Search results
Results From The WOW.Com Content Network
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]
The magnitude of the unit quaternion will be unity, corresponding to a hypersphere of unit radius. The vector part of a unit quaternion represents the radius of the 2-sphere corresponding to the axis of rotation, and its magnitude is the sine of half the angle of rotation.
A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in ^ (pronounced "v-hat"). The term normalized vector is sometimes used as a synonym for unit vector. The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e.,
Oblique vector rectifies to slerp factor. More familiar than the general slerp formula is the case when the end vectors are perpendicular, in which case the formula is p 0 cos θ + p 1 sin θ. Letting θ = t π /2, and applying the trigonometric identity cos θ = sin(π /2 − θ), this becomes the slerp formula.
The isomorphism class of a finite-dimensional vector space can be identified with the non-negative integer representing its dimension. The classification of finite simple groups enumerates the isomorphism classes of all finite simple groups. The classification of closed surfaces enumerates the isomorphism classes of all connected closed surfaces.
Verse allows defining functions within classes. These can perform various operations, such as mathematical calculations, game logic, and more. The example below is a method to determine if a character is looking at a specific location. IsLookingAtLocation(Character:fort_character, LocationToCheck: vector3, Threshold: float):logic
Zorn's lemma can be used to show that every vector space V has a basis. [13] If V = {0}, then the empty set is a basis for V. Now, suppose that V ≠ {0}. Let P be the set consisting of all linearly independent subsets of V. Since V is not the zero vector space, there exists a nonzero element v of V, so P contains the linearly independent ...
The weight vector is learned from a set of labeled training samples. Often f is a threshold function , which maps all values of w → ⋅ x → {\displaystyle {\vec {w}}\cdot {\vec {x}}} above a certain threshold to the first class and all other values to the second class; e.g.,