Delineation and construction of 2D geometries by freehand drawing and geometric reasoning

The creation of accurate and consistent line drawings is the subject of various applications. Prominent examples are the delineation of human-made objects in aerial images and the construction of technical line drawings, flow-charts, or diagrams. Interactive solutions usually restrict the user's interaction during the design process to enforce geometric relations such as orthogonality or incidence. To avoid the time-consuming selection of operational modes, a freehand approach is desirable using strokes as the only user input. In this case, the construction principles have to be inferred automatically by geometric reasoning with uncertain observations. We present and discuss the corresponding methods in the context of educational technology. By introducing and utilizing a user-friendly software tool, we offer a hands-on approach to explore the feasibility and usability of the procedure. The experiments comprise the polygonal approximation of 2D shapes, theorem proving, and the construction of human-made figures.