Point Rotation Around a Line in 3D Space: MATLAB Implementation

This documentation demonstrates how to implement point rotation around a line in 3D space using MATLAB. The program accepts a point, line definition, and rotation angle as input parameters, and outputs the rotated point coordinates. Rotation represents a fundamental operation in 3D space, making this program applicable to numerous practical scenarios. For instance, in robotics control systems, it's frequently necessary to rotate the end-effector's position and orientation around specific axes to accomplish targeted tasks. The core implementation follows this algorithmic approach: First, compute the direction vector from the line definition and normalize the rotation axis vector. Then construct a 3D rotation matrix using Rodrigues' rotation formula or MATLAB's makehgtform function to rotate the point around the axis by the specified angle. The transformed coordinates represent the final rotated point. To enhance program robustness and usability, additional features can be integrated including: - Input validation checks for point coordinates and line parameters - Automatic angle unit conversion (degrees/radians) using unit conversion functions - Error handling for degenerate cases like zero-length direction vectors - Support for multiple rotation conventions using rotation matrix variations These improvements ensure reliable performance across diverse application scenarios while maintaining mathematical precision in spatial transformations. The implementation leverages MATLAB's matrix operations for efficient computation of 3D transformations.