Plotting Big Ellipses

Sometimes Just like with arcs, the path of an elliptical curve is just to large to draw out with any convenient method. When this happens, just like with circular arcs you can "plot" the path as opposed to drawing it. This can be accomplished with either the use of a little algebra or trigonometry.

There are two methods that you can use and their respective formula look like this:

y-axis position = (Semi-Minor Axis ÷ Semi-Major Axis) × SQRT(Semi-Major Axis² – x²)
a Cos[t], b Sin[t]

The first method requires you to set off a known distance along the x major axis of the ellipse and by using the measurement of that distance with the formula, calculate the "y" distance from it. This give the location of a point directly above that point on the x-axis in the y-axis direction.

The second method requires you to work with the angles between 0° and 90°. In the second formula you plot the x-y point pair by calculating their respective positions with {aCos[t]} for the x-axis position and {bSin[t]} for the y-axis position.

All written, photographic and drawn materials property of and copyrighted by josephfusco.org 1997-2010.

No materials may be used in any way without the written permission of Joseph Fusco

	Enter your search terms Submit search form Web www.josephfusco.org CFO