IdleCuriosity Creatures

The curves are a set of macros for calculating a spline path whose ends may move while keeping the length the same. A sample spline is created then it's length calculated; bisection is then used to refine the spline path until it's length is within acceptable limits.

There are five schemes for calculating the curves.

1. One is useful for splines whose end points are roughly at the same level. It creates a loop in the spline to adjust the spline length.
2. For points that are very different in height another uses an S curve that flattens by using spline tension as the heights become closer.
3. Another S curve is available for points that may come closer to the level than for 2. This S curve changes in angle rather than tension.
4. The fourth is a mix of 1. and 3. At times when the ends are close to the same level it resembles the loop of 1. but when the points move away from the same level it becomes more like an S curve. Though this incorporates the faults of both 1. and 3. it is better for splines in which the end points may vary a lot.
5. The last curve is similar to 2. But instead of using fixed end points and adjusting the tension the tension is constant and one end point is allowed to vary to keep the length the same.