TwistMarkMath

By conventions lace makers mark twists in pair diagrams with short perpendicular lines. In our application this line goes approximately through the centre of a pair segment.

The figures below inspired the approximation (no need to be exact) of t. The final calculation used to be in the method Annotations.createTwistMark. The black figures are adapted screen shots from the interactive pages of AbleStable, follow the link to Understanding Bezier Curves

The basic idea for calculation: the ratio of the distances of the end points to both control points. Just r1/(r1+r4) is too simple as thus the direction would play no role.

Inspiration for the correction:

The following diagram illustrates the variables used in further calculations.