搜索结果: 1-15 共查到“知识库 计算几何学”相关记录28条 . 查询时间(1.82 秒)
CAD几何内核核心算法库（图）
CAD 几何内核 核心算法
2024/10/29
该成果是CAD几何内核的核心底层技术，很大程度上决定了几何引擎的稳定性。二次曲面在CAD模型中使用最为广泛，因此二次曲面的求交在所有求交任务中被调用频次最高。由于二次曲面具有特殊的代数和几何性质，它们的求交计算一般需区别于自由曲面求交来进行特殊处理，从而充分保证算法的精度和效率。
几何变分问题在临界点处的正则性与稳定性（张翼）
几何变分问题 临界点 正则性 稳定性
2023/2/22
几何不等式，特别是（包括Wullf能量下的）等周不等式和Sobolev不等式，不仅是建立分析和几何相关理论的重要基础，也是众多科研模型以及计算机算法研究中不可或缺的部分。它们所对应的变分问题的解的正则性与稳定性，也是在分析与几何交叉的相关领域中的核心问题之一。其中有大量的关键问题亟待解决。与此同时，这些问题也与数学以外的科研领域中的许多问题相关。它们的解决也将推动这些方向的理论发展与完善。
Let E : 0 ! S ! E ! Q ! 0 be a short exact sequence of
hermitian vector bundles with metrics on S and Q induced from that
on E. We compute the Bott-Chern form áe(E ) corresponding to any
characteri...
Let F be the complete °ag variety over SpecZ with the tautological
ˉltration 0 ½ E1 ½ E2 ½ ￠ ￠ ￠ ½ En = E of the trivial bundle E of rank
n over F. The trivial hermitian metric o...
Computing the obstacle number of a plane graph
obstacle number of a plane graph Computational Geometry
2011/10/9
Abstract: An obstacle representation of a plane graph G is V(G) together with a set of opaque polygonal obstacles such that G is the visibility graph on V(G) determined by the obstacles. We investigat...
Abstract: In 2008, Bukh, Matousek, and Nivasch conjectured that for every n-point set S in R^d and every k, 0 <= k <= d-1, there exists a k-flat f in R^d (a "centerflat") that lies at "depth" (k+1) n ...
A further generalization of the colourful Caratheodory theorem
Colourful Caratheodory theorem colourful simplicial depth discrete geometry
2011/10/8
Abstract: Given d+1 sets, or colours, S_1, S_2,...,S_{d+1} of points in R^d, a colourful set is a set S in the union of the S_i such that the intersection of S with any S_i is of cardinality at most 1...
前处理是数值模拟的主要性能瓶颈,高端数字样机HEDP(High End Digital Prototyping)系统的前处理用户环境HEDP/Pre包含几何处理、网格密度定义及网格生成等三个模块,结合图形交互式界面等可视交互工具,为满足前处理的诸多共性需求提供了一类适用的解决方案,其有效性已在多领域的数值模拟实践中得到初步验证,对类似软件系统的实现具有参考价值。
Geometrization of continuous characters of $\mathbb{Z}_p^\times$
Geometrization Kummer local systems
2011/1/17
We define the p-adic trace of certain Kummer local systems on the multiplicative group over p-adic numbers, using nearby cycles. For every nonnegative integer n, we prove that the p-adic trace defines...
On the numerical radius of operators in Lebesgue spaces
the numerical radius Lebesgue spaces
2010/11/24
We show that the absolute numerical index of the space $L_p(\mu)$ is $p^{-1/p} q^{-1/q}$ (where $1/p+1/q=1$). In other words, we prove that $$ \sup\{\int |x|^{p-1}|Tx|\, d\mu \, : \ x\in L_p(\mu),\,\|...
It has recently been shown that infinite matroids can be axiomatized in a way that is very similar to finite matroids and permits duality. This was previously thought impossible, since finitary infini...
By systematically applying ten well-known and inequivalent two-part relations between hypergeometric sums 3F2(...|1) to the published database of all such sums, 62 new sums are obtained. The existing...
Strongly Regular Graphs Constructed from $p$-ary Bent Functions
Strongly Regular Graphs Constructed math
2010/11/23
In this paper, we generalize the construction of strongly regular graphs in [Y. Tan et al., Strongly regular graphs associated with ternary bent functions, J. Combin.Theory Ser. A (2010), 117, 668-68...
Asymptotic behaviour of a cylindrical elastic structure periodically reinforced along identical fibers
cylindrical elastic structure identical fibers
2010/11/23
We describe the asymptotic behaviour of a cylindrical elastic body, reinforced along identical $\epsilon$-periodically distributed fibers of size $r_{\epsilon}$, with $0 < r_{\epsilon} < \epsilon$, fi...
Kernel random matrices have attracted a lot of interest in recent years, from both practical and theoretical standpoints. Most of the theoretical work so far has focused on the case were the data is s...