通过圆的渐开线的逆运算构造具有给定边界条件的螺旋
Construction of a spiral with given boundary conditions by inversion of the involute of a circle
AI总结：
本文提出通过确定两个逆不变量并基于渐开线构造弧来解决给定端点切线和曲率的螺旋构造问题。
摘要：
为构造具有单调曲率的曲线（螺旋）并给定端点的切线和曲率，作者提出以下方法：从给定边界条件确定两个逆不变量的值，然后在某些基螺旋（最初选择对数螺旋）上寻找具有相同不变量的弧段。找到的弧段的线性-分数映射解决了问题。选择圆的渐开线作为基螺旋似乎能得到最简单的解，此处予以呈现。
英文摘要：
To construct a curve with a monotonic curvature (spiral), and given tangents and curvatures at the ends, the author proposed the following method. From given boundary conditions, the values of two inverse invariants are determined. Then, on some base spiral (initially, a logarithmic spiral was chosen), an arc with the same invariant values is sought for. A linear-fractional map of the found arc solves the problem. It seems that choosing the involute of a circle as the base spiral yields the simplest solution, which we present here.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
