# Mathematically, why do pixel circles work

## Enlarge and "de-pixelate" images / graphics

"Depixing" is only possible to a very limited extent! The reason for this is that an image is also low in pixels little picture information contains. When you zoom out, you lose image information, but the other way around you can't gain any information when you enlarge it (where from?)

This becomes clearer if you choose an extreme example: Take a photo of the Brandenburg Gate (let's say in 12 megapixels). Resize it to 2x2 pixels and save it. After that, the picture only has 4 color values ​​that make up it, instead of 12 million. If you enlarge the picture to 12MP again, the program should have 99.99996% of the content guess to be able to restore it. And it can't. After all, it might as well be a photo of the Eiffel Tower.

Nevertheless, there are of course enlargement functions that any image editing program Has. Depending on the program, they use different (interpolation) methods of enlargement (many also offer them explicitly, such as Paint.NET):

• Nearest Neighbor: Pixels are repeated as you zoom in. With 2x2 to 4x4 enlargement, one pixel becomes a 2x2 block of the same color
• Linear: If there are x pixels between two pixels a and b, depending on the position, more of pixel a or pixel b is used, so that a uniform color gradient is created between pixels a and b
• Bicubic: Like linear, only that the course is not uniform, but is calculated using a cubic function. This procedure usually achieves very good results

Can you try it out in Paint.NET: simply create a 2x2-pixel image, fill it with 4 different colors and then use the corresponding process to enlarge it to 1000x1000 pixels.

After enlarging images, you can also optimize them a little by using various filter functions. But even this is only possible to a very limited extent (due to the lack of image information) and quickly appears unnatural.

If you have enlarged your clipart so that these "blocks" have been created, you have used Nearest Neighbor as the enlargement process. Try another one (e.g. using Paint.NET).

The whole is a problem in principle Raster graphics. At Vector graphics (SVG files) the problem does not exist. The image information is not given here on the basis of pixels (colors) in a grid, but are mathematical functions. The advantage of this is that you can enlarge and reduce it as you like without losing image information (you just choose different parameters for the functions). By their very nature, vector graphics are not suitable for photos, but rather shape-based graphics, logos, and ... cliparts! If your cliparts are in SVG (or you can get SVG versions from somewhere), you've practically won.