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Some transformations that are non-linear on an n-dimensional Euclidean space R n can be represented as linear transformations on the n+1-dimensional space R n+1. These include both affine transformations (such as translation) and projective transformations. For this reason, 4×4 transformation matrices are widely used in 3D computer graphics.
In computer graphics, a line drawing algorithm is an algorithm for approximating a line segment on discrete graphical media, such as pixel-based displays and printers. On such media, line drawing requires an approximation (in nontrivial cases). Basic algorithms rasterize lines in one color.
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 and thus to make it linear. Thus we write the 3-dimensional vector w = (w x, w y, w z) using 4 homogeneous coordinates as w = (w x, w y, w z, 1). [1]
They can be extended to non linear functions, such as perspective correct texture mapping, quadratic curves, and traversing voxels. In its simplest implementation for linear cases such as lines, the DDA algorithm interpolates values in interval by computing for each x i the equations x i = x i−1 + 1, y i = y i−1 + m, where m is the slope of ...
While algorithms such as Wu's algorithm are also frequently used in modern computer graphics because they can support antialiasing, Bresenham's line algorithm is still important because of its speed and simplicity. The algorithm is used in hardware such as plotters and in the graphics chips of modern graphics cards.
In mathematics, physics, and theoretical computer graphics, tapering is a kind of shape deformation. [1] [2] Just as an affine transformation, such as scaling or shearing, is a first-order model of shape deformation, tapering is a higher order deformation just as twisting and bending. Tapering can be thought of as non-constant scaling by a ...
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system .