In Euclidean geometry, translation is a transformation of Euclidean space which moves every point by a fixed distance in the same direction. It can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. Each translation is an isometry.
Matrix representation
A translation cannot be accomplished using a 3-by-3 matrix, so homogeneous coordinates are normally used.
To translate an object by a vector v = (vx, vy, vz), each homogeneous vector p = (px, py, pz, 1) would need to be multiplied with this translation matrix:
As shown below, the multiplication will give the expected result:
The inverse of a translation matrix can be obtained by negating the vector:
In Euclidean geometry, a translation, or translation operator, is an affine transformation of Euclidean space which moves every point by a fixed distance in the same direction.
If T is a translation, then the image of a subset A under the function T is the translate of A by T.
Since a translation is an affine transformation but not a linear transformation, homogeneous coordinates are normally used to represent the translation operator by a matrix.
Extended CHS addressing adds a translation step that changes the way the geometry appears in order to break the 504 MB barrier, but the addressing is still done in terms of cylinder, head and sector numbers, however, they are just translated one or more times before they get to the actual disk itself.
The translatedgeometry is still what is presented to the operating system for use in Int 13h calls.
The difference is that when using ECHS the BIOS translates the parameters used by these calls from the translatedgeometry to the drive's logical geometry.
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