The following examples are used to explain a method for creating ellipse based surfboard rockers. These rocker examples are for illustration of the method. Actual ellipse heights and lengths must be adjusted to create rockers that are suitable for specific surfboard designs.
The blue ellipse-based rocker shown above was done with 2 ellipses of different sizes joined at the (vertical) midline when completed. Both Ellipses have the same width (same as board planshape). Pick the desired nose and tail rocker heights. Draw a straight line the length of the board -- I used a rectangle instead of a straight line. Mark where the surfboard wide point would be on that straight line. Align the (vertical) midline of each ellipse with the widepoint mark on the straight line. Now place marks (or boxes) of the desired nose and tail rocker heights at the appropriate ends of the straight line. Stretch the length of each ellipse, independently of one another until each elliptical curve touches the corner of both the nose and tail boxes. Join each of the half-ellipses at their midlines and trim the ends of the ellipses off at the points where their curves are touching the box corners at each end of the straight line. This creates an ellipse-based surfboard bottom rocker.
Hope this makes sense. Turned out wordier than expected. Very simple when viewed and created as a graphic (below). Purple is the nose rocker ellipse and red is the tail rocker ellipse. Green boxes are 2.0" high (tail rocker) and 4.7" high (nose rocker). Line widths were increased from 1.0 pt to 1.5 pt for blog posting.