What Is a Polygonal Impact Crater? A Proposed Framework Toward Quantifying Crater Shapes

Impact craters are used for a wide array of investigations of planetary surfaces. A crater form that is somewhat rare, forming only & SIM;10% of impact craters, is the polygonal impact crater (or PIC). These craters have been visually, manually identified as having at least two rim segments that are best represented as straight lines. Such straight lines or edges are most often used to infer details about the subsurface crust where faults control the structure of the crater cavity as it formed. The PIC literature is scant, but almost exclusively these craters are identified manually, and the potentially straight edges are classified and measured manually. The reliance on human subjectivity in both the identification and measurement motivated us to design a more objective algorithm to fit the crater rim shape, measure any straight edges, and measure joint angles between straight edges. The developed code uses a Monte Carlo approach from a user-input number of edges to first find a reasonable shape from purely random possible shapes; it then uses an iterative Monte Carlo approach to improve the shape until a minimum difference between the shape and rim trace is found. It returns the result in a concise, parameterized form. This code is presented as a first step because, while we experimented with several different metrics, we could not find one that could consistently, objectively return an answer that stated which shape for a given crater was the best; this objective metric is an area for future improvement.