Vector GraphicsThere are two kinds of computer graphics - raster (composed of pixels) and vector (composed of mathematically-defined paths). Raster images are more commonly called bitmap images.
Adobe Photoshop is primarily a raster or paint program. The raster or paint tools include the Paintbrush Tools, Stamp and Clone Tools, Eraser, Healing Brush and Dodge, Burn and Sponge Tools which affect the pixels of an image directly,
A bitmap image uses a raster or grid of individual pixels where each pixel has an individual definition. Bitmap Images are composed of pixels in a raster and are considered "resolution-dependent" because they are defined by their number of pixels per inch, or PPI. The image at the left is an example of a raster of pixels describing a blue disk. Notice the smoothness is limited by the resolution (number of pixels per inch).
Adobe Photoshop also has vector tools, sometimes called drawing or illustration tools, such as the Pen Tools, Shape Tools and the Text Tools, to create certain types of graphic work. Adobe also has a Program dedicated to vector image creation called Adobe Illustrator, but that's a different class.
Vector graphics use mathematical relationships between points and the paths connecting them to describe an image. Vector graphics are composed of points which describe Vector Paths which can be infinitely scaled to any size without degrading the image quality. Vector Paths can define Lines and Shapes.
No matter how large you make them, the mathematical relationship between the points does not change, and so they are considered "resolution-independent."
Vector Paths are not printable in a Photoshop document until they have been Filled or Stroked with color pixels which are resolution dependent.
Curved paths, named Bezier Curves after their inventor, Pierre Bézier, are used in nearly every drawing program. The most commonly used Bezier curves are fully defined by four points: two anchor points and two control points that do not lie on the curve itself but define its shape. The anchor points describe where the line goes through. Control points create "vector influences" which warp or curve the lines from anchor point to anchor point. You can always go back and edit the anchor points and control points in Photoshop, so this is a very powerful and useful tool.
In the figure above, you see the anchor points, the path segments, direction lines, and control points. The segments constitute the path itself. The anchor points determine where the path segment will go. The direction lines, which are manipulated with the control points, determine the shape of the segment.
To create the line you see above, try the following steps:
In Adobe Photoshop, Text is defined by the Text Tool as vector graphics using point-to-point math rather than by pixels. The shape created by the path is then filled with whatever color you choose. The image to the left below is representative of a bitmap image of the letter "e" which has been enlarged in size to exaggerate the fact that the edges of a bitmap become jagged as it is scaled up. The two graphics next to it represent vector graphics, made up of points which describe a path. The one on the far right shows the bezier curves which mathematically define influences on the path and create curved lines:
Example of a raster or "bitmap" image of the letter "e"
Example of the letter "e" defined by points which describe a path
Example of the letter "e" showing the Bezier control points used to curve the paths