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The research on computer graphics (CG) has been actively studied and developed. Namely, many surface/solid models have been proposed in the field of computer aided geometric design as well as the one of CG. Since it is difficult to visualize the complex shape exactly, an approximation by generating a set of meshes is usually used. Therefore it is important to guarantee the quality of the approximation in consideration of the computational cost. In this paper, an adaptive mesh generation algorithm is proposed for a surface defined by Lie algebra, which is useful in the field of computer vision. The proposed algorithm considers the variation of normal vectors with automatic differentiation around the calculated point on the surface. By the method a set of meshes for the surface can be generated adoptively and automatically with high quality at low computational cost. And, in order to apply to the realtime system such as CAVE, determine the adaptive resolution considering the viewpoint.