# Degrafa – Introduction to Splines Part X

Continuing from Part IX, one of the features of building the Bezier spline with cubic segments (individual cubic Bezier curves) is some flexibility in how the control cages are constructed.  The mathematical details are discussed in this TechNote.  At a high level, consider the spline as a rope that is passed through rings at each knot.  Suppose you could ‘pull’ on the rope at any ring.  What would happen to the rope?

We would expect the rope to get tighter and tighter until it reached some point that it could not be pulled any further (without breaking).  Intuitively, we would call this tension.  Bezier curves (individual or composite) do not naturally have tension parameters (as say a cardinal spline).  We can fake a tension setting as a natural consequence of assigning control points.

In the Singularity Bezier spline, the tension setting is a map of a tension scale to parameter values.  The tension scale varies from 1 (loose) to 5 (tight).  The internal parameter map is open for experimentation and some limitations are discussed in the above TechNote.

From a usability standpoint, all the average user need be concerned with is the tension setting from 1-5.  The default value is 1, which can be thought of as having the rope pass ‘loosely’ through the rings.  On average, the spline appears to have more curvature when passing through the knots.

The tension parameter is exposed to MXML, and the following illustrates setting to it maximum value of 5,

```<BezierSpline id="mySpline" graphicsTarget="{[theTarget]}"
verticalCenter="0" horizontalCenter="0"
data="200,100 200,300 100,300 300,500 500,300
400,300 400,100"
fill="{myFill}" autoClose="true" tension="5">```

producing the following drawing.

1. Laurent says: