发表机构
Gyeongsang National University; Kyungpook National University（庆尚国立大学; 庆北国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究利用离散Frenet标架刻画三维欧氏空间中多边形一般螺旋线，得到固有有限步相容关系等结果，实现螺旋线相关量的重构与二阶精度收敛。
AI 中文摘要
我们利用离散Frenet标架的转角与带符号挠率角研究三维欧氏空间中的多边形一般螺旋线。对于轴线不与边切线正交的螺旋线，我们证明全局常角条件等价于存在守恒的Frenet标架向量。在通分支上，消去辅助系数可得到涉及三个连续转角和两个连续挠率角的固有有限步相容关系；互补的相位和线性子空间公式涵盖了对偶副法向量情形。这些刻画可重构螺旋轴线与螺旋角，并为每个转角给出精确界。我们还通过切线指标给出球面公式：其顶点位于单位球的平面截线上，非正交情形为小圆，正交情形恰为平面。一个非恒定Frenet数据示例说明了该准则。最后，对于光滑曲线的均匀弦长采样，离散Lancret型商与重构的螺旋方向以二阶精度收敛。
英文摘要
We study polygonal general helices in Euclidean three-space using the turning and signed torsion angles of the discrete Frenet frame. For helices whose axis is not orthogonal to the edge tangents, we prove that the global constant-angle condition is equivalent to the existence of a conserved Frenet-frame vector. On the generic branch, elimination of the auxiliary coefficient yields an intrinsic finite-step compatibility relation involving three consecutive turning angles and two consecutive torsion angles. Complementary phase and linear-subspace formulations cover the antipodal-binormal case. These characterizations reconstruct the helical axis and the helix angle and yield a sharp bound for each turning angle. We also give a spherical formulation through the tangent indicatrix: its vertices lie on a plane section of the unit sphere, which is a small circle in the non-orthogonal case, whereas the orthogonal case is exactly planar. A nonconstant Frenet-data example illustrates the criterion. Finally, for uniform chordal sampling of a smooth curve, the discrete Lancret-type quotient and the reconstructed helical direction converge with second-order accuracy.
