#!/usr/local/bin/gnuplot -persist
# set terminal canvas  rounded size 600,400 enhanced fsize 10 lw 1.6 fontscale 1 name "voxel_1" jsdir "."
# set output 'voxel.1.js'
unset border
unset key
set view 68, 28, 1.6, 0.9
set style data lines
set xzeroaxis lt black linewidth 1.000 dashtype solid
set yzeroaxis lt black linewidth 1.000 dashtype solid
set zzeroaxis lt black linewidth 1.000 dashtype solid
set xyplane at 0
set xtics axis in scale 1,0.5 nomirror norotate  autojustify
set ytics axis in scale 1,0.5 nomirror norotate  autojustify
set ztics axis in scale 1,0.5 nomirror norotate  autojustify
unset cbtics
set title "Gaussian 3D cloud of 3000 random samples\ncolored by local point density" 
set xrange [ -4.00000 : 4.00000 ] noreverse nowriteback
set x2range [ * : * ] noreverse writeback
set yrange [ -4.00000 : 4.00000 ] noreverse nowriteback
set y2range [ * : * ] noreverse writeback
set zrange [ -4.00000 : 4.00000 ] noreverse nowriteback
set cblabel "point density" 
set cbrange [ * : * ] noreverse writeback
set rrange [ * : * ] noreverse writeback
set logscale cb 10
set palette negative nops_allcF maxcolors 0 gamma 1.5 color model RGB 
set palette cubehelix start 0.5 cycles -1.5 saturation 1
set colorbox vertical origin screen 0.9, 0.2 size screen 0.05, 0.6 front  noinvert bdefault
isint(x)=(int(x)==x)
Binv(p,q)=exp(lgamma(p+q)-lgamma(p)-lgamma(q))
arcsin(x,r)=r<=0?1/0:abs(x)>r?0.0:invpi/sqrt(r*r-x*x)
beta(x,p,q)=p<=0||q<=0?1/0:x<0||x>1?0.0:Binv(p,q)*x**(p-1.0)*(1.0-x)**(q-1.0)
binom(x,n,p)=p<0.0||p>1.0||n<0||!isint(n)?1/0:  !isint(x)?1/0:x<0||x>n?0.0:exp(lgamma(n+1)-lgamma(n-x+1)-lgamma(x+1)  +x*log(p)+(n-x)*log(1.0-p))
cauchy(x,a,b)=b<=0?1/0:b/(pi*(b*b+(x-a)**2))
chisq(x,k)=k<=0||!isint(k)?1/0:  x<=0?0.0:exp((0.5*k-1.0)*log(x)-0.5*x-lgamma(0.5*k)-k*0.5*log2)
erlang(x,n,lambda)=n<=0||!isint(n)||lambda<=0?1/0:  x<0?0.0:x==0?(n==1?real(lambda):0.0):exp(n*log(lambda)+(n-1.0)*log(x)-lgamma(n)-lambda*x)
extreme(x,mu,alpha)=alpha<=0?1/0:alpha*(exp(-alpha*(x-mu)-exp(-alpha*(x-mu))))
f(x,d1,d2)=d1<=0||!isint(d1)||d2<=0||!isint(d2)?1/0:  Binv(0.5*d1,0.5*d2)*(real(d1)/d2)**(0.5*d1)*x**(0.5*d1-1.0)/(1.0+(real(d1)/d2)*x)**(0.5*(d1+d2))
gmm(x,rho,lambda)=rho<=0||lambda<=0?1/0:  x<0?0.0:x==0?(rho>1?0.0:rho==1?real(lambda):1/0):  exp(rho*log(lambda)+(rho-1.0)*log(x)-lgamma(rho)-lambda*x)
geometric(x,p)=p<=0||p>1?1/0:  !isint(x)?1/0:x<0||p==1?(x==0?1.0:0.0):exp(log(p)+x*log(1.0-p))
halfnormal(x,sigma)=sigma<=0?1/0:x<0?0.0:sqrt2invpi/sigma*exp(-0.5*(x/sigma)**2)
hypgeo(x,N,C,d)=N<0||!isint(N)||C<0||C>N||!isint(C)||d<0||d>N||!isint(d)?1/0:  !isint(x)?1/0:x>d||x>C||x<0||x<d-(N-C)?0.0:exp(lgamma(C+1)-lgamma(C-x+1)-lgamma(x+1)+  lgamma(N-C+1)-lgamma(d-x+1)-lgamma(N-C-d+x+1)+lgamma(N-d+1)+lgamma(d+1)-lgamma(N+1))
laplace(x,mu,b)=b<=0?1/0:0.5/b*exp(-abs(x-mu)/b)
logistic(x,a,lambda)=lambda<=0?1/0:lambda*exp(-lambda*(x-a))/(1.0+exp(-lambda*(x-a)))**2
lognormal(x,mu,sigma)=sigma<=0?1/0:  x<0?0.0:invsqrt2pi/sigma/x*exp(-0.5*((log(x)-mu)/sigma)**2)
maxwell(x,a)=a<=0?1/0:x<0?0.0:fourinvsqrtpi*a**3*x*x*exp(-a*a*x*x)
negbin(x,r,p)=r<=0||!isint(r)||p<=0||p>1?1/0:  !isint(x)?1/0:x<0?0.0:p==1?(x==0?1.0:0.0):exp(lgamma(r+x)-lgamma(r)-lgamma(x+1)+  r*log(p)+x*log(1.0-p))
nexp(x,lambda)=lambda<=0?1/0:x<0?0.0:lambda*exp(-lambda*x)
normal(x,mu,sigma)=sigma<=0?1/0:invsqrt2pi/sigma*exp(-0.5*((x-mu)/sigma)**2)
pareto(x,a,b)=a<=0||b<0||!isint(b)?1/0:x<a?0:real(b)/x*(real(a)/x)**b
poisson(x,mu)=mu<=0?1/0:!isint(x)?1/0:x<0?0.0:exp(x*log(mu)-lgamma(x+1)-mu)
rayleigh(x,lambda)=lambda<=0?1/0:x<0?0.0:lambda*2.0*x*exp(-lambda*x*x)
sine(x,f,a)=a<=0?1/0:  x<0||x>=a?0.0:f==0?1.0/a:2.0/a*sin(f*pi*x/a)**2/(1-sin(twopi*f))
t(x,nu)=nu<0||!isint(nu)?1/0:  Binv(0.5*nu,0.5)/sqrt(nu)*(1+real(x*x)/nu)**(-0.5*(nu+1.0))
triangular(x,m,g)=g<=0?1/0:x<m-g||x>=m+g?0.0:1.0/g-abs(x-m)/real(g*g)
uniform(x,a,b)=x<(a<b?a:b)||x>=(a>b?a:b)?0.0:1.0/abs(b-a)
weibull(x,a,lambda)=a<=0||lambda<=0?1/0:  x<0?0.0:x==0?(a>1?0.0:a==1?real(lambda):1/0):  exp(log(a)+a*log(lambda)+(a-1)*log(x)-(lambda*x)**a)
carcsin(x,r)=r<=0?1/0:x<-r?0.0:x>r?1.0:0.5+invpi*asin(x/r)
cbeta(x,p,q)=ibeta(p,q,x)
cbinom(x,n,p)=p<0.0||p>1.0||n<0||!isint(n)?1/0:  !isint(x)?1/0:x<0?0.0:x>=n?1.0:ibeta(n-x,x+1.0,1.0-p)
ccauchy(x,a,b)=b<=0?1/0:0.5+invpi*atan((x-a)/b)
cchisq(x,k)=k<=0||!isint(k)?1/0:x<0?0.0:igamma(0.5*k,0.5*x)
cerlang(x,n,lambda)=n<=0||!isint(n)||lambda<=0?1/0:x<0?0.0:igamma(n,lambda*x)
cextreme(x,mu,alpha)=alpha<=0?1/0:exp(-exp(-alpha*(x-mu)))
cf(x,d1,d2)=d1<=0||!isint(d1)||d2<=0||!isint(d2)?1/0:1.0-ibeta(0.5*d2,0.5*d1,d2/(d2+d1*x))
cgmm(x,rho,lambda)=rho<=0||lambda<=0?1/0:x<0?0.0:igamma(rho,x*lambda)
cgeometric(x,p)=p<=0||p>1?1/0:  !isint(x)?1/0:x<0||p==0?0.0:p==1?1.0:1.0-exp((x+1)*log(1.0-p))
chalfnormal(x,sigma)=sigma<=0?1/0:x<0?0.0:erf(x/sigma/sqrt2)
chypgeo(x,N,C,d)=N<0||!isint(N)||C<0||C>N||!isint(C)||d<0||d>N||!isint(d)?1/0:  !isint(x)?1/0:x<0||x<d-(N-C)?0.0:x>d||x>C?1.0:hypgeo(x,N,C,d)+chypgeo(x-1,N,C,d)
claplace(x,mu,b)=b<=0?1/0:(x<mu)?0.5*exp((x-mu)/b):1.0-0.5*exp(-(x-mu)/b)
clogistic(x,a,lambda)=lambda<=0?1/0:1.0/(1+exp(-lambda*(x-a)))
clognormal(x,mu,sigma)=sigma<=0?1/0:x<=0?0.0:cnormal(log(x),mu,sigma)
cnormal(x,mu,sigma)=sigma<=0?1/0:0.5+0.5*erf((x-mu)/sigma/sqrt2)
cmaxwell(x,a)=a<=0?1/0:x<0?0.0:igamma(1.5,a*a*x*x)
cnegbin(x,r,p)=r<=0||!isint(r)||p<=0||p>1?1/0:  !isint(x)?1/0:x<0?0.0:ibeta(r,x+1,p)
cnexp(x,lambda)=lambda<=0?1/0:x<0?0.0:1-exp(-lambda*x)
cpareto(x,a,b)=a<=0||b<0||!isint(b)?1/0:x<a?0.0:1.0-(real(a)/x)**b
cpoisson(x,mu)=mu<=0?1/0:!isint(x)?1/0:x<0?0.0:1-igamma(x+1.0,mu)
crayleigh(x,lambda)=lambda<=0?1/0:x<0?0.0:1.0-exp(-lambda*x*x)
csine(x,f,a)=a<=0?1/0:  x<0?0.0:x>a?1.0:f==0?real(x)/a:(real(x)/a-sin(f*twopi*x/a)/(f*twopi))/(1.0-sin(twopi*f)/(twopi*f))
ct(x,nu)=nu<0||!isint(nu)?1/0:0.5+0.5*sgn(x)*(1-ibeta(0.5*nu,0.5,nu/(nu+x*x)))
ctriangular(x,m,g)=g<=0?1/0:  x<m-g?0.0:x>=m+g?1.0:0.5+real(x-m)/g-(x-m)*abs(x-m)/(2.0*g*g)
cuniform(x,a,b)=x<(a<b?a:b)?0.0:x>=(a>b?a:b)?1.0:real(x-a)/(b-a)
cweibull(x,a,lambda)=a<=0||lambda<=0?1/0:x<0?0.0:1.0-exp(-(lambda*x)**a)
tstring(n) = sprintf("Gaussian 3D cloud of %d random samples\ncolored by local point density", n)
VoxelDistance = 0.31691416401353
fourinvsqrtpi = 2.25675833419103
invpi = 0.318309886183791
invsqrt2pi = 0.398942280401433
log2 = 0.693147180559945
sqrt2 = 1.4142135623731
sqrt2invpi = 0.797884560802865
twopi = 6.28318530717959
nsamp = 3000
rlow = -4.0
rhigh = 4.0
## Last datafile plotted: "$random"
splot $random using 1:2:3:(voxel($1,$2,$3)) with points pt 7 ps 0.5 lc palette