各向异性的分形地形生成方法研究
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摘要
传统的分形地形生成方法得到的地形是各向同性的,为了使生成的分形地形具有各向异性特征,提出了一种新的分形地形生成方法,该方法利用组合分形布朗曲面模型,将具有不同特征的两种分形布朗曲面相融合,使得生成的地形具有各向异性特征。对组合分形布朗曲面算法进行了仿真实验,生成了最终的分形地形。对仿真结果的分析表明,生成的分形地形的特征具有各向异性特征,和实际的自然地形特征相符合,从而证明了该算法的有效性。
The traditional fractal method for terrain generation has an isotropic fractal feature. In order to generate anisotropic terrain, a new approach to generating anisotropic terrain based on fractal is proposed in this paper. This approach uses the combined fractal Brown surface (CFBS) model and incorporates two fractal Brown surface (FBS) with different fractal features. The fractal features of the corresponding terrain are anisotropic. Finally, some simulations based on CFBS are conducted and the final figures of the corresponding terrains are shown in this paper. The analyses of the simulation results show that the fractal feature is anisotropic, which is accordant to the actual terrain. The simulation results verify the validity of the CFBS model.
The traditional fractal method for terrain generation has an isotropic fractal feature. In order to generate anisotropic terrain, a new approach to generating anisotropic terrain based on fractal is proposed in this paper. This approach uses the combined fractal Brown surface (CFBS) model and incorporates two fractal Brown surface (FBS) with different fractal features. The fractal features of the corresponding terrain are anisotropic. Finally, some simulations based on CFBS are conducted and the final figures of the corresponding terrains are shown in this paper. The analyses of the simulation results show that the fractal feature is anisotropic, which is accordant to the actual terrain. The simulation results verify the validity of the CFBS model.
引文
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9 Ebert, Musgrave, Peachey, et al. Textures and Modeling: A Procedural Approach [M]. New York: Academic Press, 2002 :102-120．
10 Falconer K. Fractal Geometry [M]. Chichester, UK: Wiley, 1990 :101-102．
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12 Lin Lan. Research on Rendering of High-precision Terrain Based on Fractal [D] . Wuhan; Huazhong University of Science and Technology,2006． [林岚.基于分形理论的高精度地形绘制算法研究[D].武汉:华中科技大学,2006． ]
13 Qin S F, Harrison R, WEST AA.et al. Development of a novel 3D simulation modeling system for distributed manufacturing [J] .Computer in Industry, 2004, 54(1) : 69-81．
14 Zhu Ju-bo, Liang Dian-nong. Combined fractal Brown motion model [J]. Science in China, (SerE), 2000, 30(4) :312-319． [朱炬波,梁甸农.组合分形Brown运动模型[J].中国科学(E辑),2000,30(4) :312-319． ]
15 Li Meng, Zhu Ling-ren, Long Hai-ying. Research on fractal and multi-fractal properties of landform surface in tianshan area, Xinjiang,china[J]. Inland Earthquake, 2003, 17(01) , 20-26． [李锰,朱令人,龙海英.新疆天山地区地貌分形与多重分形特征研究[J].内陆地震,2003,17(01) :20-26． ]
16 Xu Jing, Ren Li-liang, Cheng Yuan-hua, et al. Topographic index calculation that is independent of the DEM spatial resolution [J].Journal of Tsinghua University ( Science and Technology ) , 2008 ,48(16) ,983-986． [徐静,任立良,程媛华等.不受DEM空间分辨率影响的地形指数计算[J].清华大学学报,2008,48(16) :983-986． ]
2 Falconer K J, Levy V J. Horizons of fractional Brownian surfaces [A]. In: Royal Society of London Proceedings ( Series A ) 2000 [C] ,London, UK, 2000,456:2153-2178．
3 Embrechts P, Maejima M. Selfsimilar Processes [M]. Elizabeth, NJ,USA: Princeton University Press, 2002:50-55．
4 McGaughey D R, Aithen G J M. Statistical analysis of successive random additions for generating fractional Brownian motion [J] .Physica A, 2000, 11(1) : 25-34．
5 Yang Yan-chun, Bao Jin-song, Jin Ye. Realistic virtual lunar surface simulation method [J]. Journal of System Simulation, 2007 ,19(11) :2515-2518． [杨艳春,鲍劲松,金烨.一种真实感虚拟月面建模方 法[J].系统仿真学报,2007,19(11) :2515-2518． ]
6 Li Xu-tao, Zhu Guang-xi, CAO Han-qiang, et al. Anisotropy multi-scale self-similarity random field and terrain construction [J]. Journal of Image and Graphics, 2007,12(7) :1286-1290． [李旭涛,朱光喜,曹汉强等,各向异性多尺度自相似随机场与地形构建[J].2007,12(7) :1286-1290． ]
7 Perez M, Fernandez M, Morillo P, et al. Locally constrained synthetic LoDs generation for natural terrain meshes [J]. Future Generation Computer Systems, 2004,20(8) :1375-1387．
8 Li Qing-zhong, Gao Xiu-rong. Study on generating method for 3D controllable and realistic terrain [J]. Journal of System Simulation,2008,20(11) :2938-2941． [李庆忠,高秀荣.三维可控真实感地形生成方法研究[J].系统仿真学报,2008,20(11) :2938-2941． ]
9 Ebert, Musgrave, Peachey, et al. Textures and Modeling: A Procedural Approach [M]. New York: Academic Press, 2002 :102-120．
10 Falconer K. Fractal Geometry [M]. Chichester, UK: Wiley, 1990 :101-102．
11 Sharifi M, Golpaygani F H, Esmaeli M. A new fractal-based approach for 3D visualization of mountains in VRML standard [J].In: Proceedings of the 2nd International Conference on Computer Graphics and Interactive Techniques in Australasia and South East Asia 2004[C] , Singapore, 2004,11(6) :100-105．
12 Lin Lan. Research on Rendering of High-precision Terrain Based on Fractal [D] . Wuhan; Huazhong University of Science and Technology,2006． [林岚.基于分形理论的高精度地形绘制算法研究[D].武汉:华中科技大学,2006． ]
13 Qin S F, Harrison R, WEST AA.et al. Development of a novel 3D simulation modeling system for distributed manufacturing [J] .Computer in Industry, 2004, 54(1) : 69-81．
14 Zhu Ju-bo, Liang Dian-nong. Combined fractal Brown motion model [J]. Science in China, (SerE), 2000, 30(4) :312-319． [朱炬波,梁甸农.组合分形Brown运动模型[J].中国科学(E辑),2000,30(4) :312-319． ]
15 Li Meng, Zhu Ling-ren, Long Hai-ying. Research on fractal and multi-fractal properties of landform surface in tianshan area, Xinjiang,china[J]. Inland Earthquake, 2003, 17(01) , 20-26． [李锰,朱令人,龙海英.新疆天山地区地貌分形与多重分形特征研究[J].内陆地震,2003,17(01) :20-26． ]
16 Xu Jing, Ren Li-liang, Cheng Yuan-hua, et al. Topographic index calculation that is independent of the DEM spatial resolution [J].Journal of Tsinghua University ( Science and Technology ) , 2008 ,48(16) ,983-986． [徐静,任立良,程媛华等.不受DEM空间分辨率影响的地形指数计算[J].清华大学学报,2008,48(16) :983-986． ]
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