Here, we introduce the quadratic orthogonal projection (the problem of projecting a point onto a quadratic level set), as an extension of the linear orthogonal projection (the problem of projecting a point onto a hyperplane). As the latter problem is convex and has a closed formula solution, the former one belongs to a special class of non-convex problems. We propose an iterative algorithm for the quadratic orthogonal projection, and test it for distinct quadratic functions, showing its great potential in applications, such as in computer graphics, alternating projections, and orbit projections.

中文翻译：

---

一种将点投影到二次函数的水平集上的算法

在这里，我们介绍二次正交投影（将点投影到二次水平集上的问题），作为线性正交投影（将点投影到超平面上的问题）的扩展。由于后一个问题是凸的并且有一个封闭的公式解，前一个问题属于一类特殊的非凸问题。我们提出了一种二次正交投影的迭代算法，并针对不同的二次函数对其进行了测试，显示了其在计算机图形学、交替投影和轨道投影等应用中的巨大潜力。