Raph Levien的Spiro如何选择路径端点的角度？

I’ve thoroughly read through Raph Levien’s spline curve work and have a solid understanding of the core concepts in Chapter 8 focused on fitting piecewise polynomial spirals to point sequences. Here are the key takeaways:

• Closed Loop Mandate: This fitting approach strictly requires the path to be a closed loop. If working with an open path, two additional degrees of freedom emerge—specifically, the Newton-like iterative process does not adjust the tangent angles at the path’s endpoints.
• Optimal Endpoint Angle Optimization: For open paths (even though they’re not the intended use case), the ideal endpoint tangent angles are those that minimize the integral of the square of the first derivative along the path length. This criterion ensures the path is as smooth and efficient as possible.

Content of the question sourced from Stack Exchange, question author Anton Sherwood