![]() In the first section, we describe the two methods used for the generation of shape models. ![]() A second objective is to discuss whether and how this 3-D geometric information can be used to evaluate the different hypotheses for the formation of shatter cones and the potential of this approach to settle a debate about this fundamental question in impact science that started about 50 years ago. Therefore, the first objective of this paper is to determine whether shatter cones may be described by one or several types of quadric surfaces using a database of shape models generated for selected shatter cones from various impact sites and for different types of host rock. The study of Wilk and Kenkmann ( 2015a) focused on the morphology of the striations, and on the presence of vesicular melt films but did not address the macroscopic shape of the shatter cones produced in these experiments. The analysis of the surface morphology of the tiny sample was carried out with a Bruker AXS Contour GT-K0 white light interferometer (WLI). 3-D shape models of experimentally produced tiny shatter cones (a few millimeters in size) have been recently obtained in the context of a MEMIN experiment (Wilk and Kenkmann 2015a, 2016). ( 2004) do not allow us to assess the three-dimensional (3-D) geometry of these objects. The two-dimensional (2-D) topographic profiles recorded by Sagy et al. Cylinders, cones, and planes are particular (degenerate) cases of quadric surfaces. Such mathematical objects include ellipsoids, hyperboloids, and paraboloids. Quadric surfaces are relatively common in nature and are defined in Euclidian space as the zeroes of a quadratic polynomial. Here, we propose that shatter cones may be adequately described by quadric surfaces. However, the type of surface associated with shatter cones has never been addressed due to the lack of appropriate data. 2004) and a more general algebraic expression would be needed to describe the shape of these fractures. Even if the term shatter cone is retained for historical reasons, it has been already noted that topographic profiles originating at the apex are curved (Sagy et al. If the directrix is an ellipse, the cone is said to be an elliptical cone. If the directrix is a circle, the cone is said to be a circular cone. Each of those lines is called a generatrix of the surface. In geometry, a conical surface is the unbounded surface formed by the union of all the straight lines that pass through a fixed point-the apex or vertex-and any point of some fixed space curve-the directrix-that does not contain the apex. However, such specimens are relatively rare for most other impact structures, and the term loosely applies to a wide range of curviplanar fractures and composite objects composed of several curved fractures associated with the typical divergent striations (e.g., Ferrière and Osinski 2012). The term originated from the spectacular samples of complete and isolated cones first described from the Steinheim Basin impact structure (Branco and Fraas 1905). Shatter cones are represented by a range of curved fractures decorated with divergent striations and occurring exclusively in the context of impact structures. This requires theoretical developments, and experimental or numerical simulations of the propagation of tensile fractures associated with shock waves. The value of these shape models to discriminate between the different hypotheses of formation of shatter is still limited, as it remains to be resolved which type of surface pertains to which hypothesis. The surface characteristics are generally not consistent with the mathematical definition of a cone. The analysis of 20 shape models of shatter cones from nine different impact sites indicates that the surface of shatter cones may be described by quadric surfaces and are generally consistent with hyperboloids, whereas occurrence of paraboloid objects cannot be ruled out. The second one uses an articulated arm equipped with a digital laser scanner and produces high-resolution and precision shape models of hand-sized samples. The first one is based on images acquired using a commercial camera and may be applied on large samples in the field. Here, we apply two methods to derive shape models of shatter cones. The geometry of these objects is therefore highly variable but its significance was never addressed due to the lack of appropriate data. It also imprecisely extends to the curved or subplanar fractures decorated with striations commonly observed at impact sites. The terminology “cone” was chosen from the observation of complete or near-complete, roundish, axisymmetric objects with a well-defined apex/apical area. Shatter cones are curved fractures decorated with divergent striations that are exclusively associated with impact metamorphism.
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