论文标题
解决alhazen-ptolemy问题：确定球形表面上的镜面点散发泰坦海洋的传递
Solving the Alhazen-Ptolemy Problem: Determining Specular Points on Spherical Surfaces for Radiative Transfer of Titan's Seas
论文作者
论文摘要
给定一个光源，球形反射器和一个观察者，在球体表面上，光线会直接反射到观察者，即镜面点在哪里？这被称为Alhazen-Ptolemy问题，为球形反射器找到这个镜面点可用于从计算机渲染到大气建模再到GPS通信的应用。现有的解决方案依赖于找到四分之一方程的根，并以数值评估哪个根提供了真正的镜面点。我们提供了一种公式和两种溶液，其中正确的根是可以预定的，从而允许构建我们提供的完全分析的解决方案。在计算更快的速度中，我们的解决方案应在需要重复计算镜面点（例如蒙特 - 卡洛辐射转移）的情况下被证明是有用的，包括对泰坦碳氢化合物海域的反射。
Given a light source, a spherical reflector, and an observer, where on the surface of the sphere will the light be directly reflected to the observer, i.e. where is the the specular point? This is known as the Alhazen-Ptolemy problem, and finding this specular point for spherical reflectors is useful in applications ranging from computer rendering to atmospheric modeling to GPS communications. Existing solutions rely upon finding the roots of a quartic equation and evaluating numerically which root provides the real specular point. We offer a formulation, and two solutions thereof, for which the correct root is predeterminable, thereby allowing the construction of the fully analytical solutions we present. Being faster to compute, our solutions should prove useful in cases which require repeated calculation of the specular point, such as Monte-Carlo radiative transfer, including reflections off of Titan's hydrocarbon seas.
