Context <p>Shape-related landscape metrics are fundamental in landscape ecology, as patch geometry and boundary complexity directly influence species diversity through edge effects and the tolerance of organisms to environmental conditions and change. Patch boundaries often exhibit strong contrasts with adjacent land-cover types, giving rise to important ecological processes, particularly along sharp transitions such as forest–pasture edges. While classical metrics—such as the shape index, fractal dimension, and edge density—effectively characterize overall patch geometry, they provide limited capacity to capture local geometric properties, including vertex-level angular discontinuities.</p> Objectives <p>We introduce the BreakPointIndex (BPI), a novel landscape metric that quantifies the angular complexity along polygon boundaries. Our aims were to (i) provide a tool for detecting and mapping breakpoints using user-defined angular thresholds, and (ii) examine how threshold choice and land cover characteristics influence BPI values at the patch and shared boundary levels.</p> Methods <p>The BPI tool identifies breakpoints along polygon edges based on specified angular thresholds, generates a breakpoint point layer, computes breakpoint counts and densities (perimeter and area), and quantifies shared breakpoints and shared edge lengths between neighboring polygons. The outputs included updated shapefiles and TXT/HTML summary reports. The tool was demonstrated using the 2018 Urban Atlas dataset and applied three angular threshold ranges (5°–160°, 20°–160°, and 40°–140°). In addition, scale sensitivity was quantitatively evaluated by analyzing BPI responses across multiple levels of boundary detail.</p> Results <p>The number and distribution of breakpoints were significantly affected by the angular threshold parameters. Wider thresholds captured finer-scale irregularities, especially in natural and semi-natural classes, such as forests, pastures, and permanent crops, whereas narrower thresholds highlighted major directional changes and emphasized more regular, urban patterns. Patch-level BPI values and variability differed across land cover types, and shared-breakpoint analysis revealed structurally contrasting interfaces, such as those between forests and pastures or between agricultural and built-up areas. The scale-sensitivity analysis revealed a non-linear and class-dependent response of BPI, with many natural land cover classes showing an initial increase followed by a decline as geometric detail was reduced.</p> Conclusions <p>BPI complements conventional landscape metrics by offering a flexible, vertex-based measure of boundary complexity. It provides detailed information on polygon geometry and shared edges, supporting applications in edge analysis and habitat assessment. As the BPI is scale-dependent and sensitive to data generalization, its interpretation should consider the mapping resolution and dataset provenance. Overall, the BPI tool offers a reproducible framework for integrating boundary geometry into landscape ecological analyses. The results confirm that BPI exhibits structured and interpretable scaling behavior, supporting its application in comparative landscape analyses.</p>