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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 ...
While MS-DOS and NT always treat the suffix after the last period in a file's name as its extension, in UNIX-like systems, the final period does not necessarily mean that the text after the last period is the file's extension. [1] Some file formats, such as .txt or .text, may be listed multiple times.
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 toolkit was originally developed as the mozpotools by David Fraser for Translate.org.za. Translate.org.za had focused on translating KDE which used Gettext PO files for localization. With an internal change to focus on end-user, cross-platform, OSS software, the organisation decided to localize the Mozilla Suite. This required using new ...
For example: If the robot is a single point (zero-sized) translating in a 2-dimensional plane (the workspace), C is a plane, and a configuration can be represented using two parameters (x, y). If the robot is a 2D shape that can translate and rotate, the workspace is still 2-dimensional.
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 ...
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 ...
Here, only four parameters are needed (two translations, one scaling, one rotation). These can be determined from two known points; if more points are available then checks can be made. Sometimes it is sufficient to use the five parameter transformation, composed of three translations, only one rotation about the Z-axis, and one change of scale.