We extend our previous algorithm computing the minimum orbital intersection distance (MOID) to include hyperbolic orbits, and mixed combinations ellipse–hyperbola. The MOID is computed by finding all stationary points of the distance function, equivalent to finding all the roots of an algebraic polynomial equation of 16th degree. The updated algorithm carries about numerical errors as well, and benchmarks confirmed its numeric reliability together with high computing performance.

中文翻译：

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涉及双曲轨道的快速错误安全MOID计算

我们扩展了先前计算最小轨道交叉距离（MOID）的算法，以包括双曲线轨道以及椭圆-双曲线的混合组合。通过找到距离函数的所有固定点来计算MOID，这等效于找到16度的代数多项式方程的所有根。更新后的算法也会带来数值误差，基准测试证实了其数值可靠性以及较高的计算性能。