A curve is a path that joins a series of points.
To create a curve, enter the points and PowerShape automatically joins them with a curve. By editing the curve, you can control how the curve enters and leaves a point.
Generally, curves created within PowerShape are parametric cubic curves known as Bézier curves. In this representation, a span of the curve is defined by two control points which lie on its tangents at its end points. See figure below. C0 is the control point at end point P0, and C1 at P1.
These control points also define the tangent directions (D0 and D1) and tangent magnitudes (M0 and M1) at the end points (P0 and P1).
The effect of increasing both the tangent magnitudes simultaneously is to give more fullness to the curve as shown below.
An increase in only one of the magnitudes causes the curve to follow the tangent direction at that point for a greater part of its length before turning into the other tangent direction. This is shown below.
The tangent direction and magnitude before, after or along each point in the curve can be set or freed.
By changing the tangent directions and magnitudes you can get considerable control over the shape of the curve, including introducing discontinuities at key-points and making spans into straight lines, circular or conic arcs.
A curve can be open or closed (that is the end point of the curve is joined to the start point by the last span in the curve).