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.