Vector graphics are made of mathematical calculations that form objects or lines - they do not use pixels therefore are resolution-independent which means they can be used at the highest resolution the output device allows:

Vector graphics can be enlarged and printed at ANY SIZE!

Instead of pixels, vector graphics use objects and lines (shapes) to represent images. Vector files can be scaled to any size without losing quality.

Some Vector programs have two different views; preview/normal view which displays the image as we normally would see it and an outline/wireframe view which displays the outline of every object in the file. This vector outline/wireframe is important to some companies like engraving & vinyl-cut signs because it guides the equipment they use to create their products.



For categorizing purposes I have named the above: photo-realistic vector, vector illustration, and vector lineart.

1. Photo-realistic vector: a photograph was traced as vector using a multitude of colors to allow the image to have a closer resemblance to original. This vector image can be used in many different processes like CMYK or digital printing, but as you can see from the outline/wireframe view, there are too many objects for it to work for engraving or vinyl-cut signs. Photographs are best printed as they are - raster images..

2. Vector illustration. This is a hand-drawn, simplified illustration using a limited amount of colors and color blends. Color blends can be created in vector programs but they are actually raster effects so this image is NOT 100% vector. The raster effects show up as boxes on the outline/wireframe view. This vector image is suitable for many processes except those that are guided by the vector outline such as vinyl-cut signs or engraving.

There are other ways to achieve color blends, 
please see traced vectorization of images with color blends

3. Vector lineart. This is 100% vector art; NO COLOR BLENDS. The outline/wireframe is acceptable for all processes including those that are guided by the vector outline.

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• Common vector graphic file format: eps* ai, cdr, ps, pdfs originating from vector files
• Common vector graphic programs: drawing programs such as Illustrator, CorelDraw, FreeHand
• Common vector graphics: drawings, illustrations, cartoons

* eps and pdf files can originate from either raster or vector programs, and/or can include raster & vector elements. 

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If I am creating a new design which software should I use; Raster or Vector Graphic Program?

It depends on the design itself. If it's going to have photographic elements with continuous tones and blends of color, you are probably better off using a paint program like Photoshop which is a raster program that specializes in photo editing, or use any other PAINT program.

If you want your final design to look like an illustration instead with clear contrasts between objects & shapes, then use a vector program.

You MUST use a vector program when creating art for plotters, vinyl-cut signs, engraving and other specialty items.

Ideally a company that has a logo design with photographic elements, also has a secondary version of their logo in vector format that can be used for those specialty items that require vector art. Sample below:



Raster (Bitmap)

• Made of pixels; tiny dots or squares* of color

• Represents and edits photo and photo-like elements better than vector programs with the use of continuous tones. The use of different color pixels allows for smooth blends of colors.

Disadvantages 

• Is bound by the number of pixels in the image. It cannot be scaled up without losing quality.

•Large (dimension) & detailed images equal large file size

• Some service providers like engravers, stencil-cut signs, etc, must have vector art.

• It is more difficult to print raster images using a limited amount of spot colors

• Depending on the complexity of the image, conversion to vector may be time consuming

Vector

• Made of mathematical calculations that form objects and lines

• Can be scaled to any size without losing quality

• Resolution-independent: Can be printed at any resolution

• Number of colors can be easily increased or reduced to adjust printing budget.

• A large dimension vector graphic can maintain a small file size.

• Vector art is required by many service providers

• Can be easily converted to raster

Disadvantages 

• It is not the best format for photographs or photo-like elements with blends of color


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