I want to create really big image, but I don’t want to start this from scratch. I want to just use a small image, say, 200px x 200px, and I want to somehow make it as big as 2000px x 2000px or bigger. Obviously, if I just stretch this out, I see rough edges. How can I make this image bigger AND make its texture smooth? Blur tool? Combination of blur tool and sharp tool (in Photoshop)?

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online.education

Use a vector image to start with.

Do we assume that you are starting off with an already lossy jpeg format image?

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And how can we win, when fools can be kings

Images are blured when you stretch them alot, but in case vector image or simple drawing, tools use mathematcal formulas so you can stretch them as much you want unlike bmp, jpg or gif images.

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Since I never really try this so I am not sure whether this will help. But you can try to use high resolution. Maybe that way the image will still be ok even though you strech it.

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The vectorizing option seems the best solution. Try to google Image Resizing, you might find out something useful there. I know that there was a tutorial on this topic, using photoshop filters to make a image look undamaged. Good luck.