Doug Elrod's Scalable Normal Curve
For a talk on basic statistics, I needed a good picture of a normal distribution (sometimes
known as a "Gaussian" or "bell-shaped curve") that could be projected on a screen.
The examples I found on the Internet were generally
quite "jaggy", and didn't look good when re-scaled. After some research, I
found that the "Adobe Acrobat" (pdf) file format could generate an image that was
- Readable by a large variety of current (ca. 2004) computers.
- Capable of re-scaling (enlarging and stretching x, y axes relative to each other,
or rotating) while still portraying a smooth normal curve, within limits.
[For examples, see
the manual for a signal-detection experiment
where I started with this normal curve, and used the Mac OS applications
Keynote (to rescale and overlay the pdfs, without loss of resolution), and Preview
(to trim the labels off the bottom of the curve), and then transformed the result
into a GIF with GraphicConverter, so that it could be imbedded in a webpage.]
A small Postscript program was used to draw the normal curve using vector primitives.
This was then expanded (using Acrobat Distiller) into the pdf file, normal_curve.pdf.
The pdf file contains coordinates of a normal curve, "oversampled" at nearly 5000
x points over the range of -5*SD to +5*SD (SD= 1 standard deviation) (see
When the normal curve is drawn, these points are connected by straight line segments.
As long as the number of pixels of the display device spanned by the base of
the normal curve is less than 5000, the image can be enlarged (zoomed) without
introducing linear artifacts (flat areas in the curve).
So, basically, the pdf contains "reserve" resolution information that is
only brought into play when the image is enlarged. I like to think of the file
format as though it were an accordion that, when stretched, introduces mini-folds
so that the inter-fold distances don't become too large.
Tip: The curve will appear most smooth when the "Smooth Line Art" option of
Acrobat Reader (or other display program) is checked.
Normal_curve.pdf is "Acknowledgment-ware". Feel free to use it, but if you do,
please acknowledge me, Dr. Doug Elrod (email@example.com).
undocumented feature of Acrobat Distiller appears to discard coordinates that are
sufficiently collinear with surrounding coordinates. So, out of 7000 original evenly-spaced
x-values, the coordinates that are retained in the pdf are the ones where the absolute
value of the second derivative is highest.