@thor xb= x coordinate of blue dot, analogly for yb, xo= x coordinate of orange (transformed) dot, same fo yb.
xo=sqrt((xb)^2+(yb)^2)*cosa
yo=sqrt((xb)^2+(yb)^2*sina
a=atg(yb/xb). If you want orange dots to be equidistant add some constant to the upper equations. Hope this gives you some idea.
@thor What you want is transformation from polar to Descartes coordinate system, if you know coordinates of some point you want to transform you can express it in polar coordinate system, then using transformation equations you can project them on other coordinate system. Google "polar to rectangle coordinate system". I hope I was helpful somehow, if I understood your problem correctly.