In Algebra mathematic, rotation matrix is a type of matrix which is used to denote the rotation of angles. In Rotation Matrix, the Point revolves counter-clockwise and we get angle by this. In order to represent these points we use rotation matrix. We put these points in column of the matrix.
Euler angles are three angles which are defined in Geometry. We use these angles to get the orientation of an object about a point. In 3D geometry, these angles are used. These three angles work as three parameters. Being together these three parameters represents the composed rotation along a point.
After brief introduction of Euler angle we will focus on techniques and methods of the Euler angle in a rotation matrix. Sometimes it is very important to get Euler angle in graphics. We cannot predict the solution of Euler angle.
Rotation matrix have three axes, x, y and z.
Let us see the different-different rotations along three axes. Let us assume that, an angle have radian Ψ along the axis x. The other is having radian π along the axis y and an angle which have the radian as Ω along z axis.
Here, Ψ, π, Ω are the Euler angles. We can say the rotation matrix is an array of three different-different axes. The result will directly depend on the axis rotates about what axis.
For example, if we rotate the first x axis along the y axis then we get their product matrix. After this, we rotate the y axis along the z axis. The product matrix we get will be the euler rotation matrix of these matrices having different axis.
We can represent Euler rotation matrix in the form of equation also as:
R= Rx (Ψ) Ry (π) Rz (Ω)
R is an Euler rotation matrix.