The first part of this is a voxelized threshold of the field. Here I've come up with a different approach, consisting of two stages. There’s also a variant of this using tetrahedra, which I’ve played around with in the past ( 0, 1, 2). Probably the most popular approach to isosurfacing is an algorithm called marching cubes, which checks values of the field at the 8 corners of each cell of a cubic grid, and assigns each cell one of 256 pre-defined possible polygon topology configurations depending on how the field changes values between the corners, with some interpolation for the positions. A scalar field has a value everywhere in space, and the surface is where it switches from negative to positive, or crosses some given threshold value. These are also sometimes called isosurfaces or level sets, and they can be thought of as the equivalent of the contours of a heightfield, but in one dimension higher. With the scalar fields, I also made an implicit surface tool. For now this includes scalar, vector and frame fields. Various tools for fields do already exist in Grasshopper, both natively and as plugins, but of the ones I looked at, I couldn't find any that provided the flexibility and speed I wanted, so I put together a very simple library. For speed reasons I did not want to do this by passing millions of sample values. I wanted a simple way of defining such a field in a Grasshopper script component as an equation, or a function of distance to some geometry, then passing this field to another script component, in a way that the downstream component can easily query the value of the field at any point.
In particular, the terms quadratic in the covariant derivatives of the kinetic part of the aether lagrangian modify the gravitational action of general relativity.Spatially varying fields, which associate a value (such as a number or a vector) to every point in space, have a wide range of applications. On the other hand, in Einstein-aether theory, the Lorentz symmetry is violated by the introduction of a unitary time-like vector field, known as the ‘æther’, in the Einstein–Hilbert action. Cosmological applications of Hořava–Lifshitz theory are discussed in, while cosmological constraints on Hořava–Lifshitz theory using some of the recent cosmological data can be found in. Recently, it has been found that Hořava–Lifshitz gravity is in agreement with the observations of the gravitational-wave event GW170817. There are various physical applications of Hořava–Lifshitz gravity, some results on compact stars, black holes, universal horizons, non-relativistic gravity duality and other subjects are discussed in the review. Hořava–Lifshitz gravity is a power-counting renormalization theory with consistent ultra-violet behavior exhibiting an anisotropic Lifshitz scaling between time and space at the ultra-violet limit, while general relativity is provided as a limit. Hořava–Lifshitz gravity and Einstein-aether gravity are two theories which have been widely studied because they provide Lorentz violation. Alternative theories of gravity, where the Lorentz symmetry is violated, have drawn the attention of gravitation physicists in the last decades.
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