Visualization Notes: January 2020

Sunday, January 19, 2020

D3 Plotting and Functions

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

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%%html
<svg id='d3001' style='background-color:ghostwhite;'/>
<script>
var n=640,m=50,d=.01,
    margin={top:m,right:m,bottom:m,left:m},
    width=500-margin.left-margin.right,
    height=500-margin.top-margin.bottom; 
function f(t){
    return Math.exp(Math.pow(Math.cos(d*t),2)+
           Math.sin(d*t))-3*Math.cos(4*d*t);};
function randi(xmin,xmax){
    return Math.floor(Math.random()*(xmax-xmin+1))+xmin;};
function rcolor(i){var r=randi(i,255),g=randi(i,255),b=randi(i,255);
    return '#'+r.toString(16)+g.toString(16)+b.toString(16);} 
function make_data(k){return d3.range(1,n).map(function(t){
    return {'x':d*k*f(t)*Math.cos(d*t),
            'y':d*k*f(t)*Math.sin(d*t)}});};    
var xScale=d3.scaleLinear().domain([-5*d*m,5*d*m])
             .range([0,width+2*m]),
    yScale=d3.scaleLinear().domain([-5*d*m,5*d*m])
             .range([height+2*m,0]); 
var svg=d3.select('#d3001')
          .attr('width',width+margin.left+margin.right)
          .attr('height',height+margin.top+margin.bottom)
          .attr('transform',
                'translate('+margin.left+','+margin.top+')');
var line=d3.line().curve(d3.curveMonotoneX)
           .x(function(d){return xScale(d.x);})
           .y(function(d){return yScale(d.y);});
for (var i=1; i<m; i++) {var data=make_data(i),col=rcolor(i);
    svg.append('path').datum(data)
       .attr('class','line').attr('d',line)
       .attr('stroke',col).attr('fill','none');};

D3 Color Gradients

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

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%%html
<svg id='d3b02' style='background-color:#101050;'/><script>
var width=300,height=300,ra=3*360,
    col=['silver','darkgray','slategray','darkslategray'],
    per=['40%','60%','80%','100%'];
var svg=d3.select('#d3b02')
          .attr('width',2*width).attr('height',2*height).append('g')
          .attr('transform','translate('+width+','+height+')');
var gradient=svg.append('defs')
                .append('linearGradient').attr('id','gradient')
                .attr('x1','0%').attr('y1','50%')
                .attr('x2','50%').attr('y2','100%');
for (var i=0; i<4; i++){
    gradient.append('stop').attr('offset',per[i])
            .attr('stop-color',col[i]);};
svg.selectAll('path').data(d3.range(ra))
   .enter().append('path').attr('stroke','#fff')
   .attr('fill','url(#gradient)').attr('fill-opacity',.9)
   .attr('d',function(){return raindrop(Math.random()*100);})
   .attr('transform',function(d){
       return 'rotate('+d+')'+'translate('+
              .9*height*Math.random()+',0)'+'rotate(270)';});
function raindrop(size){
  var r=Math.cos(Math.PI*size)+Math.sqrt(size);
  return 'M'+r+',0'+'A'+r+','+r+' 0 1,1 '+-r+',0'
         +'C'+-r+','+-r+' 0,'+-r+' 0,'+-3*r
         +'C0,'+-r+' '+r+','+-r+' '+r+',0'+'Z';};

Tuesday, January 7, 2020

Graph Transformations & Bezier Paths

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import warnings; warnings.simplefilter('ignore')
def rotate_line(a,l): 
    return [[(cos(a)*x-sin(a)*y).n(),
             (sin(a)*x+cos(a)*y).n()] 
            for [x,y] in l]
def linegraph(g):
    vg=g.get_pos(); eg=g.edges(); ne=len(eg)
    return [[list(vg[eg[i][0]]),
             list(vg[eg[i][1]])] 
            for i in range(ne)]    
def rotate_bezier_path_cubegraph(m,k):
    g=graphs.CubeGraph(m) 
    lg=linegraph(g); LG=Graphics()
    rlg=[[rotate_line(j*pi/k,lg[i]) 
          for i in range(len(lg))] 
         for j in range(2*k)] 
    for i in range(2*k): 
        col=(random(),0,random())
        LG+=bezier_path(rlg[i],color=col,
                        thickness=.3)
    LG.show(axes=False,figsize=(5,5),
            title=r'$m=%d; \ k=%d$'%(m,k))
m,k=randint(3,5),randint(3,5)
rotate_bezier_path_cubegraph(m,k)

3D Line Graphs

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import warnings; warnings.simplefilter('ignore')
def col(i,p): 
    c1,c2,c3=i/p,random(),random()
    return sage.plot.colors.float_to_html(c1,c2,c3)
def linegraph3d(g,n):
    LG=Graphics(); vg=g.get_pos(); eg=g.edges() 
    nv=len(vg); ne=len(eg); k=randint(10,50)/100
    x0=mean([list(vg.values())[i][0] for i in range(nv)])
    y0=mean([list(vg.values())[i][1] for i in range(nv)])
    coord=[[list(vg[eg[i][0]]),list(vg[eg[i][1]])] 
           for i in range(ne)]
    lg=[[[x-x0,y-y0] for [x,y] in coord[i]] 
        for i in range(ne)]
    zlg=[[[(1+k*j)*x,j,(1+k*j)*y] for [x,y] in lg[i]] 
         for j in range(n) for i in range(ne)]
    for i in range(n*ne):
        LG+=line3d(zlg[i],color=col(i,ne/(n-1)))
    LG.show(frame=False,aspect_ratio=1)
linegraph3d(graphs.CubeGraph(6),5)

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import warnings; warnings.simplefilter('ignore')
def col(): 
    c1,c2,c3=.3,random(),random()
    return sage.plot.colors.float_to_html(c1,c2,c3)
def linegraph3d(g,k):
    LG=Graphics(); vg=g.get_pos(); eg=g.edges()
    nv=len(vg); ne=len(eg)
    x0=mean([list(vg.values())[i][0] for i in range(nv)])
    y0=mean([list(vg.values())[i][1] for i in range(nv)])
    coord=[[list(vg[eg[i][0]]),list(vg[eg[i][1]])] 
           for i in range(ne)]
    lg=[[[x-x0,y-y0] for [x,y] in coord[i]] 
        for i in range(ne)]
    zlg=[[[(cos(j*pi/k)*x-sin(j*pi/k)*y).n(),
           (sin(j*pi/k)*x+cos(j*pi/k)*y).n(),
           (j+1)/k] for [x,y] in lg[i]] 
         for j in range(2*k) for i in range(ne)]
    for i in range(2*k*ne): 
        LG+=line3d(zlg[i],color=col())
    LG.show(frame=False,aspect_ratio=1)
linegraph3d(graphs.CubeGraph(5),6)

Graph Transformations

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import warnings; warnings.simplefilter('ignore')
def graph2d(g,m,n):
    PG=Graphics(); k=randint(100,500)/1000
    vg=g.get_pos(); vgp=list(vg.values())
    eg=g.edges(); nv=len(vg); ne=len(eg)
    x0=mean([list(vg.values())[i][0] for i in range(nv)])
    y0=mean([list(vg.values())[i][1] for i in range(nv)])
    cp=[[vgp[i][0]-x0,vgp[i][1]-y0] for i in range(nv)]
    l=[[vg[eg[i][0]],vg[eg[i][1]]] for i in range(ne)]
    cl=[[[x-x0,y-y0] for [x,y] in l[i]] for i in range(ne)]
    cp=[[[cos(j*pi/k)*x-sin(j*pi/k)*y,
          sin(j*pi/k)*x+cos(j*pi/k)*y] 
         for j in range(n)] for [x,y] in cp]
    cl=[[[cos(j*pi/k)*x-sin(j*pi/k)*y,
          sin(j*pi/k)*x+cos(j*pi/k)*y] 
         for [x,y] in cl[i]] 
        for j in range(n) for i in range(ne)]
    for i in range(nv):
        col=(random(),random(),1)
        PG+=polygon(cp[i],color=col,alpha=.1)
    for i in range(n*ne):
        col=(random(),random(),1)
        PG+=line(cl[i],color=col,thickness=1)        
    PG.show(axes=False,figsize=7,
            title=r'$k=%.3f; \ m=%d; \ n=%d$'%(k,m,n))
m,n=randint(3,7),randint(2,9); 
g=graphs.CubeGraph(m); graph2d(g,m,n)

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import warnings; warnings.simplefilter('ignore')
def graph2d(g,m,n):
    PG=Graphics(); k=randint(100,500)/1000
    vg=g.get_pos(); vgp=list(vg.values())
    eg=g.edges(); nv=len(vg); ne=len(eg)
    x0=mean([list(vg.values())[i][0] for i in range(nv)])
    y0=mean([list(vg.values())[i][1] for i in range(nv)])
    cp=[[vgp[i][0]-x0,vgp[i][1]-y0] for i in range(nv)]
    l=[[vg[eg[i][0]],vg[eg[i][1]]] for i in range(ne)]
    cl=[[[x-x0,y-y0] for [x,y] in l[i]] for i in range(ne)]
    cp=[[[(1+k*j)*(cos(j*pi/k)*x-sin(j*pi/k)*y),
          (1+k*j)*(sin(j*pi/k)*x+cos(j*pi/k)*y)] 
         for j in range(n)] for [x,y] in cp]
    cl=[[[(1+k*j)*(cos(j*pi/k)*x-sin(j*pi/k)*y),
          (1+k*j)*(sin(j*pi/k)*x+cos(j*pi/k)*y)] 
         for [x,y] in cl[i]] 
        for j in range(n) for i in range(ne)]
    for i in range(nv): 
        col=(random(),random(),1)
        PG+=polygon(cp[i],color=col,alpha=.1)
    for i in range(n*ne):
        col=color=(random()/2,random()/2,1)
        PG+=line(cl[i],color=col,thickness=.25)        
    PG.show(axes=False,figsize=7,
            title=r'$k=%.3f; \ m=%d; \ n=%d$'%(k,m,n))
m,n=randint(3,7),randint(2,6)
g=graphs.CubeGraph(m); graph2d(g,m,n)

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()

Wednesday, January 1, 2020

CTM[m_,r_,col_,s_]:=Module[{ag,rtag,n},
ag=AdjacencyGraph[ExampleData[{"Matrix",m},
"Matrix"]["PatternArray"],DirectedEdges->False];
rtag=Table[RotationTransform[i*Pi/r,{0,
0}]/@ResourceFunction["VertexCoordinateList"][ag]//N,
{i,2r}];n=Length[rtag[[1]]];
rtag=Table[Flatten[{rtag[[i,j]],.05j}],{i,2r},{j,n}];
Graphics3D[Table[{ColorData[col][Cos[2Pi*i/r]^2],
Line[rtag[[i]]]},{i,2r}],
ImageSize->s,Boxed->False,ViewPoint->{3,1,.003n}]];
CTM["HB/dwt_1005",12,"CherryTones",700]