Absolute Measurements

The Problem

SVG stands for scalable vector graphics. The authors of the first SVG standard took the scalable part very seriously and specified the format in a way that makes it impossible to determine an absolute scale for shapes declared in an SCG document. Coordinates in an SVG document can be specified using a number of unit suffixes:

• m: One meter, as defined by the SI.
• cm: 1 m / 100.
• mm: 1 m / 1000.
• km: 1 m * 1000.
• in: One inch, defined as 25.4 mm.
• pc: 1 in / 6.
• pt: 1 in / 72.
• ft: 1 in * 12.
• yd: 1 in * 36.
• px: One pixel.

In this list, only px has no defined size in SVG 1.1. SVG 1.1 does hint at a size of 1 in / 90. Later, SVG 2 defined it to be 1 in / 96. But the harm had already been done. Inscape took the value of 1 in / 90 and produces and reads documents using that interpretation. The latest snapshots of version 0.92 changed this to 1 in / 96, making documents incompatible between older and newer versions.

SVG also allows sizes to be declared without specifying a unit, which is what e.g. Inkscape does when writing files. Guess which of the above unit is used when no unit is specified.

To make matters more complicated, the SVG standard adds a way specify an absolute size of the image represented by a document. This defines sort of a scaling factor between the measurements used in the document and the actual sizes those objects will have (I.e. one mm will not be equal to one mm anymore). To make matters even more complicated, this scaling factor is defined using four attributes on the root svg element, height, width, viewBox and preserveAspectRatio. And to make this ordeal ultimately pointless again, this "absolute size" can again be specified using the px unit, making it not absolute again. Inkscape does not even implement preserveAspectRatio and thus neither does the converter of this project.

Our Approach

Because the differences introduced by the different interpretations of the px unit are very frustrating (a scale difference of 15/16 is usually not noticed until the finished part is printed and then does not fit where it should), the converter using in this project employs some checks for documents which lack the necessary information to be converted consistently. Depending on the problem, different error messages are printed. Those error messages look like this:

[inkscape] src/test-1.dxf
Error: While processing src/test-1.svg: SVG document has no viewBox attribute. See https://github.com/Feuermurmel/openscad-template/wiki/Absolute-Measurements
Makefile:92: recipe for target 'src/test-1.dxf' failed
make: *** [src/test-1.dxf] Error 1

Because Inkscape writes all coordinates using the px units, the converter tries to determine the absolute size of a pixel using the height and viewBox attributes. Simply speaking, the height specifies an absolute value for the height of the whole document while the viewBox defines the same length as a number of pixels.

For example, in the following SVG document, the viewBox defines 100 pixels in the document to be equal to 100 mm in the real world. The width attribute is also specified, but it is ignored by the converter:

<svg
   xmlns:svg="http://www.w3.org/2000/svg"
   width="200mm"
   height="100mm"
   viewBox="0 0 200 100"
   ...

The following error messages are produced:

• SVG document has no height attribute.: Add a height attribute to the root svg element, specifying the height of the document in an absolute unit like mm or pt. An appropriate width attribute should also be added.
• Height of SVG document is not an absolute measure.: Add an absolute unit to the height attribute of the root svg element (i.e. anything other than px).
• SVG document has no viewBox attribute.: Add a viewBox attribute to the document, specifying the size of the document as a number of pixels.

The viewBox attribute is a sequence of four numbers, without units. To construct the attribute, set the first two values to 0 and compute the two following numbers from the width and height attributes of your document by converting the absolute measures of those attributes to pixels. For this, you should probably use a value of 90 or 96 pixels per inch. The following table gives the conversion factors for all SVG units. E.g. a height of 10 cm would be translated to 10 * 35.4331 = 354.331 pixels:

Unit	90 px / in	96 px/in
1 m	3543.31	3779.53
1 cm	35.4331	37.7953
1 mm	3.54331	3.77953
1 km	3543310.	3779530.
1 in	90.	96.
1 pc	15.	16.
1 pt	1.25	1.33333
1 ft	1080.	1152.
1 yd	3240.	3456.