The objective of this paper is to give a study on Bezier and B-Spline curves. The paper has divided into three parts. The first studies Bezier curves and their mathematical solutions, while the second describes B-spline curves and their mathematical solutions. Finally, the application of B-spline curves in wavelet decomposition is shown. The PeakSignal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM) are considered for evaluation, and it is justified that Bezier and B-spline curves are indispensable in the field of computer graphics.