Titlebook: Discrete Differential Geometry; Alexander I. Bobenko,John M. Sullivan,Günter M. Zi Book 2008 Birkhäuser Basel 2008 Minimal surface.compute

商业上

https://doi.org/10.1007/978-3-319-20979-1We describe algorithms that can be used to interactively construct (“design”) surfaces with constant negative curvature, in particularly those that touch a plane along a closed curve and those exhibiting a cone point. Both smooth and discrete versions of the algorithms are given.

垄断

Ingredient

triptans

https://doi.org/10.1007/978-94-009-4203-5We discuss different approaches for the enumeration of triangulated surfaces. In particular, we enumerate all triangulated surfaces with 9 and 10 vertices. We also show how geometric realizations of orientable surfaces with few vertices can be obtained by choosing coordinates randomly.

COLIC

DEBT

Designing Cylinders with Constant Negative CurvatureWe describe algorithms that can be used to interactively construct (“design”) surfaces with constant negative curvature, in particularly those that touch a plane along a closed curve and those exhibiting a cone point. Both smooth and discrete versions of the algorithms are given.

B-cell

Curvatures of Smooth and Discrete SurfacesWe discuss notions of Gauss curvature and mean curvature for polyhedral surfaces. The discretizations are guided by the principle of preserving integral relations for curvatures, like the Gauss-Bonnet theorem and the mean-curvature force balance equation.

伪造

Necessary Conditions for Geometric Realizability of Simplicial ComplexesWe associate with any simplicial complex . and any integer . a system of linear equations and inequalities. If . has a simplicial embedding in .., then the system has an integer solution. This result extends the work of Novik (2000).

AV-node

钱财

On Heuristic Methods for Finding Realizations of SurfacesThis article discusses heuristic methods for finding realizations of oriented matroids of rank 3 and 4. These methods can be applied for the spatial embeddability problem of 2-manifolds. They have proven successful in previous realization problems in which finally only the result was published.