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Looking at a this buttons recommended footprint, I found these irregularly shaped pads:

TL3315 button footprint

The protrusions from the pads are way to small to act as solder thieves, and the button itself has gull wing pins that don't mimic the form of those pads in any way:

TL3315 product picture

What is the purpose of the odd shape of those pads? Is there any reason why I shouldn't just draw those pads as rectangles on my PCB layout?

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    \$\begingroup\$ Considering the way they dimensioned the drawing, I think their engineering dept should be taken out and shot. There is not a single dimension of the pad that is specified directly. Every dimension has to be computed by subtraction, and in some cases both subtraction and its evil uncle, division. \$\endgroup\$ – mkeith Oct 22 '16 at 17:25
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    \$\begingroup\$ @mkeith Jup, from an engineering standpoint that is horrific, but I saw that on so many parts by now that I kind of got used to it. \$\endgroup\$ – iFreilicht Oct 22 '16 at 17:27
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    \$\begingroup\$ It is an all too common situation these days - people just don't think about how people are going to use these diagrams and what information they actually need. They just use the default measurements-from-origin of their cad program and have done with it. Alas... \$\endgroup\$ – Majenko Oct 22 '16 at 17:29
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I saw many datasheets and created many custom devices in EAGLE, this one is not much complex and does not involve many calculations although I tend to agree with commenters to your question that there might be better ways to describe the part's footprint.

Please notice the caption under the drawing: it says mounting rather than board footprint or whatever. This shows shape of soldering area, not shape of the pad itself. Big areas are intended for close contact with button's pins, while small perpendicular areas seem to be designed for extra solder "pour out" space.

You can make pad of any shape given the areas drawn on the mounting schematic is not covered by the solder mask.

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