Visualization Notes: 01/07/20

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)