MATLAB Implementation of Plane Fitting Algorithm with Code Examples

This documentation presents methods for implementing plane fitting algorithms using MATLAB. The core functionality requires input of minimum three spatial coordinate points to accurately fit a mathematical plane. While this implementation provides one effective approach, alternative algorithms exist such as least-squares based plane fitting methods that minimize orthogonal distances using singular value decomposition (SVD) or eigenvalue decomposition techniques. The algorithm typically involves constructing a design matrix from point coordinates and solving the normal equation using MATLAB's backslash operator or specialized functions like 'fit' from the Curve Fitting Toolbox. Key implementation steps include data normalization, matrix conditioning checks, and residual analysis for fit quality assessment. It's important to note this algorithm specializes in planar surface fitting and cannot accommodate curved surfaces or complex geometric shapes. Therefore, algorithm selection should consider specific application requirements, data characteristics, and desired accuracy levels. For non-planar surfaces, alternative approaches like polynomial fitting or surface interpolation methods would be more appropriate. The implementation includes error handling for collinear point detection and numerical stability safeguards to ensure reliable performance across various datasets.