Tachyon 3D Ray Tracers 3

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t=Tachyon(xres=600,yres=400,camera_center=(2,0,0))

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t.light((3,2,1),.3,(1,1,1))

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p1=(0,.7,0); p2=(.7,0,0)

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p3=(0,0,.7); p4=(-.7,-.7,-.7)

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t.texture('tr',ambient=.01,diffuse=.3,

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          specular=.5,opacity=.5,color=(1,0,0))

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t.texture('tg',ambient=.05,diffuse=.6,

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          specular=.75,opacity=.75,color=(0,1,0))

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t.texture('tb',ambient=.1,diffuse=.9,

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          specular=1.,opacity=1.,color=(0,0,1))

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t.sphere(p1,.2,'tr'); t.sphere(p2,.2,'tg')

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t.sphere(p3,.2,'tb'); t.fcylinder(p1,p4,.05,'tr')

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t.fcylinder(p2,p4,.05,'tg'); t.fcylinder(p3,p4,.05,'tb')

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t.show()

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Messages

Creating Maps

<script src='https://d3js.org/d3.v3.min.js'></script>
<script src='https://d3js.org/topojson.v0.min.js'></script>
was added in the page head.

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%%html

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<style>#svg1 {background-color:midnightblue;}

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.land {fill:#3636ff; stroke:silver;}

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.countries {fill:none; stroke:silver;}

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</style><svg id='svg1' width='640px' height='420px'/>

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<script type='text/javascript'>

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var projection=d3.geo.equirectangular().translate([120,260]);

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var svg=d3.select('#svg1'),g=svg.append('g');

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var path=d3.geo.path().projection(projection);

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var url1='https://raw.githubusercontent.com/n1n9-jp/',

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    url2='CSIS_map_140514/master/data/',

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    file='world-50m.json';

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d3.json(url1.concat(url2).concat(file),

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        function(world) {

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            g.attr('class','land').selectAll('land')

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             .data([topojson.object(world,world.objects.land)])

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             .enter().append('path').attr('d',path);

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            svg.attr('class','countries').selectAll('countries')

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               .data([topojson.object(world,world.objects.countries)])

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               .enter().append('path').attr('d',path);});

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Messages

Dictionary Vectorizers

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global_station_temperature=\

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[{'year':2017,'month':'Jan','temperature':113},

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 {'year':2017,'month':'Feb','temperature':141},

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 {'year':2017,'month':'Mar','temperature':137},

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 {'year':2017,'month':'Apr','temperature':115},

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 {'year':2017,'month':'May','temperature':122},

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 {'year':2017,'month':'Jun','temperature':76},

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 {'year':2017,'month':'Jul','temperature':108},

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 {'year':2017,'month':'Aug','temperature':110},

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 {'year':2017,'month':'Sep','temperature':96},

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 {'year':2017,'month':'Oct','temperature':115},

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 {'year':2017,'month':'Nov','temperature':105},

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 {'year':2017,'month':'Dec','temperature':115},

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 {'year':2018,'month':'Jan','temperature':103},

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 {'year':2018,'month':'Feb','temperature':114},

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 {'year':2018,'month':'Mar','temperature':121},

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 {'year':2018,'month':'Apr','temperature':120},

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 {'year':2018,'month':'May','temperature':100},

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 {'year':2018,'month':'Jun','temperature':86},

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 {'year':2018,'month':'Jul','temperature':106},

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 {'year':2018,'month':'Aug','temperature':90},

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 {'year':2018,'month':'Sep','temperature':89},

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 {'year':2018,'month':'Oct','temperature':111},

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 {'year':2018,'month':'Nov','temperature':97},

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 {'year':2018,'month':'Dec','temperature':121}]

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from sklearn.feature_extraction import DictVectorizer

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DV=DictVectorizer(sparse=False)

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temp_features=DV.fit_transform(global_station_temperature)

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temp_features=temp_features.astype('int16')

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print(temp_features[:3]) 

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print(DV.get_feature_names_out()[:5])

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print(DV.get_feature_names_out()[5:10])

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print(DV.get_feature_names_out()[10:])

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---

Messages

Definite Integrals

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from sage.symbolic.integration.integral import definite_integral

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var('x,y'); f1,f2=2^x,2*x-x^2; x1,x2=0,2; y1,y2=0,4; d=1 

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s=definite_integral(f1-f2,x,x1,x2)

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l=[[0,0]]+[[.01*i,f1(x=.01*i)] for i in range(200)]+\

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  [[2,0]]+[[.01*i,f2(x=.01*i)] for i in range(200,0,-1)]

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st=r'<left><font>$\displaystyle{S = %s = %s}$</font></left>'

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pretty_print(html(st%(str(s),str(s.n()))))

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p1=plot([f1,f2],(x,x1,x2),fill={0:[1]},thickness=3,

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        fillcolor='#3636ff',color='silver')

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p2=region_plot([y-f1<0,y-f2>0],(x,x1,x2),(y,y1,y2),

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               alpha=.5,incol='#3636ff',

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               borderwidth=3,bordercol='silver')

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p3=polygon2d(l,color='#3636ff',edgecolor='silver',

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             thickness=5,alpha=.5)

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g=graphics_array((p1,p2,p3))

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g.show(xmin=x1-d,xmax=x2+d,ymin=y1-d,ymax=y2+d,

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       figsize=6,aspect_ratio=1)

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definite_integral(f1-f2,x,x1,x2).n()==\

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(definite_integral(f1,x,x1,x2)-definite_integral(f2,x,x1,x2)).n()

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---

Messages

Built-in Colors

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c=list(colors.keys())

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f(x,t)=sin(5*x)^2+.02*t

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@interact

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def _(n=[20,28,..,len(c)]):

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    p=sum([polar_plot(f(x,i),(x,0,2*pi),plot_points=30,

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                      thickness=1,color=c[i-1]) 

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           for i in [1..n]])

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    p.show(figsize=(5,5),gridlines=True)

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---

Messages

Interactive Symbol Plotting

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marker_list=['$\\alpha$','$\\beta$','$\\gamma$',

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             '$\\Re$','$\\Im$']

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@interact

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def _(marker=marker_list):

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    m,mc=marker,Color('#3636ff').rgb()

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    X=[cos(t)*ln(t+1) for t in srange(0,2*pi,.1)] 

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    Y=[sin(t)^3 for t in srange(0,2*pi,.1)]

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    p=sum([text(m,(x,y),fontsize=20,rgbcolor=mc) 

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         for (x,y) in list(zip(X,Y))])

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    p.show(figsize=(5,5),ymin=-1.1,ymax=1.1)

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---

Messages

Interactive Color Exploration

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@interact

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def _(colormap=['bwr','cool','prism','jet','terrain',

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                'flag','ocean','hsv','bone','winter']):

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    def c(cm): 

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        return [colormaps[cm](12*i)[:3] for i in [1..20]]

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    g=icosahedron().stickers(c(colormap),.05,.05)

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    g.show(frame=False)

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---

Messages

Interactive Coordinates

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@interact

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def _(x=[1..10],y=[1..10],z=[1..10]):

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    from sage.plot.plot3d.plot3d import axes

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    var('u'); f=(.75*cos(u),.75*sin(u))

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    c=colormaps.jet(8*(x+y+z))[:3]; a=axes(11,.5); 

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    r=revolution_plot3d(

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        f,(u,0,2*pi),color=c,mesh=True,plot_points=10,opacity=.2)

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    t=text3d('(%.1f,%.1f,%.1f)'%(x,y,z),

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             (x,y,z+2),color=c)

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    (a+r.translate(x,y,z)+t).show()

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---

Messages

Matrix Operations

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print(r.eval("""

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a<-c(-4,-3,-5,5,4,5,-7,-7,-6)

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A<-matrix(a,3,3,byrow=T)

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print(A); cat('\n') 

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print(eigen(A)$values); cat('\n')

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round(eigen(A)$vectors)"""))

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---

Messages

Color Interpolation 2

<script src='https://d3js.org/d3.v4.min.js'></script> was added in the page head.

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%%html

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<svg id='svg001' width=150px height=150px/><script>

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var c1='#ff3636',c2='#3636ff'; var n=10000;

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var svg=d3.select('#svg1');

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d3.select('#svg001').transition().duration(n)

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  .styleTween('background-color',

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              function(){return d3.interpolate(c1,c2)});

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d3.select('#svg001').append('circle')

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  .attr('cx','50%').attr('cy','50%').attr('r',35)

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  .transition().duration(n)

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  .styleTween('fill',

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              function(){return d3.interpolate(c2,c1)});

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---

Messages

Tensor Operations

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import numpy

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A=numpy.array(range(1,9)).reshape(2,2,2)

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B=['A','B','C','D']

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B=numpy.array(B,dtype=object).reshape(2,2)

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AB1=numpy.tensordot(A,B,1)

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AB01=numpy.tensordot(A,B,(0,1))

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AB10=numpy.tensordot(A,B,(1,0))

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def pp(string,color):

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    start='<text style="color:'+color

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    start+=';">${\\mathbb{'

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    end='}}$</text>'

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    return display(html(start+string+end)) 

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def result(X):

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    pretty_print(X.shape)

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    for i in range(2): 

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        for j in range(2): 

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            for k in range(2):

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                pp(X[i,j,k],'darkblue')

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result(AB1); result(AB01); result(AB10)

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---

Messages

Interactive Style Options

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import warnings; warnings.filterwarnings('ignore')

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@interact

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def _(style=[':','-.','--','-'],thick=[2..5]):

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    g=graphs.SousselierGraph()

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    [g.set_edge_label(u,v,u) for u,v,l in g.edges()]

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    gp=g.graphplot(

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        vertex_color='w',vertex_size=700,

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        color_by_label=True,edge_thickness=thick,

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        edge_style=style).show(figsize=(5,5))

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---

Messages

Symbolic Integration

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from sage.symbolic.integration.integral import indefinite_integral

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@interact

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def _(N=[1,2,..,10]):

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    F={1:ln(2+3*x^2),2:x^(1/3)*ln(x),

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       3:sqrt(x)*atan(sqrt(x)),4:exp(x)*sin(2*x),

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       5:exp(-x)*(x+2),6:4^(-x)*(x+3),

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       7:x*ln(x)^2,8:atan(sqrt(4*x-1)),

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       9:(4*x+1)*cos(2*x),10:(x+5)*sin(3*x)}

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    s=r'<left><font>$\displaystyle{\small{\int %s\; dx=%s'

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    s+='}}$</font></left>'

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    f=F[N]; int_latex=latex(indefinite_integral(f,x).simplify())    

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    pretty_print(html(s%(latex(f),int_latex)))

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---

Messages

Interactive Graphics

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@interact

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def _(N=[20,25,..,40],M=[20,40,..,100]):

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    f(l,k)=[l*sin(pi*k/M)+sin(2*pi*k/M),\

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            -l*(1+cos(pi*k/M)+cos(2*pi*k/M))]

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    L1=[f(j,i) for j in [1..N] for i in range(-2*M,2*M+1)]

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    L2=[f(j,i) for i in range(-2*M,2*M+1) for j in [1..N]]

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    l1=line(L1,color='#3636ff'); l2=line(L2,color='#ff3636')

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    graphics_array(([l1],[l2])).show(figsize=5)

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---

Messages

Interactive 3D Polygon Plotting

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@interact

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def _(N=[12,11,..,3]):

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    def P(i): return [(cos(t),sin(t)) for t in srange(0,2*pi,2*pi/i)]

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    def col(i): return colormaps.hsv(22*(i-3))[:3]

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    p=sum([polygon2d(P(n),alpha=n/12,color=col(n)).plot3d(z=-.15*n) 

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           for n in [3..N]])

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    p.show(frame=False)

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---

Messages

Combine JavaScript Sources 2

<script src='https://d3js.org/d3.v4.min.js'></script> was added in the page head.

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%%html

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<style>

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@import 'https://fonts.googleapis.com/css?family=Ewert';

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</style>    

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<h4>Apply D3 & Google Fonts for Text Styling</h4>

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<script>

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var h4=d3.select('h4');

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h4.style('color','#3636ff').style('font-size','120%')

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  .style('font-family','Ewert')

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  .style('text-shadow','3px 3px 3px slategray');

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---

Messages