Posture

A Posture is a way to calculate hermite data (positions, tangents and curvatures) for a sequence of points. It is a method given by Shin & Singh and it involves looking at 3 consecutive points at a time and calculating the position and radius of the circle that passes through all three points. The inverse of the radius is the curvature at the middle point, and the tangent of the of the middle point is precisely the tangent on the circle at that point. This is complicated slightly by considering the edge cases of the first and last point, but we can simply consider the first three and last three points to fit the circle respectively.

You should use the Posture object if you don't have hermite data for your point set, and only have the points themselves. It is only useful in the sense that it saves you time and effort on initial calculations. Most of the solutions should have a spline helper method that uses posture data.