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The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as proj b a {\displaystyle \operatorname {proj} _{\mathbf {b} }\mathbf {a} } or a ∥ b .
Swizzles can also project from a vector of one dimensionality to a vector of another dimensionality, such as taking a three-dimensional vector and creating a two-dimensional or five-dimensional vector using components from the original vector. [2] For example, if A = {1,2,3,4}, where the components are x, y, z, and w respectively, you could ...
Eigen is a vector mathematics library with performance comparable with Intel's Math Kernel Library; Hermes Project: C++/Python library for rapid prototyping of space- and space-time adaptive hp-FEM solvers. IML++ is a C++ library for solving linear systems of equations, capable of dealing with dense, sparse, and distributed matrices.
Smoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, [1] [2] video game engines, [3] and machine learning. [ 4 ] The function depends on three parameters, the input x , the "left edge" and the "right edge", with the left edge being assumed smaller than the right edge.
The Möller–Trumbore ray-triangle intersection algorithm, named after its inventors Tomas Möller and Ben Trumbore, is a fast method for calculating the intersection of a ray and a triangle in three dimensions without needing precomputation of the plane equation of the plane containing the triangle. [1]
There has been an emergence of 2D and 3D game engines for WebGL, [56] such as Unreal Engine 4 and Unity. [57] The Stage3D/Flash-based Away3D high-level library also has a port to WebGL via TypeScript. [25] [58] A more light-weight utility library that provides just the vector and matrix math utilities for shaders is sylvester.js.
The first successful, yet partial implementation of physically-based rendering in a video game can be found in the 2013 title Remember Me, that despite being built on a game engine not natively supporting this technology (Unreal Engine 3) was properly modified to accommodate this feature. [4]
In 3D computer graphics, 3D modeling is the process of developing a mathematical coordinate-based representation of a surface of an object (inanimate or living) in three dimensions via specialized software by manipulating edges, vertices, and polygons in a simulated 3D space.