual functions, or use of dynamic memory allocation.

2. Modify the class to remove any non-POD types or virtual functions. This may involve changing the structure of the class, removing certain functionality, or replacing non-POD types with equivalent POD types.

3. Replace any dynamic memory allocation with CUDA-compatible memory allocation functions, such as cudaMalloc() and cudaFree().

4. Modify any class methods that use non-POD types or virtual functions to work with CUDA-compatible types and functions instead.

5. Test the class on a CUDA-enabled device to ensure it works correctly.

6. Optimize the class for performance on the CUDA device by using CUDA-specific optimization techniques, such as memory coalescing, shared memory, and kernel fusion.

7. Rinse and repeat until the class meets your desired performance and functionality requirements.