Geometric reasoning for the freehand-drawn delineation of 2D geometries

Abstract

The mapping from aerial imagery and the creation of technical line drawings are prominent examples of the application of interactive software. These systems usually restrict the user’s interaction to enforce human-made structures such as orthogonality and parallelism. We propose a modeless approach that evaluates freehand-drawn pen strokes as the only user input. The approximating uncertain straight line segments are the basis for a reasoning process, comprising the recognition of geometric relations and their immediate enforcement via an efficient adjustment procedure. This approach avoids the possibly tedious and time-consuming selection of appropriate tools. Furthermore, during a step-by-step construction, the user needs not to be aware of the underlying design principles explicitly. We demonstrate the feasibility and usability of the approach by considering applications in the context of educational technology and large-scale mapping from imagery—the study of closure theorems and the polygonal tracing of roof shapes in orthophotos.