基于多尺度CSRBF离散曲面融合研究
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摘要
随着电影、游戏等娱乐事业以及军事、工业等对三维技术的需求增大,三维处理技术得到了迅速的发展。伴随着各种模型获取手段的增多,无论是网格模型还是点模型,使得模型库变的异常庞大,模型资源异常丰富。如何有效的利用这些模型,使三维创作人员更加高效进行编辑操作,模型编辑技术也就应运而生。本文主要研究了两方面内容:基于点模型的布尔运算及其融合方法;基于网格模型的离散曲面融合方法。
本文的提出的两种方法,无论是布尔运算还是离散曲面融合,都涉及到隐函数,所以如何找到一个能够快速插值/拟合曲面,能够使曲面光滑过渡的隐函数,也是重要目标之一。
首先利用自适应八叉树进行插值加速,利用多尺度CSRBF(Compactly Supported RadialBasis Functions,紧支径向基函数)隐式化点模型,进行内外测试判断,最后实现布尔运算,能把简单的点模型构造成复杂的点模型。并把布尔运算技术运用到网格模型上,实现了,种曲面融合方法。
其次,根据以往一些网格模型融合算法的缺点,并结合其优点,提出了一种离散曲面融合算法。该方法首先提取融合模型间的边界轮廓线,然后进一步网格化边界轮廓线。用多尺度CSRBF插值过渡曲面,得到零值面,最后用网格细分优化算法进一步细分网格,通过控制点迭代逼近零值面。最终实现了曲面的无缝拼接及光滑过渡。因为过渡曲面的生成是受周围点的影响的,离过渡曲面越近的点,其影响度较大,反之越小,本文根据此特点,给出了一种加速插值曲面的方法,特别对于模型复杂或包含拓扑点较多的模型,加速越明显。
最后总结了全文,结合本文方法中还存在着一些不足,给出了进一步工作的思路。
With movies, games and other entertainment industry as well as the military, industry, increased demand for three-dimensional technology, three-dimensional processing technology has been rapid development. Along with the increase in a variety of models to obtain, whether it is a grid model, or point model, it makes model-base become exceptionally large and extraordinarily rich. How to effectively use these models to make officials more efficient three-dimensional editing operation, model editing techniques abound. This thesis studies two aspects: the Boolean operations on point models and the fusion; grid-based model of discrete surface fusion method.
This thesis proposed two methods, either Boolean operations or discrete surface fusion, are related to the implicit function. How can we find a implicit function which is fast interpolating / fitting surface, and make the transition surface smooth, is also a important goal.
Our thesis use of adaptive octree interpolation acceleration , and multi-scale CSRBF(Compactly Supported Radial Basis Functions) implicit point model in order to carry out internal and external testing ,and finally realization of Boolean operations which able to construct the simple point models into a complex point model. And using of Boolean computing technologies to the grid model, that achieve a surface fusion method.
Based on some mesh fusion algorithm shortcomings, combined with its merits, we present a discrete surface fusion algorithm. This method first extract the boundary contour lines between the fusion models, and then further grid the boundary contours. Using of interpolation the transition surface with multi-scale CSRBF, that generates the surface of zero-level set. At last, the mesh subdivision optimization algorithm is further subdividing the mesh. And then using of the control points iterates approximation of the zero-level set surface. Eventually we realize the seamless splicing and a smooth transition surface. Because of the generation of transition surface is subject to the points around which is the nearer, the larger impact on the surface. Based on this characteristic , we give a way to speed up the interpolation of surface, in particular, for the complex model accelerate which is the more obvious.
Finally, we conclude the thesis. The methods proposed in this thesis still have some deficiencies. And we give some suggestions for further improvement of these works.
本文的提出的两种方法,无论是布尔运算还是离散曲面融合,都涉及到隐函数,所以如何找到一个能够快速插值/拟合曲面,能够使曲面光滑过渡的隐函数,也是重要目标之一。
首先利用自适应八叉树进行插值加速,利用多尺度CSRBF(Compactly Supported RadialBasis Functions,紧支径向基函数)隐式化点模型,进行内外测试判断,最后实现布尔运算,能把简单的点模型构造成复杂的点模型。并把布尔运算技术运用到网格模型上,实现了,种曲面融合方法。
其次,根据以往一些网格模型融合算法的缺点,并结合其优点,提出了一种离散曲面融合算法。该方法首先提取融合模型间的边界轮廓线,然后进一步网格化边界轮廓线。用多尺度CSRBF插值过渡曲面,得到零值面,最后用网格细分优化算法进一步细分网格,通过控制点迭代逼近零值面。最终实现了曲面的无缝拼接及光滑过渡。因为过渡曲面的生成是受周围点的影响的,离过渡曲面越近的点,其影响度较大,反之越小,本文根据此特点,给出了一种加速插值曲面的方法,特别对于模型复杂或包含拓扑点较多的模型,加速越明显。
最后总结了全文,结合本文方法中还存在着一些不足,给出了进一步工作的思路。
With movies, games and other entertainment industry as well as the military, industry, increased demand for three-dimensional technology, three-dimensional processing technology has been rapid development. Along with the increase in a variety of models to obtain, whether it is a grid model, or point model, it makes model-base become exceptionally large and extraordinarily rich. How to effectively use these models to make officials more efficient three-dimensional editing operation, model editing techniques abound. This thesis studies two aspects: the Boolean operations on point models and the fusion; grid-based model of discrete surface fusion method.
This thesis proposed two methods, either Boolean operations or discrete surface fusion, are related to the implicit function. How can we find a implicit function which is fast interpolating / fitting surface, and make the transition surface smooth, is also a important goal.
Our thesis use of adaptive octree interpolation acceleration , and multi-scale CSRBF(Compactly Supported Radial Basis Functions) implicit point model in order to carry out internal and external testing ,and finally realization of Boolean operations which able to construct the simple point models into a complex point model. And using of Boolean computing technologies to the grid model, that achieve a surface fusion method.
Based on some mesh fusion algorithm shortcomings, combined with its merits, we present a discrete surface fusion algorithm. This method first extract the boundary contour lines between the fusion models, and then further grid the boundary contours. Using of interpolation the transition surface with multi-scale CSRBF, that generates the surface of zero-level set. At last, the mesh subdivision optimization algorithm is further subdividing the mesh. And then using of the control points iterates approximation of the zero-level set surface. Eventually we realize the seamless splicing and a smooth transition surface. Because of the generation of transition surface is subject to the points around which is the nearer, the larger impact on the surface. Based on this characteristic , we give a way to speed up the interpolation of surface, in particular, for the complex model accelerate which is the more obvious.
Finally, we conclude the thesis. The methods proposed in this thesis still have some deficiencies. And we give some suggestions for further improvement of these works.
引文
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[7]Thomas Funkhouser,Mazhdan,Philip Shilane,Patrick Min,William Kiefer,Ayellet Tal,Szymon Rusinkjewicz,and David Dobkin.Modeling by example.ACM Transactions on Graphics,23(3):652-663,2004
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[9]Start Sclaroff and Alex Pentland,Generalized Implicit Functions for Computer Graphics[A].Proceedings of SIGGRAPH 91.In Computer Graphics,25(4):247-250,1991.
[10]G.Kos,R.R.Martin,T.Varady,Methods to recover constant radius rolling ball blends in reverse engineering,Comput.Aided Geometric Des.17(2000) 127- 160.
[11]Y.Ohtake,A.Belyaev,M.Alexa,G.Turk,H.P.Seidel.Multilevel partition of unity implicts.ACM Transactions on Graphics,2003,22(3):463-470
[12]J.R.Rossignac and A.A.G.Requicha.Constant-radius blending in solid modeling.Computer Mechanics Engineering.65-73,Jul 1984.
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[14]J.Warren.Blending algebraic surfaces.ACM Transaction.Graphics,8(4),263-278,1989.
[15]C.Bajaj and I.Ihm.Algebraic Surfaces Design with Hermite Interpolation.ACM Transaction on Graphics,11,61-91,1992.
[16]W.T.Wu and D.K.Wang.On the algebraic surface-fitting problem in Computer Aided Geometry Design.Mathematics in Practice and Theory,3,26-31,1994.
[17]Wu Tie-ru,Gap Wei-guo and Feng Guo-chen.Blending of implicit algebraic surface. Proceedings of the ASCM 1995(Beijing,China,Aug.18-20),125-131,1995.
[18]F.L.Chen and T.W.Sederberg.A new implicit representation of a planar rational curve with high order singularity.Computer Aided Geometry Design,19,151-167,2002.
[19]Y.Ohtake,A.G.Belyaev,and H-P.Seidel.A multi-scale approach to 3D scattered data interpolation with compactly supported basis functions.In Shape Modeling International 2003,Seoul,Korea,153-161.
[20]Y.Ohtake,A.Belyaev,M.Alexa,G.Turk,H.P.Seidel.Multilevel partition of unity implicts.ACM Transcations on Graphics,2003,22(3):463-470
[21]M.Pauly,R.Keiser,L.Kobbelt,and M.Gross.Shape modeling with point-sampled geometry.In Proc.of ACM SIGGRAPH 03,pages 641-650,2003.
[22]S.Fleishman,D.Cohen-or,C.T.Silva.Robust moving least-squares fitting with sharp features.Proceedings of ACM SIGGRAPH,New Youk,ACM Press,2005:544-552
[23]D.Levin.The approximation power of moving least-squares.Math.Cimput,1998,67(244):1517-1531
[24]D.Levin.Mesh-independent surface interpolation.In Giometric Modeling for Scientific Visualization 2003,37-49
[25]M.Alexa,J.Behr,D.Cohen-or,S.Fleishman,D.Levin,C.T.silva.Point set surfaces.In Proc.Of the conference on(IEEE)Visualization01,2001,21-28.
[26]M.Alexa,J.Behr,D.Cohen-or,S.Fleishman,D.Levin,C.T.silva.Computing and rendering point set surfaces.IEEE Transactions on Visualization and Computer Graphics,2003,9(1),3-15
[27]A.Adamson,M.Alexa.Approximating and intersecting surfaces from points.Symposium on Geometry Processing 2003,2003,245-254
[28]N.Amenta,Y.J.KIL.Defining Point Set Surfaces.ACM Transactions on Graphics,2004,23(3):264-270.
[29]S.Fleishman,D.Cohen-or,C.T.Silva.Robust moving least-squares fitting with sharp features.Proceedings of ACM SIGGRAPH,New York,ACM Press,2005:544-552
[30]P.Reuter,P.Joyot,J.Trunzler,T.Boubekeur,C.Schlick.Surface reconstruction with enriched reproducing kernel particle approximation.In Proceedings of the IEEE/Eurograhics Symposium on Point-Based Graphics 2005,Eurographics/IEEE Computer Society,79-87
[31]Pasko A,Savchenko V.,Algbraie sums for deformation of constructive solids[A].Proceedings of the third Symposium On Solid Modeling[C].1995,403-408.
[32]Sourin A,Pako A,Function representations for seeping by a moving solid[A].Proceedings of the third Symposium On Solid Modeling[C].1995,391-403
[33]Rvachev V L,Sheiko T I,Implicit function modeling of solidification in metal castings[J].Journal of Mechanical Design,1997,119:466-473
[34]Shapiro V.,Tuskanov 1.,Implicit Function with guaranteed differential properties[A].Proceedings of the Fifth Symposium On Solid Modeling[C].1999
[35]Carr J C,Fright W R,Beatson R K.Surface Interpolation with Radial Basis Functions for Medical Imaging[J].IEEE Transactions on Medical Imaging.February,1997,16(1):96-107
[36]Franke R Scattered Data Interpolation:Tests of Some Methods[J].Mathematics of Computation.1982,38(1):181-200
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