︠8ff8ea7d-e390-4cb1-9011-d8f99a23f610i︠
#---------------------------#
# Javier Pérez Lázaro       #
# Logroño (Spain)           #
# javier.perezl@unirioja.es #
#---------------------------#

#introduction

html('<h1><center>Spirograph</center></h1>')
text1='Spirograph is a tool for drawing hypotrochoids and epitrochoids.'
text2='Assume that a A is a point attached to a circle. A can be attached to the boundary of the circle or to any exterior or interior place. If the circle rolls around the outside of a fixed circle, the curve traced by the point A is called an epitrochoid. In case the circle rolls around the inside of a fixed circle, the curve is an hypotrochoid.'
text3='If the quotient between the radii of the circles is a rational number, then the curves are periodic.'

#the code

@interact
def fun(
tex1=text_control(text1), tex2=text_control(text2), tex3=text_control(text3),
h=('Select:',list(['epitrochoid','hypotrochoid'])),
tex4=text_control('Radius of the circle. Should be a rational number with shape p/q.'),
b=input_box(default=7/30,label='radius'),
tex5=text_control("Rate between the distance of the point to the circle's center and the radius."),
rate=input_box(default=1),
u=selector(['Plot the curve. Slider of % below enabled.',
'Build an animation of the plot with the number of frames specified below.'],label='Choose:'),
per=slider(0,100,1,default=100,label='graph %'),
frames=100,
cir_bool=checkbox(True, "Show circles?"),
auto_update=false):
    draw=True
    if h=='hypotrochoid' and (b>=1 or b<=0):
        print "In a hypotrochoid, radius must be between 0 and 1."
        draw=False
    if h=='epitrochoid' and b<=0:
        print "In a epitrochoid, radius must be positive"
        draw=False
    if draw==True:
        if h=='hypotrochoid': b=-b 
        var('t')
        cx=(1+b)*cos(t*b/(1+b))
        cy=(1+b)*sin(t*b/(1+b))
        px=cx-b*rate*cos(t)
        py=cy-b*rate*sin(t)
        axeM=1+max([0,b+abs(b)*rate])
        if u=='Plot the curve. Slider of % below enabled.':
            tMax=pi*denominator(b/(b+1))*per/50
            L=parametric_plot((px,py),(t,0,max([0.001,tMax])),plot_points=10*rate*tMax)
            if cir_bool: 
                p=point((px(t=tMax),py(t=tMax)),pointsize=30,color='blue')
                c=point((cx(t=tMax),cy(t=tMax)),pointsize=30,color='red')
                cir=circle((cx(t=tMax),cy(t=tMax)),b,color='red')
                lin=line([(cx(t=tMax),cy(t=tMax)),(px(t=tMax),py(t=tMax))])
                L+=circle((0,0),1)+cir+lin+p+c    
            show(L,aspect_ratio=1,xmin=-axeM,xmax=axeM,ymin=-axeM,ymax=axeM)
        if u=='Build an animation of the plot with the number of frames specified below.':
            tMax=2*pi*denominator(b/(b+1))
            step=tMax/(frames-1)
            curva=Graphics()
            v=[]
            for a in srange(step,tMax,step):
                curva+=parametric_plot((px,py),(t,a-step,a))
                L=curva
                if cir_bool:
                    cx_a=cx(t=a)
                    cy_a=cy(t=a)
                    px_a=cx_a-b*rate*cos(a)
                    py_a=cy_a-b*rate*sin(a)
                    p=point((px_a,py_a),pointsize=30,color='blue')
                    c=point((cx_a,cy_a),pointsize=30,color='red')
                    cir=circle((cx_a,cy_a),b,color='red')
                    lin=line([(cx_a,cy_a),(px_a,py_a)])
                    L+=circle((0,0),1)+cir+lin+c+p         
                v.append(L)
            animate(v,xmin=-axeM,xmax=axeM,ymin=-axeM,ymax=axeM,aspect_ratio=1).show()
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