17 Feb
2007
17 Feb
'07
2:54 p.m.
On 2/17/07, Steve Gray <stevebg@adelphia.net> wrote:
What about the locus of points such that d(A)+kd(B) is constant, where k is a real number and A,B are the focii. Wouldn't that make an oval?
Steve Gray
This gives a rather nice pointy oval, if k is chosen just less than (string length)/(focal distance), being the critical value where the curve becomes limacon-like. The equation is ((x^2 + (y-a)^2) + c^2*(x^2 + (y+a)^2) - 4*b^2)^2 - 4*(x^2 + (y-a)^2)*c^2*(x^2 + (y+a)^2) = 0, where 2a = focal distance, 2b = string length, c = Gray weighting k; with say a = 1, b = 1.5, c = 1.35 inside a 3x3 box. WFL