File:Unknown curve animated.gif

English: Unknown curve in 2-space. It's parametric representation is as follows:

x = 5cost - 5cos80tsint;

y = 4sint - 2sin80t,

t ∈ [0,2π]

This animation's frames were generated using AutoCAD 2009 and a modified version of the following AutoLISP code:

   (defun x_gen (x)
   (* 5 (- (cos x)  (* (cos (* 80 x)) (sin x)) ) )
   )
   (defun y_gen (x)
   (* 2 (- (* (sin x) 2 ) (sin (* 80 x)) ))
   )
   (defun drawfc ()
   (command "._spline")
   (while (< start ende)
   (command (list (x_gen start) (y_gen start)))
   (setq start (+ start delta))
   )
   (command (list (x_gen ende) (y_gen ende)) "" "" "")
   )
   (defun c:draw_para2 (/ start ende delta)
   (setvar "CMDECHO" 0)
   (setq start (getreal "\nStart value (X): "))
   (setq ende (getreal "\nEnd value (X): "))
   (setq delta (getreal "\nPrecision: "))
   (drawfc)
   (princ)
   )

Note that the "spline" command was used for interpolation. Step size used was 0.01 units. Original uncropped jpeg frames may be made available upon request.