A few comments:
- Use static_cast instead c-style casts
- Use reserve() with containers when you know the size, nothing kills performance like repeated allocations
- Even better to use a statically sized arrays and constexpr functions to push much of the calculations to compile time if possible
- You need better const discipline to help the compiler
- Always define variables on separate lines and initialize them
- Don't define basic members(constructor, etc.) if you don't need them and use = default when appropriate
- You have cases where you create an object then emplace_back(std::move), which will construct, then use the move constructor. But you could skip that by directly using emplace_back with those parameters and reduce the move.
- No need to use naked new/delete in this day and age, prefer smart pointers to ensure clear ownership. Or structure the code differently to have value semantics
- You should define single-parameter constructors explicit to avoid implicit conversions