![]() Therefore, the most effective methods employ spherical coordinates. ( 2017).įor applications over large geographical areas, the Earth's curvature must be taken into consideration. Meanwhile, methods based on swarm intelligence have been introduced to solve the inversion problem by Zhan & Zhao ( 2010) and Pallero et al. ( 2006), Chakravarthi & Sundararajan ( 2007) and Chai & Hinze ( 1988) investigated inversion methods of an interface that has depth-dependent density variations and that yields superior results when dealing with the sedimentary rocks. The latter is based on the method proposed by Parker ( 1973) in the spectral domain. ( 1996) introduced forward and inverse methods of a density interface using the Parker–Oldenburg method (Oldenburg 1974). Guspí ( 1992) proposed a method of inverting for a density contrast using Fourier transforms. The inversion may be approached in either the spatial or spectral domains. The inversion problem is satisfied by determining depths of the prisms that can reproduce the observed gravitational data. Methods discussed in the literature generally use Cartesian or spherical coordinate systems.įor local studies, the surface undulation of the interface, for example, the basement depths of a sedimentary basin, is normally represented by a set of juxtaposed right-rectangular prisms. The determination of the geometry of the interface is approached as an inversion problem using the gravitational data. In general, the problem can be summarized as solving for the deviations of an objective interface that separates two media with respect to a reference surface. Such studies are important because they have significant implications for tectonic interpretations or regional estimates of isostasy. 2004 Bagherbandi 2012a, b Uieda & Barbosa 2017) or the estimation of the geometry of an arbitrarily shaped mass body (D'Urso 2015 D'Urso & Trotta 2017 Ren et al. 2006 Chakravarthi & Sundararajan 2007), determination of the Moho discontinuity (Zhang et al. Existing techniques have led to numerous applications such as the estimation of basement relief (Guspí 1992 Silva et al. It's not going to interactively change your model, and you can't use the history once you've cut this thing into triangles - but maybe it's a start.Lunar and planetary geodesy and gravity, Planetary interiors, Crustal structure, Planetary tectonics 1 INTRODUCTIONĪ classical problem in the analysis of gravitational data is the estimation of the geometric properties, usually depth and surface undulations, of an interface with a density contrast (Barbosa et al. Change the tessellation of the NURBS object, then duplicate the polygon and do the same thing. So this is the basis of the construction - leave this polygon alone, duplicate it, then extract half the faces to get two equilateral triangles made up of equilateral triangles. If you go back to your NURBS surface, you can adjust the "Number U" and "Number V" in the Tessellation attributes, and your polygon surface will change with it because of the historical connection between the two. You'll get a polygon parallelogram consisting of 18 equilateral triangular faces. In the options box, check "Match Render Tessellation" and click "apply". Select the surface, go to "Modify -> Convert Nurbs to Polygons" and select the options box. If your triangles are not equilateral, go to the Edit Nurbs menu and reverse either the U or the V direction of the surface, and the tessellation will change. When you do this, you should see 18 equilateral triangles. NOTE: The Tessellation Display is not supported in Viewport 2.0 you'll see something but it will be WRONG! Switch your hardware renderer to the Legacy Viewport. Under the "Primary Tessellation Attributes", make sure that the Mode U and Mode V are set to "Per Span # of Isoparms", and set the number to the same in both U and V (my illustration uses 3). In the Attribute Editor for this surface, open up the "Tesselation" rollout, and check the box marked "Enable Advanced Tessellation". I duplicated the curve, moved it 5 units in X and lofted the two curves together. There are a few ways to do this - I created an EP curve by snapping one EP at the center of the grid, then snapping another 5 units up on the Y axis then I rotated that curve 30 degrees in Z. This is essentially two equilateral triangles in one surface. Not sure if this will help you - but try this - (it's a little kludgy and not really ready for prime-time, but interesting - and maybe you can derive a script from it).Ĭreate an equilateral parallelogram in NURBS with an angles of 60 and 120 degrees on opposite corners. You can get this kind of triangular tessellation in NURBS geometry, but the geometry has to be four-sided.
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