When acting on a matrix each column of the matrix represents a different vector.
Rotation about x axis matrix.
Matrix for rotation by 180 matrix for reflection in y axis.
When acting on a matrix each column of the matrix represents a different vector.
Matrix for reflection in the line y x.
Rotation about the z axis.
2 1 axis angle to matrix if u v and w form a right handed orthonormal set then any point can be represented as x u 0u v 0v w 0w.
The rotation matrix is closely related to though different from coordinate system transformation matrices bf q discussed on this coordinate transformation page and on this transformation.
A rotation in the x y plane by an angle θ measured counterclockwise from the positive x axis is represented by the real 2 2 special orthogonal matrix 2 cosθ sinθ sinθ cosθ.
In linear algebra a rotation matrix is a matrix that is used to perform a rotation in euclidean space for example using the convention below the matrix rotates points in the xy plane counterclockwise through an angle θ with respect to the x axis about the origin of a two dimensional cartesian coordinate system to perform the rotation on a plane point with standard.
Introduction a rotation matrix bf r describes the rotation of an object in 3 d space.
R rotx ang creates a 3 by 3 matrix for rotating a 3 by 1 vector or 3 by n matrix of vectors around the x axis by ang degrees.
For an alterative we to think about using a matrix to represent rotation see basis vectors here.
Axes x y z proper euler angles share axis for first and last rotation z x z both systems can represent all 3d rotations tait bryan common in engineering applications so we ll use those.
Matrix for rotation by 90 clockwise.
If we consider this rotation as occurring in three dimensional space then it can be described as a counterclockwise rotation by an angle θ about the z axis.
If we take the point x 1 y 0 this will rotate to the point x cos a y sin a if we take the point x 0 y 1 this will rotate to the point x sin a y cos a 3d rotations.
Matrix for stretch with the scale factor 2 in the direction of the x axis.
It was introduced on the previous two pages covering deformation gradients and polar decompositions.
R rotx ang creates a 3 by 3 matrix for rotating a 3 by 1 vector or 3 by n matrix of vectors around the x axis by ang degrees.
Matrix for enlargement with scale factor 2 center.
For the rotation matrix r and vector v the rotated vector is given by r v.
Matrix for stretch with the scale factor 2 in the direction of the y axis.
Rotation of x about the axis w by the angle produces rx u 1u v 1v w 1w.
The other two components are changed as if a 2d rotation has been.
