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I've been told in the past that Photoshop shapes aren't vectors. The context was that vectors can be resized without loss of resolution.

Do Photoshop shapes (if saved as psd or psb files) lose resolution when resized like rasterized layers?

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Yes, Adobe Photoshop treat its custom shapes as vectors, but you can also draw vectors with Pen Tool. And after saving as psd Photoshop will retain its properties.

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If you save the document as a PDF or EPS, it should retain the shapes just fine. I'm not sure exactly how PS interprets shapes but in some cases they do hold up just like a vector.

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    I would appreciate a "down vote" followed with something to back it up. My comment is valid and although may not answer the question precisely, there is value there. – ErickP Dec 24 '15 at 19:27
  • I didn't downvote you but I can clarify that shapes and paths in Photoshop are vector-based and remain vectors unless/until one "renders" them in some other way. See mrserge answer previously. – bemdesign Dec 24 '15 at 20:35
  • @bemdesign EPS keeps the paths if you save the paths, even if it flattens everything! So technically this answer is right (even if you didn't downvote!) – go-junta Dec 24 '15 at 22:01
  • Question originally was about psd and psb files. And by the way it's 2015 outside, maybe you could forget about eps finally? You received down vote, because second half of your answer is guessing without knowledge. This is more comment than answer. – mrserge Dec 25 '15 at 19:28
  • @mrserge You are absolutely correct about the original question but I wanted to explore it further and see how a PSD/PSB file holds up after you export it in a format that would retain "vector" data. My apologies for doing so. You're comment about the ".eps" format was very nice. I'm sure you feel good about that one. At the end of the day it's just a file format and although it is an older format falling by the waist-side people still use it. Other formats will replace these and so on. It's a cycle, that's life. We are all just trying to help, that all. – ErickP Dec 25 '15 at 20:02
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Yes, shapes are vectors and no, you will not degrade quality of shape if you will resize it. But, in the same time do remember, that shape is rasterised afterwards in the resolution of your canvas. Take that in mind, when saving lo-res psd and then wondering, why it's not printing in hi-res.

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