Fermat原理求解柱锥系统二阶反射问题

Determination of second-order reflection points in the system of cylinder and cone using Format's principle

以圆柱和圆锥二阶系统的反射寻迹为例,结合费马原理和反射定律,推导出各反射点Z坐标的解析表达式,从而减少了寻迹方程中未知数个数,使计算时间显著缩短,也提高了结果精度,文中给出了应用实例.利用类似的方法可以解决其他类型的二阶反射寻迹问题,也对高阶反射问题求解起一定的参考作用.

The ray tracing of the second and higher order reflection is an important and difficult problem. The tracing equations in earlier papers involve several parameters, which leads to taking more time to solve the equations using the numerical searching method. In this paper, the analytical formulations for every reflection point's Z coordinate are deduced by using Fermat's principle and law of reflection in the system of cylinder and cone. Some application examples are given to illustrate that the tracing-time is dramatically reduced and the operational precision is improved. The method presented in this paper can be expanded to solve the ray tracing of the second order reflection of some other model and used as a reference to solve the higher order reflection problem.