Matrix YawPitchRoll rotation

This function calculates the 3D rotation of a solid using the quaternion.

The unit of measurement for angles can be switched between degrees or radians

Active rotation (rotating object) or passive rotation (rotating coordinates) can be calculated

To perform the calculation, enter the rotation angles. Then click the button 'Calculate'

Matrix rotation with the quaternion

This function calculates the 3D rotation of a solid with the quaternion. The quaternion is an extension of the complex numbers. In contrast to rotation with Euler angles, this avoids the problem that arises when two axes of rotation are superimposed in a configuration.

The matrices of the two methods differ because the assignment of the axes and the order of the calculation is different.

Calculator of a rotation with Euler angles can be found here.

The calculator assumes a roll-pitch-yaw rotation order when creating a rotation matrix, ie an object is first rotated around the Z axis, then around the X axis and finally around the Y axis.

Rotation with Euler angles

Calculator of a rotation with Euler angles can be found here.

Active Rotation

With active rotation, the vector or the object is rotated in the coordinate system. The active rotation is also called a geometric transformation. The rotation is counterclockwise.

Example of a 90 ° rotation of the X-axis

Passive rotation

With passive rotation, the coordinate system is rotated. The vector remains unchanged. The rotation is clockwise.

Example of a 90 ° rotation of the X-axis

Yaw, Pitch, Roll Rotation

A 3D body can be rotated around three axes. These rotations are called yaw pitch rolls.

Yaw

Yaw is the counterclockwise rotation of the Z-axis. The rotation matrix looks like this

Pitch

Pitch is the counterclockwise rotation of the Y-axis. The next figure shows the rotation matrix for this

Roll

Roll is the counterclockwise rotation of the X axis. The rotation matrix for the X-axis is shown in the next figure

Formulas of the Yaw, Pitch, Roll rotation

Each rotation matrix is a simple extension of the 2D rotation matrix. For example, the Yaw matrix essentially performs a 2D rotation with respect to the coordinates while the coordinate remains unchanged. So the third row and the third column look like part of the identity matrix, while the top right part looks like the 2D rotation matrix.

The yaw, pitch and roll rotations can be used to place a 3D body in any direction. A single rotation matrix can be formed by multiplying the matrices.