摘要：Some local algorithms for the,preprocessing,of empirical data for both curves and surfaces are proposed so that the modified data,a polygon for curve data and a triangulation for surface data,can be used not only to approximate the given data with required accuracy,but also to preserve the shape and geometric and mathematical properties of the data such as convexity and monotonicity *** algorithms would produce small errors (O(h￣4)) if the initial data are accurate and reasonably distributed.