Minimum Bounding Rectangle Fitting Based on Convex Hull Boundary

This MATLAB program performs minimum bounding rectangle fitting based on convex hull boundaries, serving as a computational tool that calculates the smallest enclosing rectangle for a convex polygon represented by a set of points. The implementation leverages computational geometry theories and algorithms, processing input point clouds to achieve optimal rectangle fitting with applications in image processing and computer vision domains. The core algorithm involves: 1) Computing the convex hull using MATLAB's convhull function to eliminate interior points, 2) Implementing rotating calipers method to find the minimum-area rectangle by testing all edge-aligned orientations, 3) Calculating rectangle parameters through vector rotations and extreme point comparisons. Users must input a coordinate matrix of points, where the program automatically outputs the bounding rectangle's position coordinates, area, length, width, and orientation angles. The code structure includes modular functions for hull calculation, rotation transformation, and rectangle optimization, allowing customization for specific requirements like performance optimization or additional parameter extraction. Key functions include boundary detection for convex hull generation and geometric minimization routines for rectangle fitting.