Question

I would like to draw a rectangle (or more) which printed on paper shows the rectangle in units of cm.
So

Graphics[{Rectangle[{0, 0}, {19, 28}], Orange, Rectangle[{0, 0}, {1, 1}]}]

will print out as two rectangles which can be measured as exactly 1cm x 1cm (orange one) and the black one as 19×28 cm.

It seems that some variables are important:
The ImageSize and of course the AspectRatio.

I used AspectRatio->19/28 and for the ImageSize various settings like ImageSize->{19*27,28*27} but it keeps being not very accurate.

I export the graphics to TIFF and then print out with windows photo gallery to a full page photo. Does anyone have experience with this? There must be a formula instead of trial and error.

UPDATE:
I tried the suggestion of @Szabolcs and I used the following code:

   g = Graphics[{White, EdgeForm[Directive[Thick, Black]], 
   Rectangle[{0, 0}, {18, 28}], Orange, Rectangle[{0, 0}, {10, 10}]}]

   final = Show[g, AspectRatio -> Automatic, 
   PlotRange -> {{-0.5, 18.5}, {-0.5, 28.5}}]

   cm = 72/2.54

   Export["final.pdf", Show[final, ImageSize -> {19 cm, 29 cm}]]

This works great. The orange rectangle of 10x10cm is when measured exactly 10x10cm

the cm 72/2.54 value was not what I expected since I though Windows uses 96dpi and Mac 72dpi (reading from the www). However 72 is the value that works.
I’ve also beenn playing with the frames but then it gets ugly. Haven’t found a way to get the right results dispite playing with all possible settings. What should work is create the frames/ticks etc myself inside the selected boundaries but that’s not the path I would like to pursue..

Answer 1

g = Graphics[{Rectangle[{0, 0}, {19, 28}], Orange, Rectangle[{0, 0}, {1, 1}]}]

Okay, first thing you need to do is set the x and y directions to use the same units, which means

Show[g, AspectRatio -> Automatic]

But this is already the default.

Second thing you need to do is choose a size and range for your plot area. Let’s make it 21 by 30 with your rectangles centred:

plotArea = {{0, 21}, {0, 30}} - {1, 1}
Show[g, AspectRatio -> Automatic, PlotRange -> plotArea]

Third thing you need to do is turning off adding any padding/margins that make the actual size of your figure larger than your plot range:

final = Show[g, AspectRatio -> Automatic, PlotRange -> plotArea, PlotRangePadding -> 0, ImagePadding -> 0]

I believe ImageMargins does not make a difference, but if it does, set that to 0 as well.

The final thing you need to do is export this to a printable format that preserves the image dimensions, and set the size of the image so that 1 cm will be 1 unit on your plot. Mathematica accepts image sizes in printer’s points, so let’s define:

cm = 72/2.54
Export["final.pdf", Show[final, ImageSize -> 21 cm]]

We want the plot to be 21 cm wide because it’s 21 units wide. Use PDF as export format, not TIFF. The ImageSize needs to be used inside Show to work around some problems with Export …

Now open your PDF in Adobe Reader, open the print dialogue, and make sure that Page Scaling is set to None! I don’t know how to do this in other readers … Also make sure your figure fits the paper (21 by 30 cm is too large for A4 …)

I’m not going to do a test print, so let me know if this works for you 🙂 The size of the PDF generated this way is exactly 21 by 30 cm, so if something goes wrong, it must happen at the printing stage.