Convex Hull → Maximum Inscribed Rectangle

A desktop tool that takes a set of points, builds their convex hull, and finds the largest axis-aligned rectangle that fits inside it.

The interesting part is the split: the geometry runs in C#, the optimisation runs in Python. The WinForms app collects the points and computes the hull with Graham's scan, writes the hull as a set of half-plane constraints to src/data.json, and hands it to src/cvx_optimization.py, which solves for the maximum inscribed rectangle with CVXPY and returns the result for the app to draw.

Layout

Path	What it does
GrahamScan.cs	Convex hull by Graham's scan
AlgorithmBase.cs	Shared algorithm scaffolding
Form1.cs	Canvas, point input, rendering of hull and rectangle
src/cvx_optimization.py	Maximum inscribed rectangle as a convex program (CVXPY)
src/data.json	Hull constraints passed between the two halves

Running it

pip install cvxpy

Open ConvexHullRectangleApp.csproj in Visual Studio and run. Click to place points; the hull and the inscribed rectangle are redrawn on each change.

Computational geometry course project, Taras Shevchenko National University of Kyiv.