A normal Christmas tree

Rick_SAS — Tue, 17 Dec 2024 20:02:38 GMT

I'm sure @tc will post an awesome Christmas-themed graphic soon, but you can enjoy this one until he does:

/* A normal Christmas tree: Each branch is a normal PDF (shaded) */
data NormalTree;
array x[101];    /* for efficiency, store (x, phi(x)) values in an array */
array phi[101];
 
/* compute the standard normal PDF on [-xMax,xMax] */
xMax = 2.5;
dx = 2*xMax / (dim(x)-1);        /* step size for x */
do i = 1 to dim(x);
   x[i] = -xMax + (i-1)*dx;      /* the i_th point in [-xMax,xMax] */
   phi[i] = pdf("Normal", x[i]); /* phi(x) is normal PDF */
end;
 
b = 4;     /* width of the tree base; the interval is [-b/2, b/2] */
h = 6;     /* height of tree; the interval is [0, h] */
nSegs = 8; /* number of normal curves to overlay to construct the tree */
 
/* linear transformation of Y from [0,maxPhi] to [0, 2*dy]. Use for ALL branches. */
maxPhi = pdf("Normal", 0);
dy = h / (nSegs+1);  /* height of each normal curve */
do i = 1 to dim(x);
   phi[i] = 2*dy / maxPhi * phi[i];
end;
 
/* Translate curve and baseline up by k*dy units.
   Linearly transform X from [-xMax,xMax] to [-xR, xR].
   If you slice the right triangle with base b/2 and height h 
   at L=k*dy, the width of the slice is xR = (b/2)/h * (h-L) */
do k = 0 to nSegs-1;
   baseline = k*dy;
   xR = (b/2)/h * (h - baseline);
   do i = 1 to dim(x);
      t = xR / xMax * x[i];   /* t is the scaled version of X for k_th branch */
      y = baseline + phi[i];  /* vertically translate Y values */
      output;
   end;
end;
keep k i baseline t y;
run;
 
/* Fill/shade the PDF: https://blogs.sas.com/content/iml/2015/07/20/density-shaded-tails.html */
ods graphics / width=480px height=480px;
title "A Normal Christmas Tree";
proc sgplot data=NormalTree noautolegend aspect=1 noborder;
  band x=t upper=y lower=baseline / group=k fill fillattrs=(color=DarkGreen) outline lineattrs=(color=black);
  xaxis display=none;
  yaxis display=none;
run;

How did he do that? See https://blogs.sas.com/content/iml/2024/12/16/normal-christmas-tree.html

And I acknowledge @Ksharp for his inspiration last year.

Re: A normal Christmas tree

Ksharp — Wed, 18 Dec 2024 01:50:54 GMT

Rick,

I have already read your blog .GREAT !

I think you should rename this post as
Fun With SAS ODS Graphics: A normal Christmas tree

to make @tc notice it .

topic Re: A normal Christmas tree in Graphics Programming

A normal Christmas tree

Re: A normal Christmas tree