debugging - Plotting hypotrochoids using Python -

i have been trying use computer plot hypotrochoids, i've run issues. unfamiliar, parametric equations of hypotrochoid are:

x(theta) = (r - r)cos(theta) + d*cos((r-r)/r*theta) 

and

y(theta) = (r - r)sin(theta) - d*sin((r-r)/r*theta) 

the definition on wikipedia of hypotrochoid can further explain:

a hypotrochoid roulette traced point attached circle of radius r rolling around inside of fixed circle of radius r, point distance d center of interior circle.

so hypotrochoid values r = d = 1 , r = 3, should this:

but not ending using computing method. hypotrochoid (with same values) looks this:

since x , y values determined function of x , y @ angle theta assumed loop through values of theta 0 2pi , calculate x , y values separately @ intervals, plot coordinate in polar form (where r**2 = x**2 + y**2), suppose thought wrong. maybe formulae wrong checked on few guys on @ math stackexchange , couldn't figure out what's wrong. methods should used calculate hypotrochoid if methods wrong?

here code:

class _basecurve(event.eventaware):      # basic curve class other curves inherit (as     # see below hypotrochoid class). happens     # each new curve class must implement function (relation) calculate     # radius of equation @ each angle interval, plots equation in     # other code elsewhere.      def __init__(self, radius, init_angle, end_angle, speed, acceleration, *args, **kwargs):          # initialize geometric data...         self.radius = radius          # initialize curve start , end angles...         self.init_angle = init_angle         self.end_angle = end_angle          # initialize time-based curve attributes...         self.speed = speed         self.accel = acceleration         self.current_pos = 0          # initialize defaults...         self.max_speed = inf         self.min_speed = neginf          self.args = args         self.kwargs = kwargs      def set_max_speed(self, speed):         """set maximum speed path can achieve."""         if speed < self.min_speed:             errmsg = "max speed cannot less min speed."             raise valueerror(errmsg)         self.max_speed = speed      def set_min_speed(self, speed):         """set minimum speed path can achieve."""         if speed > self.max_speed:             errmsg = "min speed cannot greater max speed."             raise valueerror(errmsg)         self.max_speed = speed      def set_acceleration(self, acceleration):         """set new acceleration path."""         self.accel = acceleration      def move(self):         """progress path forward 1 step.          amount progressed each time (curve).move called         depends on path's speed parameter , distance         (i.e. angle_difference) has travel. calculation         follows:          angle = angle_difference * current_position + init_angle          current_position position incremented         set speed in (curve).move().         """         self.current_pos += self.speed         if self.accel != 1:             new_speed = self.speed * self.accel             self.speed = max(min(new_speed, self.max_speed), self.min_speed)      def angle(self):         """return angle of curve @ current position."""         return self.angle_difference * self.current_pos + self.init_angle      def relation(self):         """return relationship of current angle radius.          blank function left filled in subclasses of         _basiccurve. return value function must function         (or lambda expression), of function's return value should         radius of curve @ current position. parameters of         return equation should follows:          (assuming `r` function representing relation):          radius = r(current_angle, *args, **kwargs)          *args , **kwargs additional *args , **kwargs specified         upon initializing curve.         """         return notimplemented      def position(self):         """calculate position on curve @ current angle.          return value of function coordinate in polar         form. view coordinate in cartesian form, use         `to_cartesian` function. # ignore `to_cartesian` function in code snippet, converts polar cartesian coordinates.          note: function requires self.relation implemented.         """         r = self.relation()         theta = self.current_angle          args = self.args         kwargs = self.kwargs          radius = self.radius*r(theta, *args, **kwargs)         return radius, theta      @property     def angle_difference(self):         """the difference between start , end angles specified."""         return (self.end_angle - self.init_angle)      @property     def current_angle(self):         """the current angle (specified self.current_pos)."""         return self.angle_difference * self.current_pos + self.init_angle  curve = _basecurve  class hypotrochoid(curve):     def relation(self):         def _relation(theta, r, r, d):             x = (r - r)*math.cos(theta) + d*math.cos((r - r)/r * theta)             y = (r - r)*math.sin(theta) - d*math.sin((r - r)/r * theta)             return (x**2 + y**2)**(1/2)         return _relation 

it mistake transform x,y , theta polar form output. theta parameter of parametric equation, not polar angle of curve point (really polar angle of small circle center)

so x , y ready-to use descartes' coordinates. plot point ever step. delphi test draws wanted (canvas.pixels[x, y] draws point (x,y) coordinates)

   r := 120;    rr := 40;    d:= 40;    := 0 999 begin      := * 2 * pi / 1000;      y := 200 + round((r - rr) * sin(a) - d*sin((r-rr)/rr*a));      x := 200 + round((r - rr) * cos(a) + d*cos((r-rr)/rr*a));      canvas.pixels[x, y] := clred;    end;