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I tried to make a logo with a square with rounded corners. But the angles are not very smooth.

non smooth edges

top square

I'm using Inkscape and I'm exporting my image in png. What is the technique in Inkscape to export a png logo with smooth angles?

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Your problem is caused by exporting the PNG at too small a size, then zooming in more than 100%. If you do that, you will see the pixels, since PNG is a raster format made of pixels. If you export a PNG image at 600dpi instead, you will have to zoom in much further to see the pixels. More pixels = finer detail.

All raster images are made of pixels, and no matter what software you use to make them, if you zoom in far enough you will see the pixels. This is normal.

See this example, note the PNG export settings I applied. Note also that I have zoomed in to 560%, and still the edges of the PNG look smooth.

Screenshot of Inkscape and Export settings

However, even with that PNG at 600dpi, if you zoom in close enough you will eventually see the pixels.

PNG zoomed in

Compare that with the vector zoomed in to the same level. Vectors are different because they aren't made of pixels. If you want, rather than PNG you can save your graphic as an SVG vector file. Unlike a PNG, you can zoom in or rescale a vector image as much as you want, and you will never see any pixels.

Vector zoomed in

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