邓建松
计算机辅助几何设计与计算机图形学。
个性化签名
- 姓名:邓建松
- 目前身份:
- 担任导师情况:
- 学位:
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学术头衔:
博士生导师, 教育部“新世纪优秀人才支持计划”入选者
- 职称:-
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学科领域:
计算机科学技术
- 研究兴趣:计算机辅助几何设计与计算机图形学。
邓建松,山东威海人,1989年9月进入中国科学技术大学数学系本科学习(五年制),1993年提前毕业,获学士学位。随后被保送攻读中国科技大学数学系计算机辅助几何设计方向的博士学位。1998年毕业获博士学位,并留校任教至今。
研究工作简历:1998年留校工作至今,曾先后到香港科技大学的cad/cam中心(半年),英国伯明翰大学alan a. ball主持的几何建模小组(2年)访问工作。现为教授。主要从事几何造型方面的研究。
工作简历
1998.6 -- 至今:中国科学技术大学数学系(2001年任职副教授,2005年12月任职教授)
1998.8 -- 1999.2 香港科技大学机械工程系cad中心,访问学者
2001.7 -- 2003.7 英国birmingham大学工程学院机械制造与工程系 助理研究员(research fellow)
感兴趣研究领域:计算机辅助几何设计与计算机图形学。
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2010-08-31
邓建松, chunlin wu†, jiansong deng‡, falai chen‡, and xuecheng tai§
siam j. imaging sciences vol. 2, no.2, pp. 670-709,-0001,():
-1年11月30日
discrete filtering of information over triangulated surfaces has proved very useful in computer graphics applications. this technique is based on diffusion equations and has been extensively applied to image processing, harmonic map regularization and texture generating, etc. [c. l. bajaj and g. xu, acm trans. graph., 22 (2003), pp. 4–32], [c. wu, j. deng, and f. chen, ieee trans. vis. comput. graph., 14 (2008), pp. 666–679]. however, little has been done on analysis (especially quantitative analysis) of the behavior of these filtering procedures. since in applications mesh surfaces can be of arbitrary topology and the filtering can be nonlinear and even anisotropic, the analysis of the quantitative behavior is a very difficult issue. in this paper, we first present the discrete linear, nonlinear, and anisotropic filtering schemes via discretizing diffusion equations with appropriately defined differential operators on triangulated surfaces, and then use concepts of discrete scale-spaces to describe these filtering procedures and analyze their properties respectively. scale-space properties such as existence and uniqueness, continuous dependence on initial value, discrete semigroup property, grey level shift invariance and conservation of total grey level, information reduction (also known as topology simplification), and constant limit behavior have been proved. in particular, the information reduction property is analyzed by eigenvalue and eigenvector analysis of matrices. different from the direct observation of the local filtering to the diffusion equations and other interpretation methods based on wholly global quantities such as energy and entropy, this viewpoint helps us understand the filtering both globally (information reduction as image components shrink) and locally (how the image component contributes to its shrink rate). with careful consideration of the correspondence between eigenvalues and eigenvectors and their features, differences between linear and nonlinear filtering, as well as between isotropic and anisotropic filtering, are discussed. we also get some stability results of the filtering schemes. several examples are provided to illustrate the properties.
scale-space,, discrete filtering,, diffusion equation,, triangulated mesh surface
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2010-08-31
邓建松, xiaohong jia∗, falai chen, jiansong deng
computer aided geometric design 26(2009)287-299,-0001,():
-1年11月30日
an algorithm is presented to compute the self-intersection curves of a rational ruled surface based on the theory of μ-bases. the algorithm starts by constructing the principal subresultants for a μ-basis of the rational ruled surface. the principal subresultant coefficients provide information about not only the parametric loci of the self-intersection curves, but also the orders of the self-intersection curves. based on this observation, an efficient algorithm is provided to compute the parametric loci of the self-intersection curves as well as their corresponding orders. the isolated singular points of the rational ruled surface are also computed.
ruled surface self-intersection curve singular point parametric locus μ-basis moving plane subresultant
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2010-08-31
邓建松, 欧阳宏, 金良兵
中国科学技术大学学报,2008,38(9):1068~1074,-0001,():
-1年11月30日
给出了求解代数曲面上两点之间测地线的一种算法。在算法中,把决定代数曲面测地线的微分方程组离散为一个非线性方程组,然后采用迭代数值方法求解。为此,给出了一种基于细分的初值生成方法。最后给出了一些数值算例用来验证算法的有效性。
代数曲面, 测地线, 测地曲率
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2010-08-31
邓建松, jiansong deng*, falai chen, xin li, changqi hu, weihua tong, zhouwang yang, yuyu feng
graphical models 70(2008)76-86,-0001,():
-1年11月30日
in this paper, we introduce a new type of splines—polynomial splines over hierarchical t-meshes (called pht-splines) to model geometric objects. pht-splines are a generalization of b-splines over hierarchical t-meshes. we present the detailed construction process of spline basis functions over t-meshes which have the same important properties as b-splines do, such as nonnegativity, local support and partition of unity. as two fundamental operations, cross insertion and cross removal of pht-splines are discussed. with the new splines, surface models can be constructed efficiently and adaptively to fit open or closed mesh models, where only linear systems of equations with a few unknowns are involved. with this approach, a nurbs surface can be efficiently simplified into a phtspline which dramatically reduces the superfluous control points of the nurbs surface. furthermore, pht-splines allow for several important types of geometry processing in a natural and efficient manner, such as conversion of a pht-spline into an assembly of tensor-product spline patches, and shape simplification of pht-splines over a coarser t-mesh. pht-splines not only inherit many good properties of sederberg’s t-splines such as adaptivity and locality, but also extend t-splines in several aspects except that they are only c1 continuous. for example, pht-splines are polynomial instead of rational; cross insertion/removal of pht-splines is local and simple.
t-mesh t-splines nurbs local refinement surface fitting shape simplification
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2010-08-31
邓建松, xuhui wang falai chen jiansong deng
,-0001,():
-1年11月30日
this paper discusses implicitization and parametrization of quadratic surfaces with one simple base point. the key point to fulfill the conversion between the implicit and the parametric form is to compute three linearly independent moving planes which we call the weak μ-basis of the quadratic surface. beginning with the parametric form, it is easy to compute the weak μ-basis, and then to find its implicit equation. inversion formulas can also be obtained easily from the weak μ-basis. for conversion from the implicit into the parametric form, we present a method based on the observation that there exists one self-intersection line on a quadratic surface with one base point. after computing the self-intersection line, we are able to derive the weak μ-basis, from which the parametric equation can be easily obtained. a method is also presented to compute the self-intersection line of a quadratic surface with one base point.
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2010-08-31
邓建松, zhangjin huanga, b, ∗, jiansong dengc, guoping wanga
computer aided geometric design 25(2008)457-469,-0001,():
-1年11月30日
a catmull–clark subdivision surface (ccss) is a smooth surface generated by recursively refining its control meshes, which are often used as linear approximations to the limit surface in geometry processing. for a given control mesh of a ccss, by pushing the control points to their limit positions, another linear approximation-a limit mesh of the ccss is obtained. in general a limit mesh might approximate a ccss better than the corresponding control mesh. we derive a bound on the distance between a ccss patch and its limit face in terms of the maximum norm of the second order differences of the control points and a constant that depends only on the valence of the patch. a subdivision depth estimation formula for the limit mesh approximation is also proposed. for a given error tolerance, fewer subdivision steps are needed if the refined control mesh is replaced with the corresponding limit mesh.
catmull-clark subdivision surfaces limit mesh distance bound subdivision depth
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2010-08-31
邓建松, xuchuan fan, jiansong deng∗, falai chen
journal of computational and applied mathematics 216(2008)563-573,-0001,():
-1年11月30日
polynomials with perturbed coefficients, which can be regarded as interval polynomials, are very common in the area of scientific computing due to floating point operations in a computer environment. in this paper, the zeros of interval polynomials are investigated. we show that, for a degree n interval polynomial, the number of interval zeros is at most n and the number of complex block zeros is exactly n if multiplicities are counted. the boundaries of complex block zeros on a complex plane are analyzed. numeric algorithms to bound interval zeros and complex block zeros are presented.
interval polynomial, interval zero, complex block zero, boundary polynomial
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2010-08-31
邓建松, 刘海晨
中国科学技术大学学报,2008,38(2):113~120,-0001,():
-1年11月30日
提出了一种散乱点的参数化方法和两个拟合算法来解决用圆盘和球域控制点bézier/b样条曲线和曲面拟合散乱数据的问题,还设计了一些例子来说明这些算法。
圆盘/, 球域控制点bézier/, b样条曲线/, 曲面, 散乱点的参数化, 拟合
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2010-08-31
邓建松, ying, li zhouwang yang, jiansong deng
,-0001,():
-1年11月30日
this paper addresses the problem of spherical parametrization, i.e., mapping a given polygonal surface of genus-zero onto a unit sphere. we construct an improved algorithm for parametrization of genus-zero meshes and aim to obtain high-quality surfaces fitting with pht-splines. this parametrization consists of minimizing discrete harmonic energy subject to spherical constraints and solving the constrained optimization by the lagrange-newton method. we also present several examples which show that parametric surfaces of pht-splines can be constructed adaptively and efficiently to fit given meshes associated with our parametrization results.
spherical parametrization,, genus-zero meshes,, discrete harmonic energy,, constrained optimization,, the lagrange-newton method
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2010-08-31
邓建松, 陈越强, 吴卉
中国科技技术大学学报,2007,37(7):777~784,-0001,():
-1年11月30日
讨论了三角域上球形控制点的bézier曲面的降阶逼近问题,给出了次数从n到n-m(1≤m≤n-1)的降阶逼近的方法。在逼近过程中,要求低阶球形控制点的bézier曲面包含原来的实体,同时两者的差别在某种意义下尽可能地小。还给出了一些例子来说明该方法。
三角域, 球形控制点, 区间bézier曲面, 降阶逼近
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