The anatomy of the distorted and topologically disrupted images of an extended object after reflection by curved mirrors, and of their refraction analogues, e.g. in gravitational lensing, is determined by the caustic surfaces enveloping the ray family issuing from each point of the object. Simulations are presented of reflections of the same object when organised by each of the five caustics (elementary catastrophes) that are stable in three-dimensional space: the fold, cusp, swallowtail, elliptic and hyperbolic umbilic catastrophes. The object is a picture of a face, whose familiar features make the image distortions and disruptions easier to understand. An important distinction is between mirrors curved in one direction and those curved in two.

扩展物体在被曲面镜反射后的扭曲和拓扑破坏图像及其折射类似物（例如在引力透镜中）的解剖结构由包围从物体每个点发出的光线族的焦散面确定。当由在三维空间中稳定的五种焦散（基本灾难）中的每一个组织时，同一对象的反射的模拟呈现：褶皱、尖头、燕尾、椭圆和双曲脐带灾难。该对象是一张人脸图片，其熟悉的特征使图像失真和中断更容易理解。一个重要的区别是向一个方向弯曲的镜子和向两个方向弯曲的镜子。