AI 中文总结
该研究结合球面clothoid相关定理、旋量参数化与积分求值方法，推导非螺旋三维clothoid的弧长显式笛卡尔坐标，并得到其显式渐近线相关结果。
AI 中文摘要
我们结合Lucas与Ortega-Yagues的球面clothoid重构定理、球面clothoid的显式旋量参数化，以及Kummer乘积积分的Kampe de Feriet求值方法，得到所有非螺旋三维clothoid的弧长显式笛卡尔坐标；Kummer渐近分析进一步给出显式渐近线，包括其伽马-双伽马偏移量与轴线间夹角。
英文摘要
We combine the spherical-clothoid reconstruction theorem of Lucas and Ortega-Yagues with an explicit spinorial parametrization of the spherical clothoid and a Kampe de Feriet evaluation of Kummer-product integrals. This gives explicit Cartesian coordinates, in arclength, for every nonhelical three-dimensional clothoid. Kummer asymptotics then yield explicit asymptotic lines, including their gamma-digamma offsets and the angle between their axes.
Comments11 pages, 1 figure. Includes reproducible Python code
