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Algorithm for drawing an arc

  1. May 6, 2013 #1
    Hi,
    I'm working through thinkpython and there is an exercise which requires drawing flowers and arcs. I'm having some trouble understanding the arc function.

    Code (Text):
    def arc(t, r, angle):
        """Draws an arc with the given radius and angle.

        t: Turtle
        r: radius
        angle: angle subtended by the arc, in degrees
        """
        arc_length = 2 * math.pi * r * abs(angle) / 360
        n = int(arc_length / 4) + 1
        step_length = arc_length / n
        step_angle = float(angle) / n

        # making a slight left turn before starting reduces
        # the error caused by the linear approximation of the arc
        lt(t, step_angle/2)
        polyline(t, n, step_length, step_angle)
        rt(t, step_angle/2)
    Here's the polyline code called from the above function:
    Code (Text):
    def polyline(t, n, length, angle):
        """Draws n line segments.

        t: Turtle object
        n: number of line segments
        length: length of each segment
        angle: degrees between segments
        """
        for i in range(n):
            fd(t, length)
            lt(t, angle)
     

    I'm unsure about this part:
    Code (Text):
     n = int(arc_length / 4) + 1
    I'm guessing the purpose of n is to divide up the movements into separate iterations. How come it's set to arc_length / 4 + 1


    Code (Text):
    step_angle = float(angle) / n
    I'm guessing this is dividing up the total angle subtended by the arc into little bits which it gradually carves out....
     
  2. jcsd
  3. May 6, 2013 #2
    It looks like the value for n (number of arc segments) is fairly arbitrary, and you're right, the step angle is what an arc segment subtends for a given segment of the total arc.
     
  4. May 6, 2013 #3
    What are the units of 'r' ?

    I think those are the same units of the dividing 4

    So, it seems to me that they are choosing to draw an arc as small straight lines, except when the arc is smaller than 4, in which the division yields a number smaller than 1 and the int() operation yields zero, which leaves you back with the + 1

    In other words, they are choosing the "small segments" to be approx 4 units long, or so, every time.

    make sense? or am I missing something?
     
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