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The KTX 2.0 extension for universal texture compression enables 3D models in the glTF format to be highly compressed and to use natively supported texture formats, reducing file size and boosting rendering speed. [28] Draco is a glTF extension for mesh compression, to compress and decompress 3D meshes, to help reduce the size of 3D files.
Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
A rotation can be represented by a unit-length quaternion q = (w, r →) with scalar (real) part w and vector (imaginary) part r →. The rotation can be applied to a 3D vector v → via the formula = + (+). This requires only 15 multiplications and 15 additions to evaluate (or 18 multiplications and 12 additions if the factor of 2 is done via ...
The effect is a rotation with uniform angular velocity around a fixed rotation axis. When the initial end point is the identity quaternion, slerp gives a segment of a one-parameter subgroup of both the Lie group of 3D rotations, SO(3), and its universal covering group of unit quaternions, S 3. Slerp gives a straightest and shortest path between ...
For applications in physics and specially in mechanics, a change of basis often involves the transformation of an orthonormal basis, understood as a rotation in physical space, thus excluding translations. This article deals mainly with finite-dimensional vector spaces.
To plot any dot from its spherical coordinates (r, θ, φ), where θ is inclination, the user would: move r units from the origin in the zenith reference direction (z-axis); then rotate by the amount of the azimuth angle (φ) about the origin from the designated azimuth reference direction, (i.e., either the x– or y–axis, see Definition ...
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Coot displays electron density maps and atomic models and allows model manipulations such as idealization, real space refinement, manual rotation/translation, rigid-body fitting, ligand search, solvation, mutations, rotamers, and Ramachandran idealization. The software is designed to be easy-to-learn for novice users, achieved by ensuring that ...