1. What is Rotation Matrix?

A rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For 2D rotation around the origin, the matrix transforms the coordinates (x, y) to (x', y') through a specified angle θ.

2. How Rotation Calculation Works

The basic 2D rotation formulas are:

Where:

• \( x, y \) — Original coordinates
• \( x', y' \) — Rotated coordinates
• \( \theta \) — Rotation angle in radians

3. Applications of Rotation

Details: Rotation calculations are fundamental in computer graphics, robotics, physics simulations, and engineering applications where objects need to be transformed in space.

4. Using the Calculator

Tips: Enter the original coordinates, rotation angle in radians (π radians = 180°), and select the rotation axis. The calculator supports both 2D (Z-axis) and 3D rotations.

5. Frequently Asked Questions (FAQ)

Q1: How to convert degrees to radians?
A: Multiply degrees by π/180. Example: 90° = 90 × π/180 = π/2 radians.

Q2: What's the difference between 2D and 3D rotation?
A: 2D rotation occurs around a single point (Z-axis), while 3D rotation can occur around any of the three axes (X, Y, or Z).

Q3: Does rotation preserve distance?
A: Yes, rotation is a rigid transformation that preserves distances between points.

Q4: What is the rotation matrix for 3D?
A: 3D rotation matrices are more complex and depend on the axis of rotation. The calculator implements all three basic 3D rotation matrices.

Q5: Can I rotate around an arbitrary axis?
A: This calculator handles principal axes only. Arbitrary axis rotation requires more complex matrix operations.