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The three-way comparison operator or "spaceship operator" for numbers is denoted as <=> in Perl, Ruby, Apache Groovy, PHP, Eclipse Ceylon, and C++, and is called the spaceship operator. [2] In C++, the C++20 revision adds the spaceship operator <=>, which returns a value that encodes whether the 2 values are equal, less, greater, or unordered ...
Trilinear interpolation is a method of multivariate interpolation on a 3-dimensional regular grid. It approximates the value of a function at an intermediate point ( x , y , z ) {\displaystyle (x,y,z)} within the local axial rectangular prism linearly, using function data on the lattice points.
In the theory of three-dimensional rotation, Rodrigues' rotation formula, named after Olinde Rodrigues, is an efficient algorithm for rotating a vector in space, given an axis and angle of rotation. By extension, this can be used to transform all three basis vectors to compute a rotation matrix in SO(3) , the group of all rotation matrices ...
In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space.For example, using the convention below, the matrix = [ ]
A general 3d rotation of a vector a, about an axis in the direction of a unit vector ω and anticlockwise through angle θ, can be performed using Rodrigues' rotation formula in the dyadic form a r o t = R ⋅ a , {\displaystyle \mathbf {a} _{\mathrm {rot} }=\mathbf {R} \cdot \mathbf {a} \,,}
For example, if A = {1,2,3,4}, where the components are x, y, z, and w respectively, you could compute B = A.wwxy, whereupon B would equal {4,4,1,2}. Additionally, one could create a two-dimensional vector with A.wx or a five-dimensional vector with A.xyzwx. Combining vectors and swizzling can be employed in various ways.
Letting θ = t π /2, and applying the trigonometric identity cos θ = sin(π /2 − θ), this becomes the slerp formula. The factor of 1/sin Ω in the general formula is a normalization, since a vector p 1 at an angle of Ω to p 0 projects onto the perpendicular ⊥p 0 with a length of only sin Ω.
In linear algebra, linear transformations can be represented by matrices.If is a linear transformation mapping to and is a column vector with entries, then there exists an matrix , called the transformation matrix of , [1] such that: = Note that has rows and columns, whereas the transformation is from to .