Study And Application Of Arc Spline

Arc spline is widely used in CNC. At first, this paper summerizes the main methods in freedom curve and surface and the application of NURBS methods in CNC .We introduce the background of arc spline which includes single arc spline, biarc and triarc.Secondly, this paper introduces the establishing method of plane biarc, then extends the method to establish space biarc. The paper presents the method of the interpolating points by biarc. It has important meaning to the curve shape control. This paper gives the biarc application in approximating the fair and error space points,which includes the formula of distance between space point and arc, the algorithm of judgement whether the distance between space points and arc is exceed the given error bound ,and the algorithm of point projection for a curve.Thirdly, this paper gives the method of approximating the NURBS curve in the plane and space by biarc. The main idea is to approximate the NURBS curve with a polygon, then to approximate the polygon with biarcs within the required tolerance. This paper gives the computation method between the line segment and an arc on the plane. This makes the computation more precise. This paper proposes a conputation method between the line segment and an arc in the space. This method computes the biggest distance by the optimization method. We use two approximation algorithms to approximate a NURBS curve by fewer biarc segments in the given error bound.At last, based on summerizing the triarc establishing method in the local system of coordinates, this paper proposes a necessary condition of triarc exist. This paper proposes a NURBS method to esteblish a triarc. On the plane, the triarc has a free parameter with one control point, and. proof that this control point is restrict in a line. The paper discusses the triarc shape and the bound of that control point in the line. This paper gives the method of exteblishing spapce triarc. Space triarc doesn't have free parameter. This establishing method is simple and easy to program.