Optimal Circular and Linear Intepolation of Curve

Hi Community,

I am develop a software CAM inside CorelDraw for cutting laser machine. I need transform the parametric curves in Lines and Circular Arcs for obtain G Code compatible with CNC Laser. I have readed the article "Efficient circular arc interpolation based on active tolerance control", of Xunnian Yang and I have implement the first interpolation biarc and this works.

But I dont understand How implement the second part. I dont know How check if the three arcs form a spiral. Too say that the formula is of decrecient curvature. Is it a limiting for the implementation?

With biarc interpolation the precision is very good but the GCode generated is very big. How I can minimize the size of GCode inside the tolerance?

I have checked Spline G Code but this is very slow for this reason I want try with lines and circular arc inside the tolerance. The laser machines are very fast in your movements and I need obtain similar characteristics, but if I generate very big code G with G01 for aproximate a curve the speed is very slow. I have tried with G64 P0.01 but is slow too.