Pöörlemismaatrikse

Pöörlemismaatrikse is a mathematical tool used to describe rotations in Euclidean space. It is a square matrix, typically of size 2x2 for 2D rotations or 3x3 for 3D rotations. The elements of the matrix are trigonometric functions of the angle of rotation. For a 2D rotation by an angle theta counterclockwise in the xy-plane, the matrix is [[cos(theta), -sin(theta)], [sin(theta), cos(theta)]]. When this matrix is multiplied by a vector representing a point, the resulting vector represents the rotated point. In three dimensions, there are specific rotation matrices for rotations around the x, y, and z axes. A general 3D rotation can be represented as a composition of these fundamental rotations. Rotation matrices are orthogonal matrices, meaning their transpose is equal to their inverse. This property ensures that rotations preserve lengths and angles. They are fundamental in various fields including computer graphics, robotics, physics, and engineering for transforming coordinates and representing orientations.