I'm an artist trying to sculpt shapes that I would describe as ellipsoids. I am wanting to sew together fabric to form these shapes, and although I know the dimensions of the ellipsoid I want to form, I don't know how to calculate the curvature of the pieces of fabric so they come together to form the ellipsoid (similar to gores on a globe).
For a sphere, I found the formula for the edges of the fabric to be: y = +/- R (pi/N) cos(x/R). N is the amount of gores, and x is the angular height. Source: https://www.themathdoctors.org/making-a-sphere-from-flat-material/?unapproved=21662&moderation-hash=f9644b82fc5759e707821810bd9753e8#comment-21662
But I'm not sure how to translate this formula into elliptical terms. The ellipsoid I'm trying to form has radii of 4.5 and 2.75 in. Does anyone have any suggestions, or know where I could turn to study this more?
Interesting question. I assume your gores are lens shaped and flat. You make $N$ large enough so that the completed figure is spherical enough for your purpose.
Now note that your ellipsoid is just a sphere stretched out uniformly along the $x$ axis. So you can just stretch that dimension of the gores.
In this image
with $N$ gores the gore when flattened has central width $$ w = \frac{a \pi}{N} . $$ Its edges have equation $$ y = \pm w \cos(\pi x/b) . $$