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  2. Swizzling (computer graphics) - Wikipedia

    en.wikipedia.org/wiki/Swizzling_(computer_graphics)

    In computer graphics, swizzles are a class of operations that transform vectors by rearranging components. [1] 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]

  3. Free body diagram - Wikipedia

    en.wikipedia.org/wiki/Free_body_diagram

    Then the vector value of the resultant force would be determined by the missing edge of the polygon. [2] In the diagram, the forces P 1 to P 6 are applied to the point O. The polygon is constructed starting with P 1 and P 2 using the parallelogram of forces (vertex a). The process is repeated (adding P 3 yields the vertex b, etc.). The ...

  4. Rodrigues' rotation formula - Wikipedia

    en.wikipedia.org/wiki/Rodrigues'_rotation_formula

    Vector geometry of Rodrigues' rotation formula, as well as the decomposition into parallel and perpendicular components. Let k be a unit vector defining a rotation axis, and let v be any vector to rotate about k by angle θ ( right hand rule , anticlockwise in the figure), producing the rotated vector v rot {\displaystyle \mathbb {v} _{\text ...

  5. Force - Wikipedia

    en.wikipedia.org/wiki/Force

    Resolving force vectors into components of a set of basis vectors is often a more mathematically clean way to describe forces than using magnitudes and directions. [30] This is because, for orthogonal components, the components of the vector sum are uniquely determined by the scalar addition of the components of the individual vectors.

  6. Resultant force - Wikipedia

    en.wikipedia.org/wiki/Resultant_force

    The forces and torques acting on a rigid body can be assembled into the pair of vectors called a wrench. [3] If a system of forces and torques has a net resultant force F and a net resultant torque T, then the entire system can be replaced by a force F and an arbitrarily located couple that yields a torque of T.

  7. Tangential and normal components - Wikipedia

    en.wikipedia.org/wiki/Tangential_and_normal...

    Illustration of tangential and normal components of a vector to a surface. In mathematics, given a vector at a point on a curve, that vector can be decomposed uniquely as a sum of two vectors, one tangent to the curve, called the tangential component of the vector, and another one perpendicular to the curve, called the normal component of the vector.

  8. Scalar–vector–tensor decomposition - Wikipedia

    en.wikipedia.org/wiki/Scalar–vector–tensor...

    The decomposition states that the evolution equations for the most general linearized perturbations of the Friedmann–Lemaître–Robertson–Walker metric can be decomposed into four scalars, two divergence-free spatial vector fields (that is, with a spatial index running from 1 to 3), and a traceless, symmetric spatial tensor field with ...

  9. Four-vector - Wikipedia

    en.wikipedia.org/wiki/Four-vector

    A four-vector A is a vector with a "timelike" component and three "spacelike" components, and can be written in various equivalent notations: [3] = (,,,) = + + + = + = where A α is the magnitude component and E α is the basis vector component; note that both are necessary to make a vector, and that when A α is seen alone, it refers strictly to the components of the vector.

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