Visualization Notes: 01/04/20

Saturday, January 4, 2020

Random Polygon Plotting

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var('t,k'); n=randint(16,24)
a,b,c=randint(8,16),randint(13,19),2*randint(3,6)
s1=r'<p style="color:#00aaff;">'
s2=r'$a=%d; \; b=%d; \; c=%d; \; n=%d$</p>'
pretty_print(html(s1+s2%(a,b,c,n)))
fy(t,k)=cos(pi*t/n+2*k*pi/c)
fy(t,k)=fy(t,k)+cos(a*pi*t/n+2*k*pi/c)+cos(b*pi*t/n+2*k*pi/c)
fx(t,k)=sin(pi*t/n+2*k*pi/c)
fx(t,k)=fx(t,k)-sin(a*pi*t/n+2*k*pi/c)+sin(b*pi*t/n+2*k*pi/c)
L=[[[fx(t,k),fy(t,k)] 
    for t in range(2*n)] for k in range(2*c)]
sum([polygon2d(L[i],color=(0,random(),random()),
               thickness=.5,alpha=.1,axes=False) 
     for i in range(2*c)]).show(figsize=7)

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var('t,k'); n=randint(16,36)
a,b,c=randint(5,11),randint(13,19),2*randint(3,6)
s1=r'<p style="color:#ff00aa;">'
s2=r'$a=%d; \; b=%d; \; c=%d; \; n=%d$</p>'
pretty_print(html(s1+s2%(a,b,c,n)))
fy(t,k)=cos(pi*t/n+2*k*pi/c)
fy(t,k)=fy(t,k)+cos(a*pi*t/n+2*k*pi/c)+cos(b*pi*t/n+2*k*pi/c)
fx(t,k)=sin(pi*t/n+2*k*pi/c)
fx(t,k)=fx(t,k)-sin(a*pi*t/n+2*k*pi/c)+sin(b*pi*t/n+2*k*pi/c)
L=[[[fx(t,k),fy(t,k)] 
    for t in range(2*n)] for k in range(2*c)]
sum([polygon2d(L[i],color=(1,random(),random()),
               thickness=.5,fill=False,axes=False) 
     for i in range(2*c)])

Random Parametric 3D Plotting 2

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var('t'); a,b,c=randint(2,12),1+random(),randint(1,7)
r=[-c..c]; th=randint(1,9)
def col(): 
    return sage.plot.colors.float_to_html(random(),random(),random())
st=r'<p style="color:#aa00ff;">$a=%d; \; b=%f; \; c=%d$</p>'
pretty_print(html(st%(a,b,c)))
fx=(a+cos(b*t))*cos(t); fy=(a+cos(b*t))*sin(t); fz=a*sin(b*t)
sum([parametric_plot3d(
    [i*fx,j*fy,i*fz],(-2*pi,2*pi),frame=False,thickness=th/10,
    color=col()) for i in r for j in r])

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a,b,c=randint(1,3),randint(3,5),randint(2,4)
d,e,f=randint(10,12),randint(13,18),randint(1,3)
var('t'); r=[-1..1]; th=randint(1,9)
def col(): 
    return sage.plot.colors.float_to_html(random(),random(),random())
st1=r'<p style="color:#aa00ff;">$a=%d; \; b=%d; \; c=%d$</p>'
st2=r'<p style="color:#aa00ff;">$d=%d; \; e=%d; \; f=%d$</p>'
pretty_print(html(st1%(a,b,c)))
pretty_print(html(st2%(d,e,f)))
fx=-d*cos(t)-f*cos(b*t)+e*sin(a*t)
fy=-e*cos(a*t)+d*sin(t)-f*sin(b*t)
fz=d*cos(c*t)
sum([parametric_plot3d(
    [i*fx,j*fy,k*fz],(0,2*pi),color=col(),frame=False,thickness=th/10) 
     for i in r for j in r for k in r])

Random Parametric 3D Plotting

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import numpy,pylab,random
from mpl_toolkits.mplot3d import Axes3D
a,b,c=random.randint(2,12),1.5,random.randint(1,7) 
print('a=%d; b=%.1f; c=%d'%(a,b,c))
r=numpy.arange(1,c+1); th=.1+random.random() 
t=numpy.arange(-2*b*numpy.pi,2*b*numpy.pi,5/10**random.randint(1,3)) 
fx=(a+numpy.cos(b*t))*numpy.cos(t)
fy=(a+numpy.cos(b*t))*numpy.sin(t)
fz=numpy.sin(b*t)
fig,ax=pylab.subplots(
    figsize=(6.5,6.5),subplot_kw={"projection": "3d"})
for i in r:
    for j in r:
        for k in r:
            col=[random.random() for l in range(3)]
            ax.plot(i*fx,j*fy,k*fz,c=col,linewidth=th)
pylab.tight_layout(); pylab.axis('off'); pylab.show()

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import numpy,pylab,random
from mpl_toolkits.mplot3d import Axes3D
a,b=random.randint(1,3),random.randint(4,6)
c,d=random.randint(2,4),random.randint(9,11)
e,f=random.randint(14,16),random.randint(1,3)
print('a=%d; b=%d; c=%d; d=%d; e=%d; f=%d'%(a,b,c,d,e,f))
r=[-1,0,1]; th=.1+random.random() 
t=numpy.arange(0,2*numpy.pi+.5,1/10**random.randint(1,3)) 
fx=-d*numpy.cos(t)-f*numpy.cos(b*t)+e*numpy.sin(a*t)
fy=-e*numpy.cos(a*t)+d*numpy.sin(t)-f*numpy.sin(b*t) 
fz=d*numpy.cos(c*t)
fig,ax=pylab.subplots(
    figsize=(6.5,6.5),subplot_kw={"projection": "3d"})
for i in r:
    for j in r:
        for k in r:
            col=[random.random() for l in range(3)]
            ax.plot(i*fx,j*fy,k*fz,c=col,linewidth=th)
pylab.tight_layout(); pylab.axis('off'); pylab.show()