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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.
The computer graphics pipeline, also known as the rendering pipeline, or graphics pipeline, is a framework within computer graphics that outlines the necessary procedures for transforming a three-dimensional (3D) scene into a two-dimensional (2D) representation on a screen. [1]
A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane.
Free-Form Deformation is used in computer graphics for solid geometric models. For example, the Lattice Modifier in Blender (software). It is used in the image registration in both rigid and non-rigid transformation. [4]
3-D computer graphics rely on many of the same algorithms as 2-D computer vector graphics in the wire-frame model and 2-D computer raster graphics in the final rendered display. In computer graphics software, 2-D applications may use 3-D techniques to achieve effects such as lighting, and similarly, 3-D may use some 2-D rendering techniques.
Shear matrices are often used in computer graphics. [ 4 ] [ 5 ] [ 6 ] An algorithm due to Alan W. Paeth uses a sequence of three shear mappings (horizontal, vertical, then horizontal again) to rotate a digital image by an arbitrary angle.
Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts. Homogeneous coordinates have a range of applications, including computer graphics and 3D computer vision, where they allow affine transformations and, in general, projective transformations to be easily represented by a matrix.
In 3D computer graphics, a wire-frame model (also spelled wireframe model) is a visual representation of a three-dimensional (3D) physical object. It is based on a polygon mesh or a volumetric mesh, created by specifying each edge of the physical object where two mathematically continuous smooth surfaces meet, or by connecting an object's constituent vertices using (straight) lines or curves.