计算几何中几何偏微分方程的构造
CONSTRUCTION OF GEOMETRIC PARTIAL DIFFERENTIAL EQUATIONS IN COMPUTATIONAL GEOMETRY
查看参考文献25篇
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文摘
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平均曲率流、曲面扩散流和Willmore流等著名的几何流除了在理论方面有重要的意义之外,在计算机辅助几何设计、计算机图形学以及图像处理等领域也得到了广泛的应用.然而在解决实际问题时,人们经常要根据问题的特点构造其它具有指定性质的几何流.本文从统一的观点出发,对于参数曲面以及水平集曲面,给出了几类重要几何偏微分方程(包括L~2梯度流、H~(-1)梯度流以及H~(-2)梯度流)的构造.这几类几何流的包容十分广泛,上述提到的几个几何流均为其特例. |
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其他语种文摘
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It is well-known that mean curvature flow, surface diffusion flow and Willmore flow have played important roles in the field of geometry analysis. They are also widely used in the fields of computer aided geometric design, computer graphics and image processing. However, in the real applications one often needs to construct various different flows according to the specific requirements of the problems to be solved. In this paper, we propose a generic framework for constructing geometric partial differential equations, including L~2, H~(-1) and H~(-2) gradient flows. These flows are general, which contain mean curvature flow, surface diffusion flow and Willmore flow as their special cases. |
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来源
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计算数学
,2006,28(4):337-356 【核心库】
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关键词
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计算几何
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能量泛函
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梯度下降流
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欧拉-拉格朗日算子
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地址
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中科院数学与系统科学院, 科学与工程计算国家重点实验室, 北京, 100080
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语种
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中文 |
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文献类型
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研究性论文 |
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ISSN
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0254-7791 |
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学科
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数学 |
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基金
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国家自然科学基金
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国家973计划
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文献收藏号
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CSCD:2553611
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参考文献 共
25
共2页
|
|
1.
N Andrei. Gradient flow algorithm for unconstrained optimization unpublished manuscript.
http://www.ici.ro/camo/neculai/anpaper.htm,2004
|
被引
1
次
|
|
|
|
|
2.
B Andrews. Contraction of convex hypersurface in Euclidean space.
Calc Var &P D E,1994,2:151-171
|
被引
10
次
|
|
|
|
|
3.
T Aubin.
Nonlinear Analysis on Manifolds Monge-Ampère Equations,1982
|
被引
1
次
|
|
|
|
|
4.
M Botsch. An intuitive framework for real-time freeform modeling.
ACM Transaction on Graphics,2004,23(3):630-634
|
被引
11
次
|
|
|
|
|
5.
Y Chen. Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations.
J Diff Geom,1991,33:749-786
|
被引
4
次
|
|
|
|
|
6.
B Chow. Deforming convex hypersurfaces by the nth root of the Gauss curvature.
J Diff Geom,1985,22:117-138
|
被引
7
次
|
|
|
|
|
7.
U Clarenz. Enclosure theorems for extremals of elliptic parametric functionals.
Calc Var,2002,15:313-324
|
被引
1
次
|
|
|
|
|
8.
U Clarenz. On generalized mean curvature flow in surface processing In H Karcher and S Hildebrandt editors.
Geometric Analysis and Nonlinear Partial Differential Equations pages,2003
|
被引
1
次
|
|
|
|
|
9.
M Droske. A level set formulation for Willmore flow.
Interfaces and Free Boundaries,2004,6:361-378
|
被引
3
次
|
|
|
|
|
10.
L C Evans.
Measure Theory and Fine Properties of Functions,1992
|
被引
33
次
|
|
|
|
|
11.
L C Evans. Motion of level sets by mean curvature I.
J Diff Geom,1991,33:636-681
|
被引
2
次
|
|
|
|
|
12.
W J Firey. On the shapes of worn stones.
Mathematika,1974,21:1-11
|
被引
5
次
|
|
|
|
|
13.
M Giaquinta. Calculus of Variations Vol I Number 310 in A Series of Comprehensive Studies in Mathematics.
Calculus of Variations,Vol.I,Number 310 in A Series of Comprehensive Studies in Mathematics.,1996
|
被引
1
次
|
|
|
|
|
14.
B Goldlücke.
Proc.European Conference on Computer Vision (ECCV'04),2004,2:366-378
|
被引
1
次
|
|
|
|
|
15.
D Liu. A general sixth order geometric partial differential equation and its application in surface modeling.
International Symposium on Information and Computational Science'06
|
被引
1
次
|
|
|
|
|
16.
W W Mullins. Two-dimensional motion of idealised grain boundaries.
J Appl Phys,1956,27:900-904
|
被引
24
次
|
|
|
|
|
17.
W W Mullins. Theory of thermal grooving.
J Appl Phys,1957,28:333-339
|
被引
34
次
|
|
|
|
|
18.
A Polden. Curves and Surfaces of Least Total Curvature and Fourth-Order Flows PhD thesis Universit(a)t Tübingen.
Curves and Surfaces of Least Total Curvature and Fourth-Order Flows,PhD thesis,1996
|
被引
1
次
|
|
|
|
|
19.
M Spivak.
A Comprehensive Introduction to Differential Geometry volume 3.third edition,1999
|
被引
1
次
|
|
|
|
|
20.
J E Taylor. Mean curvature and weighted mean curvature.
Acta Metall Mater,1992,40:1475-1485
|
被引
2
次
|
|
|
|
|
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