Analysis of Csupra(k)-subdivision surfaces at extraordinary points

This paper gives an analysis of surfaces generated by subdividing control nets of arbitrary topology. We assume that the underlying subdivision algorithm is stationary on the regular parts of the control nets and described by a matrix iteration around an extraordinary point. For these subdivision schemes we derive conditions on the spectrum of the matrix and its generalized eigenvectors such that surfaces are produced which are regular and k-times differentiable at their extraordinary points

Fan Clouds - An Alternative To Meshes

A fan cloud is a set of triangles that can be used to visualize and work with point clouds. It is fast to compute and can replace a triangular mesh representation: We discuss visualization,multiresolution reduction, refinement, and selective refinement. Algorithms for triangular meshes can also be applied to fan clouds. They become even simpler, because fans are not interrelated. This localness of fan clouds is one of their main advantages. No remeshing is necessary for local or adaptive refinement and reduction

Mixed honeycomb pushing refinement

We generalize the honeycomb scheme, dualize it and combine both the primal and the dual scheme into self-dual subdivision schemes for convex polyhedra which generate surfaces without line segments different from the honeycomb scheme, which generates surfaces having line and even planar segments

Triangular Gk-splines

In this paper a new approach is presented to construct piecewise polynomial G^k-surfaces of arbitrary topology and smoothness order k>= 1 of degree O(k). This approach generalizes some results presented in 1997 in CAGD and in 1999 at the St. Malo conference, respectively. In our construction only 4n polynomial patches are needed to fill an n-sided hole in a generalized C^k-(half)-boxspline surface. This is achieved by coalescing certain control points while at the same time maintaining a regular parametrization

Die Wahrheit der Legende.: Geltungsbedingungen und Geltungsstrategien legendarischen Erzählens am Beispiel der Legenda aurea

From a modern rationalist viewpoint, the credibility of Christian hagiography must appear at least doubtful. At the same time, legendary narratives claim to report what really happened in history, when God acted out of transcendence in immanence, in a saint’s life. This truth and reality of the Holy is revealed in the veneration of the saint by the faithful public of the legend. Hagiography thus generates a specific claim of its own to truth, which stands at the variance with the modern and secular separation of facticity and fiction, of ‚truth‘ and ‚legend‘. The present article discusses how, in the Legenda aurea, the most important collection of hagiographies of the high Middle Ages, this claim is realized in institutional and narrative strategies that present the individual legends as part of the liturgically recalled history of salvation. Therefore, the Legenda aurea affirms to impart authenticated facts, even where it acknowledges uncertainties in tradition and dubious embellishments. This conception of reality is replaced only in the Reformation’s criticism of legendary narratives, making history as a historical event the standard for the value of a sacred life