Abstract: In order to obtain the decomposition and reconstruction of Bézier curves and surface that are more suitable to be used in Internet transmission, the ribs and fans of Bézier curves and surfaces with endpoints G1 continuity are studied in this paper, and the corresponding smooth parts and detailed parts of the curves and surfaces are derived. On the other hand, given the smooth parts and detailed parts of a Bézier curve, the reconstruction algorithm of the curve is presented. In addition, the concepts of ribs and fans are generalized to triangular Bézier surfaces. The degree n triangular Bézier surface can be decomposed into one rib of degree n－1, one fan of degree n－3 and three Bézier curves(fans) of degree n－4. Numerical examples show that the decomposition of smooth parts and detailed parts of curves and surfaces in the paper is more effective and more convenient.