1 Reply Latest reply on Mar 8, 2013 7:06 AM by Per Engberg

    Superellipse

    Frederik Hansen

      Hi

       

      I would like to draw a superellipse but I am having trouble with the "Equation Driven Curve" tool.

      I input the equation as so, as parametric: x=a*cos(t)^(2/n) and y=b*sin(t)^(2/n) where a, b and n is replaced with real numbers (I.E. a=2.3 b=4.2 n=3).

      These inputs only gives me a quater of the curve, where I would like the whole ellipse.

       

      I know I can just use the quater curve to make the whole, but is it not possible to get the whole curve at once?

       

      Reference: http://en.wikipedia.org/wiki/Superellipse

       

      Regards

      Frederik - Denmark

        • Re: Superellipse
          Per Engberg

          The formula you are using is only defined for 0 > t > pi/2. If you need the whole curve in one formula you need the next formula (from wikipedia):

           

           \begin{align} x\left(\theta\right) &= {|\cos \theta|}^{\frac{2}{n}} \cdot a \sgn(\cos \theta) \\ y\left(\theta\right) &= {|\sin \theta|}^{\frac{2}{n}} \cdot b \sgn(\sin \theta). \end{align}

           

          I don't think the sgn-funktion is available directly in sw. I would use the quarter-curve and either mirror the scetch or the feature.

           

          PS I made a super-ellipse protecting steel plate for my fireplace using the mirror technique :-)