Abstract
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.
Highlights
1.1 MotivationHuman-made objects and their models predominantly feature geometric relationships such as parallelism or orthogonality
In total, we have seven geometric constraints: three pairs of straight line segments forming right angles, and four triplets of segments intersecting in a point
Following the approach presented in (Meidow and Lucks, 2019), we discuss geometric reasoning in the context of educational technology. This comprises the approximation of strokes by straight line segments and the enforcement of automatically recognized constraints by adjustment
Summary
Human-made objects and their models predominantly feature geometric relationships such as parallelism or orthogonality. These constructions must feature topological consistency, completeness, and integrity (Mantyla, 1987) These properties are usually enforced during the design process by restricting the user’s interactions. In total, we have seven geometric constraints: three pairs of straight line segments forming right angles, and four triplets of segments intersecting in a point. Given six of these constraints, the seventh constraint can be deduced. We argue that a stringent and rigorous stochastic approach is decisive to recognize the construction principles automatically Following this paradigm, the user needs not be explicitly aware of the sequential construction process and there is less interaction required since the selection of appropriate construction tools or modes by the user is dispensable. The double-blind peer-review was conducted on the basis of the full paper
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