A Kind Of Methods To Produce An Interpolation Smooth Curves Automatically

The interpolation of curves and surfaces has a long history.From traditional polynomial interpolation to the commonly used spline interpolation,and the recent basic function interpolation methods,there are a wide range of practical applications or theoretical significance.The curve surface interpolation studied in this paper is mainly to give a set of ordered point columns or grid points,construct a smooth curve or a surface through the point column or grid point.In this paper,we mainly study the construction of interpolation curves and surfaces by focusing on algebra and geometry.In the method of partial algebra,this paper studies the construct ion of segmented low-order Bézier curves,which are combined into a smooth interpolation curve through all given points by orderly s plicing.The inserted control vertices are obtained from a fixed-form linear formula provided in this paper.Interpolation curves with diff erent successive orders can be obtained using different interpolation formulas.The outstanding advantage of this method is that the sha pe of the curve is locally adjustable,with affine invariance and line ar correctness.The algorithm is simple and has more advantages fo r the interpolation of massive data.From the interpolation method,a series of interpolation basis functions are easily derived,and the basis function can quickly construct a smooth interpolation surfaceor reconstruct a surface.In the geometric method,this paper introduces the concept of using the generalized bump column,and proposes a new method of inserting three new control points based on the conserved continuous condition between each adjacent two points by using the intrinsic property of the polyline connected by ordered points.The method innovatively transforms the G-2 conserved convex continuous condition into an intuitive geometric condition,so that the five control points of the segmented four-time Bézier curve can be obtained at one time,thereby constructing the overall G-2 conserving convex continuous curve.This method can also produce G-2 continuous curves for non-generalized bump columns,and is generalized convex one by one.These methods have simple algorithms,a unified calculation format,and convenient calculation.Finally,an example is given to illustrate the effectiveness of the method.