What is an ellipse? (Rewritten from an article dated 1915, All drawings are edited to enhance the original text by Bud Goodman). If a plane is passed through a cone or cylinder perpendicular to the axis, the line of the intersection will be a circle. If, however, the plane is passed oblique to the axis of the cone or cylinder the line of the intersection will be an ellipse.
An ellipse is a closed curve which has two axes, namely, a major axis, or longest diameter, and a minor axis, or shortest diameter. It also has two points on the major axis called the foci, which lie equidistant from it's center. Note: in nearly all cases where an eliptical curve is wanted, The dimensions of the long and short axes are known.
There are a number of methods by which an ellipse may be drawn. With the exception of the first method, to be explained, they all depend upon the location of a number of points through which a curved line is to be drawn with the irregular curve. This in many cases will not lead to good results, especially if the ellipse is small, under 3 inches long. To offset this difficulty many ingenious methods have been devised to draw ellipse with circular arcs. These methods will not give true eliptic curve, but are accurate enough in nearly all cases where such a curve is wanted. First Method (by intersecting arcs) Having given the length of the major and minor axes AB and CD respectively. Find the foci (F and F') by drawing small arcs with AO as a radius and C as a center, cutting AB in F and F'. With F as a center and any radius greater than AF, say AG, discribe a small arc. From F' as a center and GB as a radius, discribe a small arc intercesting the first arc in H. This will be one point on the required curve. Again with F as a center and AJ as the radius,draw another arc; and with F' as a center and JB as a radius draw an arc intersecting the first arc at K,. which will be another point on the curve. Similarly, other points may be found, through which a smooth curve may be drawn.
Notice the length from A to B is that of the same F to C and down to F'
Note: ---FC + CF' = AB, Also FH + HF' = AB, etc. Other methods are...
By Trammel Method / with intersecting lines (Not arcs as shown above) / Approximate ellipse using four circular arcs.
