DELINEATION AND CONSTRUCTION OF 2D GEOMETRIES BY FREEHAND DRAWING AND GEOMETRIC REASONING

Abstract. 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. </jats:p

ENHANCEMENT OF GENERIC BUILDING MODELS BY RECOGNITION AND ENFORCEMENT OF GEOMETRIC CONSTRAINTS

Many buildings in 3D city models can be represented by generic models, e.g. boundary representations or polyhedrons, without expressing building-specific knowledge explicitly. Without additional constraints, the bounding faces of these building reconstructions do not feature expected structures such as orthogonality or parallelism. The recognition and enforcement of man-made structures within model instances is one way to enhance 3D city models. Since the reconstructions are derived from uncertain and imprecise data, crisp relations such as orthogonality or parallelism are rarely satisfied exactly. Furthermore, the uncertainty of geometric entities is usually not specified in 3D city models. Therefore, we propose a point sampling which simulates the initial point cloud acquisition by airborne laser scanning and provides estimates for the uncertainties. We present a complete workflow for recognition and enforcement of man-made structures in a given boundary representation. The recognition is performed by hypothesis testing and the enforcement of the detected constraints by a global adjustment of all bounding faces. Since the adjustment changes not only the geometry but also the topology of faces, we obtain improved building models which feature regular structures and a potentially reduced complexity. The feasibility and the usability of the approach are demonstrated with a real data set

ENHANCEMENT OF GENERIC BUILDING MODELS BY RECOGNITION AND ENFORCEMENT OF GEOMETRIC CONSTRAINTS

Many buildings in 3D city models can be represented by generic models, e.g. boundary representations or polyhedrons, without expressing building-specific knowledge explicitly. Without additional constraints, the bounding faces of these building reconstructions do not feature expected structures such as orthogonality or parallelism. The recognition and enforcement of man-made structures within model instances is one way to enhance 3D city models. Since the reconstructions are derived from uncertain and imprecise data, crisp relations such as orthogonality or parallelism are rarely satisfied exactly. Furthermore, the uncertainty of geometric entities is usually not specified in 3D city models. Therefore, we propose a point sampling which simulates the initial point cloud acquisition by airborne laser scanning and provides estimates for the uncertainties. We present a complete workflow for recognition and enforcement of man-made structures in a given boundary representation. The recognition is performed by hypothesis testing and the enforcement of the detected constraints by a global adjustment of all bounding faces. Since the adjustment changes not only the geometry but also the topology of faces, we obtain improved building models which feature regular structures and a potentially reduced complexity. The feasibility and the usability of the approach are demonstrated with a real data set.</jats:p