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A reflection about a line or plane that does not go through the origin is not a linear transformation — it is an affine transformation — as a 4×4 affine transformation matrix, it can be expressed as follows (assuming the normal is a unit vector): [′ ′ ′] = [] [] where = for some point on the plane, or equivalently, + + + =.
Each bone has a three-dimensional transformation from the default bind pose (which includes its position, scale and orientation), and an optional parent bone. The bones therefore form a hierarchy. The full transform of a child node is the product of its parent transform and its own transform. So moving a thigh-bone will move the lower leg too.
In computer graphics, free-form deformation (FFD) is a geometric technique used to model simple deformations of rigid objects. It is based on the idea of enclosing an object within a cube or another hull object, and transforming the object within the hull as the hull is deformed.
UV texturing is an alternative to projection mapping (e.g., using any pair of the model's X, Y, Z coordinates or any transformation of the position); it only maps into a texture space rather than into the geometric space of the object. The rendering computation uses the UV texture coordinates to determine how to paint the three-dimensional surface.
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 ...
Blender was initially developed as an in-house application by the Dutch animation studio NeoGeo (no relation to the video game brand), and was officially launched on January 2, 1994. [12] Version 1.00 was released in January 1995, [13] with the primary author being the company co-owner and software developer Ton Roosendaal.
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Hankel transform, the determinant of the Hankel matrix; Discrete Chebyshev transform. Equivalent, up to a diagonal scaling, ... additional terms may apply.