Astrid Sturm

Approximation of an open polygonal curve with a minimum number of circular arcs and biarcs

An algorithm for approximating a given open polygonal curve with a minimum number of circular arcs is introduced. In computer-aided manufacturing environments the paths of cutting tools are usually described with circular arcs and straight line segments. Greedy algorithms for approximating a polygonal curve with curves of higher order can be found in the literature. Without theoretical bounds it is difficult to prove anything about the quality of these algorithms. We present an algorithm which allows us to build a directed graph of all possible arcs and look for the shortest path from the start point to the end point of the polygonal curve. We can prove a runtime of O(n 2 logn), for n the number of vertices of the original polygonal chain.

Recovering structure from r -sampled objects

For a surface in 3‐space that is represented by a set S of sample points, we construct a coarse approximating polytope P that uses a subset of S as its vertices and preserves the topology of . In contrast to surface reconstruction we do not use all the sample points, but we try to use as few points as possible. Such a polytope P is useful as a ‘seed polytope’ for starting an incremental refinement procedure to generate better and better approximations of based on interpolating subdivision surfaces or e.g. Bézier patches.

Cost-effectiveness of conservation payment schemes for species with different range sizes

Payments to compensate landowners for carrying out costly land-use measures that benefit endangered biodiversity have become an important policy instrument. When designing such payments, it is important to take into account that spatially connected habitats are more valuable for many species than isolated ones. One way to incentivize provision of connected habitats is to offer landowners an agglomeration bonus, that is, a bonus on top of payments they are receiving to conserve land if the land is spatially connected. Researchers have compared the cost-effectiveness of the agglomeration bonus with 2 alternatives: an all-or-nothing, agglomeration payment, where landowners receive a payment only if the conserved land parcels have a certain level of spatial connectivity, and a spatially homogeneous payment, where landowners receive a payment for conserved land parcels irrespective of their location. Their results show the agglomeration bonus is rarely the most cost-effective option, and when it is, it is only slightly better than one of the alternatives. This suggests that the agglomeration bonus should not be given priority as a policy design option. However, this finding is based on consideration of only 1 species. We examined whether the same applied to 2 species, one for which the homogeneous payment is best and the other for which the agglomeration payment is most cost-effective. We modified a published conceptual model so that we were able to assess the cost-effectiveness of payment schemes for 2 species and applied it to a grassland bird and a grassland butterfly in Germany that require the same habitat but have different spatial-connectivity needs. When conserving both species, the agglomeration bonus was more cost-effective than the agglomeration and the homogeneous payment; thus, we showed that as a policy the agglomeration bonus is a useful conservation-payment option.

Payments for conservation measures to incentivize connected habitats: cost‐effectiveness of agglomeration payments, agglomeration bonuses and spatially homogeneous payments in the presence of two endangered species

Payments to compensate landowners for carrying out costly land-use measures that benefit endangered biodiversity have become an important policy instrument. When designing such payments, it is important to take into account that spatially connected habitats are more valuable for many species than isolated ones. One way to incentivize provision of connected habitats is to offer landowners an agglomeration bonus, that is, a bonus on top of payments they are receiving to conserve land if the land is spatially connected. Researchers have compared the cost-effectiveness of the agglomeration bonus with 2 alternatives: an all-or-nothing, agglomeration payment, where landowners receive a payment only if the conserved land parcels have a certain level of spatial connectivity, and a spatially homogeneous payment, where landowners receive a payment for conserved land parcels irrespective of their location. Their results show the agglomeration bonus is rarely the most cost-effective option, and when it is, it is only slightly better than one of the alternatives. This suggests that the agglomeration bonus should not be given priority as a policy design option. However, this finding is based on consideration of only 1 species. We examined whether the same applied to 2 species, one for which the homogeneous payment is best and the other for which the agglomeration payment is most cost-effective. We modified a published conceptual model so that we were able to assess the cost-effectiveness of payment schemes for 2 species and applied it to a grassland bird and a grassland butterfly in Germany that require the same habitat but have different spatial-connectivity needs. When conserving both species, the agglomeration bonus was more cost-effective than the agglomeration and the homogeneous payment; thus, we showed that as a policy the agglomeration bonus is a useful conservation-payment option.