Abstract: Construction of Bézier surfaces with area-preservation parameterization constraints is one of the important topics in surface modeling.In order to construct biquadratic Bézier surfaces with area-preservation parameterization,two algorithms are proposed to automatically construct biquadratic Bézier surfaces in this paper.Firstly,the standard conditions of bilinear and biquadratic Bézier surfaces with area-preservation parameterization are obtained by using the first fundamental form,and the fact that the only bilinear rational Bézier surfaces satisfying area-preservation conditions are parallelograms is drawn.Next,according to the standard conditions,a method of surface construction is designed,and the conclusion that the only biquadratic Bézier surfaces with area-preservation parameterization are planar is drawn.Besides,a method of surface construction with great modeling ability is designed,thanks to the fact that the standard conditions have been relaxed.Finally,some biquadratic Bézier surfaces satisfying the area-preserving criteria are given,which shown in the created Windows-based applications using C++.Several examples of tessellation and texture mapping demonstrate that surfaces generated by proposed algorithms are area-preserving.