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Vector VS Raster
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There are two different types of computer graphics today - raster graphics (made up of pixels) and vector graphics (composed of paths). While both are equally neccessary in the graphics world, each has its own applicable uses and situations of need.
Raster images (commonly referred to as bitmap images) use a grid of individual pixels where each pixel can be a different color or shade from the prior. For this reason bitmap images are great for photos and oother full color processed images.
Vector graphics use mathmatical formulas between points called paths. They connect to each other and describe an image in mathmatical terms. These paths automatically reconfigure when zoomed or scaled to produce a clean, crisp image, regardless of size and scale.
Raster (bitmap) image formats: (.psd, .tif, .gif, .jpg, .png)
Vector (path) image formats: (.ai, .eps, .pdf)
Take a look at the below images for a good reference on the difference between raster and vector images when scaled up to 400% their actual size. The bitmap image (left) shows pixelation while the vectored image remains crisp even at a 400% increase in size.
Vector Artwork Sample (200%)

Raster Artwork Sample (200%)

Raster images require higher resolutions for smooth appearances while Vector graphics are mathmatically described and appear smooth at any size or resolution. This plays a major part in file sizes and implimentation into artwork files.
When it's possible, use vector based formats for all type, line art, and illustration work and raster images for photos and images with complex shading and gradient work. When in doubt, for print work processing, always default to vector based formats
EPS Format for Images
If you're unable to obtain or do not have a vector based art program, some raster based programs (Adobe Photoshop) can open and view vectored files for editing. The EPS format is a great format to save in when a vector based program is no available. EPS files are self-contained post script files that contain the same mathmatical data as vector files and can be opened at any size or resolution as a raster image. It will still display exactly as it was drawn at whatever size or resolution you specified upon opening.
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