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In 3D computer graphics software, vertex painting refers to interactive editing tools for modifying vertex attributes directly on a 3D polygon mesh, using painting tools similar to any digital painting application but working in a 3D viewport on a perspective view of a rotated model.
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.
Morph target animation, per-vertex animation, shape interpolation, shape keys, or blend shapes [1] is a method of 3D computer animation used together with techniques such as skeletal animation. In a morph target animation, a "deformed" version of a mesh is stored as a series of vertex positions.
Most attributes of a vertex represent vectors in the space to be rendered. These vectors are typically 1 (x), 2 (x, y), or 3 (x, y, z) dimensional and can include a fourth homogeneous coordinate (w). These values are given meaning by a material description. In real-time rendering these properties are used by a vertex shader or vertex pipeline.
For a polygonal mesh, each vertex can have a blend weight for each bone. To calculate the final position of the vertex, a transformation matrix is created for each bone which, when applied to the vertex, first puts the vertex in bone space then puts it back into mesh space. After applying a matrix to the vertex, it is scaled by its ...
Let = (,) be a graph (or directed graph) containing an edge = (,) with .Let be a function that maps every vertex in {,} to itself, and otherwise, maps it to a new vertex .The contraction of results in a new graph ′ = (′, ′), where ′ = ({,}) {}, ′ = {}, and for every , ′ = ′ is incident to an edge ′ ′ if and only if, the corresponding edge, is incident to in .
Blender is available for Windows 8.1 and above, and Mac OS X 10.13 and above. [243] [244] Blender 2.80 was the last release that had a version for 32-bit systems (x86). [245] Blender 2.76b was the last supported release for Windows XP, and version 2.63 was the last supported release for PowerPC.
The formula can be proved by using mathematical induction: starting with a triangle, for which the angle sum is 180°, then replacing one side with two sides connected at another vertex, and so on. The sum of the external angles of any simple polygon, if only one of the two external angles is assumed at each vertex, is 2π radians (360°).