599 research outputs found

    Computing a Compact Spline Representation of the Medial Axis Transform of a 2D Shape

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    We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The instability of the medial axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable medial axis transform is then approximated by spline curves in 3D to produce a smooth and compact representation. These spline curves are computed by minimizing the approximation error between the input shape and the shape represented by the medial axis transform. Our results on various 2D shapes suggest that our method is practical and effective, and yields faithful and compact representations of medial axis transforms of 2D shapes.Comment: GMP14 (Geometric Modeling and Processing

    Participation in the classroom as a basis for democracy education? A conceptual analysis of the concept of student participation

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    In our conceptual analysis, we focus on the concept of student participation and argue for a differentiated consideration of the same. To this end, we elaborate on constituent elements and first address the definitional understanding of the concept considered as well as the participation postulate. Furthermore, we name and discuss possible purposes and qualities of participatory practice and we give an overview of the established conceptualization of participation by means of a stage model and the interdependence of autonomy and heteronomy expressed in this model. We then address participatory fields in the classroom, concrete practices of participatory decision-making, prerequisites and implications of participatory classroom practices, and possible scopes of participatory influence
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