On 2/21/07, Steve Witham <sw@tiac.net> wrote:
For the Ovaloid where |P - F1| + k|P - F2| = c... ... If you make pictures before I do, I wouldn't mind if you posted them somewhere on the web.
The following script may be pasted directly into the window of Richard Morris' Algebraic Surface Solver at http://www.javaview.de/services/algebraic/index.html Reset resolution (coarse) from 8 to 32, click on "calculate". ((x^2 + y^2 + (z-a*w)^2) + c^2*(x^2 + y^2 + (z+a*w)^2) - 4*b^2*w^2)^2 - 4*c^2*(x^2 + y^2 + (z-a*w)^2)*(x^2 + y^2 + (z+a*w)^2); a = 1; b = 3/2; c = 4/3; w = 3/4; The resulting solid "egg" is the surface of rotation of Steve Gray's weighted oval about a vertical axis, substituting y -> z and x^2 -> x^2+y^2 in the original equation, and introducing a homogenising variable w to make rescaling easier. As before, 2a = focal distance, 2b = string length, c = Gray weighting (k). These may now be tinkered with at will within the range 1 <= c <= b/a; but if c > b/a, the curve becomes a limacon, and the bottom of the egg must be truncated [by adjusting the domain, increasing the scale factor 1/w, or slicing off with a teaspoon] to view the interior lobe. Fred Lunnon