All shapes in Artstream are based on a resolution-independent method for describing curves named after the French mathematician Pierre Bezier. A Bezier curve is comprised of one or more segments, where each segment consists of four points..
Two single Bezier curve segments
The first and last point of each of these segments are referred to as anchor points. The two interior points of the segment are referred to as direction points. The lines that are drawn to connect an anchor point to it's neighboring direction point are referred to as a direction lines.
Multiple segments can be joined to form a contour, where the end point of one segment is shared with the start point of the next segment. A contour can have a minimum of one anchor point, but will not be visible until it has at least two, enough to form a single line or curve segment. Each subsequent point then adds a segment which can be connected with either a smooth point, or either of three types of a corner point.
A smooth point is an anchor point through which the curve passes without any discontinuities, or sharp direction changes. There is a pair of connected direction points at every smooth point, where there is some distance between them, and their direction lines pass though their shared anchor point in exactly opposite directions.
A corner point in an anchor point where a sharp direction change occurs. There are three varieties of corner points. A straight corner point is where the anchor point has no apparent directions points. A straight line results from two consecutive corner points, and a peak with two straight sides results from three. A curved corner point is where the direction lines connected to the shared anchor point have different, non-opposite directions. Curved corner points are useful for creating a peak with two curved sides. A combination corner point, as you might guess, is the mixture of a straight and curved corner point, where the shared anchor point has only one apparent direction point. A combination corner point allows the creation of a peak with one curved and one straight side.
For example, with Artstream's Pen Tool, each button click creates an anchor-direction point pair. The button down sets the anchor point to the current cursor position then, after optionally dragging the curve, the button up sets the direction point at the new, cursor position. A direction point is only apparent if the cursor has been dragged a distance from the button down point. If the direction point for the start of a new segment is dragged, (in the absence of modifier keys), it automatically resets the direction point at the end of the neighboring segment to mirror itself, with the same distance and opposite direction from their shared anchor point, causing the creation of a smooth point.
The contours that are built from Bezier curves can be either open or closed. An open contour has a distinct start and end anchor point, with any number of anchor points between them. A closed contour has an end point exactly equal to the start point. A closed contour can have any number of anchor points, but appears to have no start or end point.
Lastly, during the creation of curves, as with the Pen Tool, it is useful to become familiar with the range of curves that are possible between two anchor points of a given distance. As this familiarity grows, it will become possible to reduce to a minimum the number of points to express a given shape.