Sunday, November 8, 2015

Elliptical Pizza Theorem

So to find the ellipse you find 2 additional points with the formulas above and then the well known method for drawing a conic through 5 points: conic through 5 points.. I think it does a nice job of describing how a pizza will look with perspective if lines perpendicular to the viewing plane are drawn to the right, top, and left of the pizza, calling those P1, P2, and P3 respectively...


Actually I was suggesting my above answer to the people at and they told me about this nice parametric equation that only needs the center point and any 2 points on the ellipse, where A is the center:


at 0 it equals C, at 1/2)*Pi it equals B, then at 2*pi back to C! 
This one just wows me after as hard as I worked to figure out the one above...
And from that I derived this one:

f(t) = (1/2)*D+(1/2)*B+((1/2)*B-(1/2)*D)*sin(t)+(C-(1/2)*D-(1/2)*B)*cos(t)

Which given 3 points on the ellipse parameterizes it so that between B and D is the shorter axis...

f(pi) gives the opposing point on the long axis that C is on...

Alternative Ellipse:


  1. please i need to draw minimum ellipse containing 3 points and the major axis must pass through origin .can you help me?

  2. Ah yeah I started putting my ideas in a different place a while back try this link:

    I added to this page as well, that facebook page I linked has a lot of newer stuff too!