Convex Hull Relative Isoperimetric Profile

Click to add points. Drag points to move them. Right-click a point to delete it. The convex hull is computed in JavaScript; the profile is computed client-side in Python via Pyodide. The red overlay shows the optimal circular arc or chord at the maximizing area fraction.

Add at least three non-collinear points.
The app will form the convex hull and compare its profile with the equal-area disk.

Loading client-side Python runtime…

Input points
0
Hull vertices
0
Best ratio
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Best area fraction α
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polygon profile equal-area disk profile ratio optimal arc / chord
The plots are scale-normalized. Internally the hull is rescaled to area π, so the horizontal axis is α = A / |P| and the main vertical axis is IP(α|P|) √(π/|P|). This is equivalent to comparing the hull with the disk of the same area.

Normalized profiles

Blue: polygon. Dashed orange: disk with the same total area.

Relative profile ratio

The green curve is IP(α|P|) / ID(α|P|); the marker shows the numerically refined maximum.