Matrix YawPitchRoll rotation
Online computer calculates the rotation of a 4x4 matrix around the Y, X and Z axes
The calculator on this page calculates the rotation of a matrix with 4 x 4 elements. To perform the calculation, enter the values of the angles. Then click the button 'Calculate'.
You can choose between active matrix rotation (rotating object) and passive matrix rotation (rotating coordinates).
The unit of measurement for the angle can be switched between degrees or radians
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Description of the matrix X, Y and Z axes rotation
The matrix rotation distinguishes between active and passive rotation.
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.
Matrix 3x3 Functions
Addition • Subtraction • Multiplication • Scalar Multiplication • Rotation X axis • Rotation Y axis • Rotation Z axis • Y, P, R Rotation quaternion • Y, P, R Rotation Euler angles • Invert • DeterminantMatrix 4x4 Functions
Addition • Subtraction • Multiplication • Scalar Multiplication • Rotation X axis • Rotation Y axis • Rotation Z axis • Y, P, R Rotation • Vector Rotation • Invert • Determinant • interpolationQuaternion Functions
Addition • Subtraction • Division • Multiplication • Concatenate • Length • Interpolation • Normalize • Scalar Multiplication • Dot Product • Yaw-Pitch-RollMore Vector Functions
Addition • Subtraction • Multiplication • Scalar Multiplication • Division • Scalar Division • Dot Product • Cross Product • Interpolation • Distance • Distance Squaret • Normalization • Reflection • Magnitude • Squared-Magnitude • Triple-Product
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