(proc is the equivalent to a putpixel function. this is strictly out of the Allegro graphics library)

/* do_ellipse: *  Helper function for the ellipse drawing routines. Calculates the points *  in an ellipse of radius rx and ry around point x, y, and calls the  *  specified routine for each one. The output proc will be passed first a  *  copy of the bmp parameter, then the x, y point, then a copy of the d  *  parameter (so putpixel() can be used as the callback). */void do_ellipse(BITMAP *bmp, int x, int y, int rx, int ry, int d, void (*proc)()){   int ix, iy;   int h, i, j, k;   int oh, oi, oj, ok;   if (rx < 1)       rx = 1;    if (ry < 1)       ry = 1;   h = i = j = k = 0xFFFF;   if (rx > ry) {      ix = 0;       iy = rx * 64;      do {	 oh = h;	 oi = i;	 oj = j;	 ok = k;	 h = (ix + 32) >> 6; 	 i = (iy + 32) >> 6;	 j = (h * ry) / rx; 	 k = (i * ry) / rx;	 if (((h != oh) | | (k != ok)) && (h < oi)) {	    proc(bmp, x+h, y+k, d); 	    if (h) 	       proc(bmp, x-h, y+k, d);	    if (k) {	       proc(bmp, x+h, y-k, d); 	       if (h)		  proc(bmp, x-h, y-k, d);	    }	 }	 if (((i != oi) | | (j != oj)) && (h < i)) {	    proc(bmp, x+i, y+j, d); 	    if (i)	       proc(bmp, x-i, y+j, d);	    if (j) {	       proc(bmp, x+i, y-j, d); 	       if (i)		  proc(bmp, x-i, y-j, d);	    }	 }	 ix = ix + iy / rx; 	 iy = iy - ix / rx;      } while (i > h);   }    else {      ix = 0;       iy = ry * 64;      do {	 oh = h;	 oi = i;	 oj = j;	 ok = k;	 h = (ix + 32) >> 6; 	 i = (iy + 32) >> 6;	 j = (h * rx) / ry; 	 k = (i * rx) / ry;	 if (((j != oj) | | (i != oi)) && (h < i)) {	    proc(bmp, x+j, y+i, d); 	    if (j)	       proc(bmp, x-j, y+i, d);	    if (i) {	       proc(bmp, x+j, y-i, d); 	       if (j)		  proc(bmp, x-j, y-i, d);	    }	 }	 if (((k != ok) | | (h != oh)) && (h < oi)) {	    proc(bmp, x+k, y+h, d); 	    if (k)	       proc(bmp, x-k, y+h, d);	    if (h) {	       proc(bmp, x+k, y-h, d); 	       if (k)		  proc(bmp, x-k, y-h, d);	    }	 }	 ix = ix + iy / ry; 	 iy = iy - ix / ry;      } while(i > h);   }}/* ellipse: *  Draws an ellipse. */void ellipse(BITMAP *bmp, int x, int y, int rx, int ry, int color){   int clip, sx, sy, dx, dy;   if (bmp->clip) {      sx = x-rx-1;      sy = y-ry-1;      dx = x+rx+1;      dy = y+ry+1;      if ((sx >= bmp->cr) | | (sy >= bmp->cb) | | (dx < bmp->cl) | | (dy < bmp->ct))	 return;      if ((sx >= bmp->cl) && (sy >= bmp->ct) && (dx < bmp->cr) && (dy < bmp->cb))	 bmp->clip = FALSE;      clip = TRUE;   }   else      clip = FALSE;   do_ellipse(bmp, x, y, rx, ry, color, bmp->vtable->putpixel);   bmp->clip = clip;}

x(theta) = rx cos(theta)
y(theta) = ry sin(theta)
where 0 < theta < 2 pi
rx being the radius in the x, ry being the radius in the y.
So simply take the angle of your point, place it into the equation and find out if it is further from the origin than the point passed back by the equation.

This info was stolen from http://www.swin.edu.au/astronomy/pbourke/
check under geometry for nice 4D shapes and superellipsoid geometry

The algebraic definition is...

 x^2     y^2     z^2----- + ----- + ----- = 1rx^2    ry^2    rz^2

The parametric definition requires 2 spherical angles and goes something like this...

   X = rx*cos(Phi)*Sin(Theta)   Y = ry*sin(Phi)   Z = rz*cos(Phi)*cos(Theta)

- C.P.I. / ASMiNC

where 0 < theta < 2 pi

I used to have the sin(theta) and cos(theta) the other way around, but this way it normally produces a horizontal ellipse when rx is bigger than ry and gamma = 0
(I just did this off the top of my own head from the trigonometry I could remember, so if it's wrong....)

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just kidding, I have no idea