Vector Image File Formats
EPS
Adobe's EPS format (Encapsulated PostScript) is perhaps the most common vector image format. It is the standard interchange format in the print industry. It is widely supported as an export format, but due to the complexity of the full format specification, not all programs that claim to support EPS are able to import all variants of it. Adobe Illustrator and recent versions of CorelDRAW have very good support for reading and writing EPS. Ghostview can read it very well but does not have any editing capabilities. Inkscape can only export it.
SVG
The W3C standard vector image format is called SVG (Scalable Vector Graphics). Inkscape and recent versions of Adobe Illustrator and CorelDRAW have good support for reading and writing SVG. Further information on the SVG format may be found on the official SVG website.
Adobe's PDF format (Portable Document Format) is very widely used as a general-purpose platform-independent document format. And while it is not exclusively used as such, it is also a very good vector image format. Adobe gives away the Acrobat PDF reader but sells the tools required to create PDF files (third party tools that perform the same task are also for sale). Those tools work with any program that is able to print. Support for reading and editing PDF files is much more limited.
AI
The native format of Adobe Illustrator is the AI format (Adobe Illustrator Artwork), a modified version of the older EPS format. The AI format is fairly widely supported but is less ubiquitous than the EPS format, and most programs that read AI can also read EPS.
DXF
Drawing eXchange Format. A CAD format from Autodesk, used by CAD tools from many different vendors. Some programs have difficulty reading DXF files with splines (curves), so the Desktop Edition supports line+spline as well as line only output modes.
There are numerous other vector formats: CDR is the CorelDRAW native format and XAR is the Xara Xtreme native format, to name a couple.
Bitmap Image File Formats
There is a large number of different bitmap formats. Some of the most common are: JPEG, PNG, GIF, BMP, and TIFF. Broadly speaking, they fall into two categories:
Lossy formats
These have smaller file sizes but do not store a perfect copy of the image. They are best suited to photographs and other images where perfect accuracy is not important. They are also commonly used on the web to save bandwidth.
One of the most widely-used image formats. It has excellent compression characteristics and has the nice feature that the user may specify what level of compression they desire, trading off fidelity for file size.
We do not recommend using JPEG files for rasterized vector art, as the compression artifacts substantially degrade the quality of the image near edges.
Lossless formats
These store an exact pixel-by-pixel representation of the image, but require more space. They are more suitable for things like logos.
PNG
The best of the lossless image formats is called PNG (Portable Network Graphics). This format is widely supported by web browsers and image viewers/editors.
BMP
There are actually several BMP formats (BitMaP). Windows and Macintosh have their own formats, both of which are called BMP. Most modern image editing tools are able to read both.
In any case, all of the variants of BMP should be avoided when possible, as they use little to no compression and consequently have unnecessarily large file sizes.
Tagged Image File Format is used to store raw bitmap data by some programs and devices such as scanners. This format comes in a compressed and an uncompressed variant. The former is comparable to PNG, while the latter is more like BMP.
Using the uncompressed variant is not advised.
More details can be found on the VectorMagic website.
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