function circle_y(x,r,cx=0,cy=0) = (2*cy + sqrt(8*cx*x-4*cx*cx-4*(x)*(x)+4*r*r))/2;

function curve_r(curve_h,curve_w)=(pow(curve_h,2)+pow(curve_w,2))/(2*abs(curve_w));

function mix(base,target,ratio) = base*(1-ratio)+target*ratio;