Well this can be confusing and a bit complex, there are a lot of possible variables and I fear there is no one right, fits all, answer!
So consider this as just general guidance.
Also pages 22 & 23 in the AR manual have very useful information on printing, regarding things to consider before starting a painting.
The important thing is the resolution of your painting i.e pixels/dots per inch. This will determine how well it prints.
Try and get into the habit of setting up a new painting canvas each time you start a new project. Set it up using the Print Size tab, not Screen Size.
AR's default is 72 pixels/dots per inch but for printing you will probably want something around 300. At higher resolutions + a large canvas you may find AR slows a little when using large brushes and when performing internal calculations depending on how fast your computer is.
With something you've already painted you are going to have to try and upscale it by resizing. But remember when you upscale a picture you are telling the program doing it to makeup and add new pixels. At best they will be an educated guess, so don't expect miracles!
1:
Re-size it in AR by going to; Edit > Re-size Painting…
Once you have it re-sized you may well want/need to over paint/draw or replace if need be, any resulting fuzzy areas, edges and lines. This is a bit easier to do if you have used different layers for the different elements within the picture.
2:
If you have Photoshop or Photoshop Elements or something similar, you can use that to re-size and upscale your painting, after you have exported it from AR in your chosen image format, e.g .jpg.
In Photoshop (and possibly depending on version here) from the Menu Bar at the top, choose; Image > Resize > Image Resize. In the popup menu that opens check; Constrain Proportions, Re-sample Image and Scale Styles (you will need to select one to be used).
As with all things digital, work/experiment on a copy of your original file, just in case!
When you have something ready to print, ask the printer what file format they prefer to work with. But AR's .ptg format is not going to be one of them!
As to your family skeptics, get them to draw or paint something with AR. They will soon find out that it will only do what they tell it to do and nothing more. If they can't draw on paper, then they still wont be able to in AR!
Hope this is of help.
Maker Of Replica Macoys
Techie Stuff:
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