2 Replies Latest reply on Nov 19, 2010 8:12 AM by Harold Brunt

    limited complexity of equation driven curve?

      This is a 2D optical 4th-order aspheric curve of the form Dx^4+x^2/(R+(R^2+x^2(k+1) )^.5) that I'm trying to sketch, then revolve:


          y(x)= .0002629*x^4+x^2/(39.5194+(1561.78-27.7483*x^2)^.5)    -11 <= x <= 11


      and SW fails on it.  Click on the green checkmark and it just disappears w/o a trace.  Anyone know why?  Is there a limit on the length of the equation or the number of of nested parentheses?

        • Re: limited complexity of equation driven curve?
          Harold Brunt

          If I start plugging in the formula as written to an excel spreadsheet, several of the results for 1561.78-27.7483*x^2 are negative. Even after adding the 39.154 the square root will fail. Perhaps it is your order of operations.


          I couldn't resist playing with this. Is it also possible that your conic value should be -.2517? That way -27.7483 would just be -.7483 and the curve would look like this:


          Also, you might make your sketch from 0 to 11 so that you can revolve the curve about the center axis.


          4th order.JPG

          • Re: limited complexity of equation driven curve?
            Harold Brunt

            I have been thinking about this some more. I don't sleep much....


            I am more familiar with the conic formula in the form: y(x) = (x^2/R)/(1+(1-(1+(K))*(x/R)^2)^.5)


            It is a formula for a Rho variable driven conic curve where X determines the start and end points; K is the Rho variable where 0 = circle, 0 > K > -1 = ellipse, -1 = parabolic, and K < -1 is hyperbolic; R is the radius of curvature. To expand this for even coefficeints it would be: y(x) = (x^2/R)/(1+(1-(1+(K))*(x/R)^2)^.5) + Dx^2 + Dx^4...


            Another thing you might consider is that a revolved surface will be less accurate than a boundary surface when used as an optical reference surface. This a thread where the topic was discussed a while ago: https://forum.solidworks.com/message/157294#157294