1. Option A: By duplicating and reflecting Option \(A\), the curved elements can be rearranged to recreate parts of the original design on the left. Thus, \(A\) is correct.
2. Option B: Option \(B\) can also be duplicated and reflected to construct elements of the original design, including its symmetrical structure. Hence, \(B\) is correct.
3. Option C: The structure of \(C\) does not align with any part of the original image, even after duplication, rotation, or reflection. Thus, \(C\) is incorrect.
4. Option D: Option \(D\) provides the vertical and angular elements required to complete the original design when combined with other parts. Therefore, \(D\) is correct.
Conclusion: The correct options to recreate the design are \(A, B, D\).