Study on algorithm to generating quintic spline curve

Quintic spline curve based on arc length parameterization can realize second derivative continuity of combined curve, so the smooth transition for feed rate, acceleration and jerk could be ensured in the meaning of geometrical features of curve in high speed machining. First, the usual method to construct combined quintic spline curve through a series of discrete points on the original curve was introduced and it was pointed out that the system of equations of coefficient of quintic spline curves may be ill-conditioning during constructing them further. In order to solve the ill-conditioning system of equations of coefficient of them, the iterative improvement method to solve ill-conditioning system of equations was used to attempt to overcome this defect. Then, the performance of the constructed combined quintic spline curve was investigated with adaptive interpolation. Simulation on a piece of cardioid indicates iterative improvement method can be used to solve this kind of ill-conditioning system of equations of coefficient effectively. At last, the method to construct combined quintic spline curve was analyzed and discussed further.