Given a non-planar graph G with a subdivision of K5 as a subgraph, we can either transform the K5-subdivision into a K3,3-subdivision if it is possible, or else we obtain a partition of the vertices of G\K5 into equivalence classes. As a result, we can reduce a projective planarity or toroidality algorithm to a small constant number of simple planarity checks [6] or to a K3,3-subdivision in the...

The ability to control boundary behaviors is critical for the subdivision surface to become a useful representation in computer aided geometric design. Previous methods achieve boundary control by extending the boundary vertices of the control mesh, or by applying different subdivision rules to the boundary edges and vertices. This paper presents an open uniform quadratic subdivision scheme der...

Studies have shown that land and climate interact in complex ways through multiple biophysical biogeochemical feedbacks. In this interaction mechanism, the carbon fixation effect among different land-use types objective conditions regions significant gaps, leading to heterogeneous impact of on change. This study takes temperature change as observation index reflect change, analyzes process use ...

Exurban development is consuming wildlife habitat within the Greater Yellowstone Ecosystem with potential consequences to the long-term conservation of grizzly bears Ursus arctos. We assessed the impacts of alternative future land-use scenarios by linking an existing regression-based simulation model predicting rural development with a spatially explicit model that predicted bear survival. Usin...