XFree86 Video Timings HOWTO
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# 17. Plotting Monitor Capabilities

To plot a monitor mode diagram, you'll need the gnuplot package (a freeware plotting language for UNIX-like operating systems) and the tool modeplot, a shell/gnuplot script to plot the diagram from your monitor characteristics, entered as command-line options.

Here is a copy of modeplot:

    #!/bin/sh
    #
    # modeplot -- generate X mode plot of available monitor modes
    #
    # Do `modeplot -?' to see the control options.
    #

    # Monitor description. Bandwidth in MHz, horizontal frequencies in kHz
    # and vertical frequencies in Hz.
    TITLE="Viewsonic 21PS"
    BANDWIDTH=185
    MINHSF=31
    MAXHSF=85
    MINVSF=50
    MAXVSF=160
    ASPECT="4/3"
    vesa=72.5	# VESA-recommended minimum refresh rate

    while [ "$1" != "" ]
    do
    	case $1 in
    	-t) TITLE="$2"; shift;;
    	-b) BANDWIDTH="$2"; shift;;
    	-h) MINHSF="$2" MAXHSF="$3"; shift; shift;;
    	-v) MINVSF="$2" MAXVSF="$3"; shift; shift;;
    	-a) ASPECT="$2"; shift;;
    	-g) GNUOPTS="$2"; shift;;
    	-?) cat <<EOF
    modeplot control switches:

    -t "<description>"	name of monitor            defaults to "Viewsonic 21PS"
    -b <nn>           	bandwidth in MHz           defaults to 185
    -h <min> <max>   	min & max HSF (kHz)        defaults to 31 85
    -v <min> <max>   	min & max VSF (Hz)         defaults to 50 160
    -a <aspect ratio>	aspect ratio               defaults to 4/3
    -g "<options>"   	pass options to gnuplot

    The -b, -h and -v options are required, -a, -t, -g optional.  You can
    use -g to pass a device type to gnuplot so that (for example) modeplot's
    output can be redirected to a printer.  See gnuplot(1) for  details.

    The modeplot tool was created by Eric S. Raymond <esr@thyrsus.com> based on
    analysis and scratch code by Martin Lottermoser <Martin.Lottermoser@mch.sni.de>

    This is modeplot $Revision: 1.25 $
    EOF
    		exit;;
    	esac
    	shift
    done

    gnuplot $GNUOPTS <<EOF
    set title "$TITLE Mode Plot"

    # Magic numbers.  Unfortunately, the plot is quite sensitive to changes in
    # these, and they may fail to represent reality on some monitors.  We need
    # to fix values to get even an approximation of the mode diagram.  These come
    # from looking at lots of values in the ModeDB database.
    F1 = 1.30	# multiplier to convert horizontal resolution to frame width
    F2 = 1.05	# multiplier to convert vertical resolution to frame height

    # Function definitions (multiplication by 1.0 forces real-number arithmetic)
    ac = (1.0*$ASPECT)*F1/F2
    refresh(hsync, dcf) = ac * (hsync**2)/(1.0*dcf)
    dotclock(hsync, rr) = ac * (hsync**2)/(1.0*rr)
    resolution(hv, dcf) = dcf * (10**6)/(hv * F1 * F2)

    # Put labels on the axes
    set xlabel 'DCF (MHz)'
    set ylabel 'RR (Hz)' 6	# Put it right over the Y axis

    # Generate diagram
    set grid
    set label "VB" at $BANDWIDTH+1, ($MAXVSF + $MINVSF) / 2 left
    set arrow from $BANDWIDTH, $MINVSF to $BANDWIDTH, $MAXVSF nohead
    set label "max VSF" at 1, $MAXVSF-1.5
    set arrow from 0, $MAXVSF to $BANDWIDTH, $MAXVSF nohead
    set label "min VSF" at 1, $MINVSF-1.5
    set arrow from 0, $MINVSF to $BANDWIDTH, $MINVSF nohead
    set label "min HSF" at dotclock($MINHSF, $MAXVSF+17), $MAXVSF + 17 right
    set label "max HSF" at dotclock($MAXHSF, $MAXVSF+17), $MAXVSF + 17 right
    set label "VESA $vesa" at 1, $vesa-1.5
    set arrow from 0, $vesa to $BANDWIDTH, $vesa nohead # style -1
    plot [dcf=0:1.1*$BANDWIDTH] [$MINVSF-10:$MAXVSF+20] \
      refresh($MINHSF, dcf) notitle with lines 1, \
      refresh($MAXHSF, dcf) notitle with lines 1, \
      resolution(640*480,   dcf) title "640x480  " with points 2, \
      resolution(800*600,   dcf) title "800x600  " with points 3, \
      resolution(1024*768,  dcf) title "1024x768 " with points 4, \
      resolution(1280*1024, dcf) title "1280x1024" with points 5, \
      resolution(1600*1280, dcf) title "1600x1200" with points 6

    pause 9999
    EOF

Once you know you have modeplot and the gnuplot package in place, you'll need the following monitor characteristics:

- video bandwidth (VB)

- range of horizontal sync frequency (HSF)

- range of vertical sync frequency (VSF)

The plot program needs to make some simplifying assumptions which are not necessarily correct. This is the reason why the resulting diagram is only a rough description. These assumptions are:

- All resolutions have a single fixed aspect ratio AR = HR/VR. Standard resolutions have AR = 4/3 or AR = 5/4. The modeplot programs assumes 4/3 by default, but you can override this.

- For the modes considered, horizontal and vertical frame lengths are fixed multiples of horizontal and vertical resolutions, respectively:

      	HFL = F1 * HR
      	VFL = F2 * VR

As a rough guide, take F1 = 1.30 and F2 = 1.05 (see Computing Frame Sizes.

Now take a particular sync frequency, HSF. Given the assumptions just presented, every value for the clock rate DCF already determines the refresh rate RR, i.e. for every value of HSF there is a function RR(DCF). This can be derived as follows.

The refresh rate is equal to the clock rate divided by the product of the frame sizes:

    	RR = DCF / (HFL * VFL)		(*)

On the other hand, the horizontal frame length is equal to the clock rate divided by the horizontal sync frequency:

    	HFL = DCF / HSF			(**)

VFL can be reduced to HFL be means of the two assumptions above:

    	VFL = F2 * VR
    	    = F2 * (HR / AR)
    	    = (F2/F1) * HFL / AR	(***)

Inserting (**) and (***) into (*) we obtain:

    	RR = DCF / ((F2/F1) * HFL**2 / AR)
    	   = (F1/F2) * AR * DCF * (HSF/DCF)**2
    	   = (F1/F2) * AR * HSF**2 / DCF

For fixed HSF, F1, F2 and AR, this is a hyperbola in our diagram. Drawing two such curves for minimum and maximum horizontal sync frequencies we have obtained the two remaining boundaries of the permitted region.

The straight lines crossing the capability region represent particular resolutions. This is based on (*) and the second assumption:

    	RR = DCF / (HFL * VFL) = DCF / (F1 * HR * F2 * VR)

By drawing such lines for all resolutions one is interested in, one can immediately read off the possible relations between resolution, clock rate and refresh rate of which the monitor is capable. Note that these lines do not depend on monitor properties, but they do depend on the second assumption.

The modeplot tool provides you with an easy way to do this. Do modeplot -? to see its control options. A typical invocation looks like this:

    	modeplot -t "Swan SW617" -b 85 -v 50 90 -h 31 58

The -b option specifies video bandwidth; -v and -h set horizontal and vertical sync frequency ranges.

When reading the output of modeplot, always bear in mind that it gives only an approximate description. For example, it disregards limitations on HFL resulting from a minimum required sync pulse width, and it can only be accurate as far as the assumptions are. It is therefore no substitute for a detailed calculation (involving some black magic) as presented in Putting it All Together. However, it should give you a better feeling for what is possible and which tradeoffs are involved.

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