基于Nurbs曲面的地下三维数据模型研究
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摘要
三维数据模型是三维地理信息系统研究的基础,以面片表示三维地层模型是地质环境三维地理信息系统研究的一项重要内容。由于多项式曲面等数学解析曲面的表现形式对于复杂的地质情况无法准确表示,甚至无法表示出来,而拟合曲面要准确表示地层情况会使得拟合次数太高而难于计算,同时有些插值逼近的曲面不会通过预先给定的地层控制点而降低拟合精度。多层TIN或多层DEM表示的地层面片虽然在模型精度表示上有较大的提高,但是带来的问题是数据量极其庞大,在数据的存储和分析方面受到很大的制约。针对这些问题,本文提出了将Nurbs(非均匀有理B样条曲面)作为地层曲面模型表示的统一表现形式,并引入到地层三维数据模型中。Nurbs曲线曲面具有明显的几何解释,计算速度快并且稳定,而且具有透视、反射投影不变性,同时具有强的凸包性。将Nurbs优良的性质引入到三维数据模型中,能简化三维数据结构,并能得到较好的结果。利用Nurbs曲线、曲面以及三参数实体模型建立三维数据模型,得到统一的GIS三维数据结构,在此基础上能更好地建立三维地理信息系统。
本文的主要研究工作与创新点如下：
1分析了利用Nurbs表达地层曲面的可能性和必要性,提出了适应于Nurbs表示的地层分层的方法和过程,并给出了根据钻孔数据的特征对地层进行分层的方法；
2提出了应用Nurbs曲面模型来表达地下环境三维数据模型的统一的表达方式,对空间对象分别采用Nurbs参数曲面来表达；并分析了几种用于Nurbs曲面模型的数据插值加密方法,通过插值结果得出自反射分形插值对钻孔数据在水平和垂直方向都有比较好的结果,适合于地层本身的自反射分形特征,特别是数据量小的情况下分形插值较其他几种方法能保持地层的自反射分形结构,插值速度也优于所分析的其他几种方法；
3建立了基于Nurbs(非均匀有理B样条曲面)的地层三维曲面模型,对空间对象点、线、面的Nurbs统一模型进行了构建,并提出利用三参数Nurbs实体模型来表达实体,使得Nurbs曲面模型除了能表示对象的边界以后,也能按照Nurbs的统一表达方式能表达对象的内部；
4对建立的Nurbs曲面模型,设计了模型的存储结构,以及各种空间对象模型拓扑关系,针对Nurbs曲面模型的强凸包的特点,拓展了空间对象相邻的概念,这种相邻关系的描述适应Nurbs曲面的权因子的变化对曲面模型对象间关系的影响；
5推导了Nurbs地层模型的空间计算与分析方法及公式,重点建立了曲面上曲线长、曲面面积、体积的Nurbs计算过程与方法,并对计算结果进行了实验；给出了曲面模型的剖面切割运算以及“挖坑”计算过程；
6提出了对几种特殊的地质对象的Nurbs建模方法,并对曲面模型的地层表面纹理进行了分析,给出了曲面分形纹理的建立过程与方法,分形纹理能很好的表现地层的粗糙度,对表现地层表面具有很好的效果；
本文得出了基于Nurbs的地下环境三维数据模型的整体结构以及模型的构建和计算,实验证明这种模型与其他模型相比具有模型简单、低存储和高效的运算效率,对地下环境提供了统一的模型表达方式。
Three-dimensional data model is one of the important content of the3D(three-dimensional) geographic information system. The3D formation model represented by patches is the important respects of geological environment3D geographical information system. As polynomial surface and other surface manifestations of mathematical analysis cannot represent the complicated geologic situation accurately, and fitting surfaces may cause high fitting numbers hard to calculate, meanwhile the interpolation fitting surface will not reduce accuracy by pre-specified control points. The formation in film based on multi-TIN or multi-DEM not only has a great improvement on the model accuracy, but it brings vast amounts of data, resulted in a great restriction on data storage and analysis. With the considerations of the above issues, the dissertation proposes to use Nurbs(non-uniform rational b-spline surface) as the unified representation form of the ground surface model to bring into the formation three-dimensional data model, accordingly the good properties of Nurbs also introduced in.
In this dissertation, main work includes the followings:
(1) Based on the borehole data, the strata is stratified, and the stratifying methods and processes are presented.Tentative method has been proposed to use Nurbs surface model to represent underground environment three-dimensional data model as the unified representation form, Nurbs parameter surface is used to represent the spatial objects;
(2) Several data interpolation encryption methods have been analyzed, and according to the interpolation results, it is proved that self-reflection fractal interpolation to borehole data has good results both in the horizontal and vertical direction, which is suitable for self-reflection fractal of strata itself, especially under the situation of the small data amount, and that the fractal interpolation can maintain the strata self-reflection fractal structure different from other, and the interpolation speed is also faster than others;
(3) The formation three-dimensional surface model has been build, based on Nurbs (non-uniform rational b-spline surface), and by the way of building and testing the unified Nurbs model of spatial points, polyline and polygon, the dissertation proposed to use three parameter Nurbs entity model to represent entities, enabling Nurbs surface model to represent the object's internal according the Nurbs unified representation form, except representing the object boundary;
(4) The Nurbs surface model is built, and the storage structure, along with the topology of various spatial object models are given;
(5) The main calculating method of Nurbs formation model are given, focused on the Nurbs calculating process and method of surface length, area and volume, and experiments are carried out to check the calculating results;
(6) The Nurbs modeling method of several special geological objects is given, and the modeling process and method of surface fractal texture, which can well represent the strata roughness and have excellent effects to represent strata surface, based on the analysis on the strata surface texture of the surface model;
The dissertation has built the underground environment three-dimensional data model, which is based on Nurbs and its overall structure, modeling process and calculating are also given. Through the experiments it is proved that this model, compared with other models, reveals characters of simplicity, low storage and efficient operation.
本文的主要研究工作与创新点如下：
1分析了利用Nurbs表达地层曲面的可能性和必要性,提出了适应于Nurbs表示的地层分层的方法和过程,并给出了根据钻孔数据的特征对地层进行分层的方法；
2提出了应用Nurbs曲面模型来表达地下环境三维数据模型的统一的表达方式,对空间对象分别采用Nurbs参数曲面来表达；并分析了几种用于Nurbs曲面模型的数据插值加密方法,通过插值结果得出自反射分形插值对钻孔数据在水平和垂直方向都有比较好的结果,适合于地层本身的自反射分形特征,特别是数据量小的情况下分形插值较其他几种方法能保持地层的自反射分形结构,插值速度也优于所分析的其他几种方法；
3建立了基于Nurbs(非均匀有理B样条曲面)的地层三维曲面模型,对空间对象点、线、面的Nurbs统一模型进行了构建,并提出利用三参数Nurbs实体模型来表达实体,使得Nurbs曲面模型除了能表示对象的边界以后,也能按照Nurbs的统一表达方式能表达对象的内部；
4对建立的Nurbs曲面模型,设计了模型的存储结构,以及各种空间对象模型拓扑关系,针对Nurbs曲面模型的强凸包的特点,拓展了空间对象相邻的概念,这种相邻关系的描述适应Nurbs曲面的权因子的变化对曲面模型对象间关系的影响；
5推导了Nurbs地层模型的空间计算与分析方法及公式,重点建立了曲面上曲线长、曲面面积、体积的Nurbs计算过程与方法,并对计算结果进行了实验；给出了曲面模型的剖面切割运算以及“挖坑”计算过程；
6提出了对几种特殊的地质对象的Nurbs建模方法,并对曲面模型的地层表面纹理进行了分析,给出了曲面分形纹理的建立过程与方法,分形纹理能很好的表现地层的粗糙度,对表现地层表面具有很好的效果；
本文得出了基于Nurbs的地下环境三维数据模型的整体结构以及模型的构建和计算,实验证明这种模型与其他模型相比具有模型简单、低存储和高效的运算效率,对地下环境提供了统一的模型表达方式。
Three-dimensional data model is one of the important content of the3D(three-dimensional) geographic information system. The3D formation model represented by patches is the important respects of geological environment3D geographical information system. As polynomial surface and other surface manifestations of mathematical analysis cannot represent the complicated geologic situation accurately, and fitting surfaces may cause high fitting numbers hard to calculate, meanwhile the interpolation fitting surface will not reduce accuracy by pre-specified control points. The formation in film based on multi-TIN or multi-DEM not only has a great improvement on the model accuracy, but it brings vast amounts of data, resulted in a great restriction on data storage and analysis. With the considerations of the above issues, the dissertation proposes to use Nurbs(non-uniform rational b-spline surface) as the unified representation form of the ground surface model to bring into the formation three-dimensional data model, accordingly the good properties of Nurbs also introduced in.
In this dissertation, main work includes the followings:
(1) Based on the borehole data, the strata is stratified, and the stratifying methods and processes are presented.Tentative method has been proposed to use Nurbs surface model to represent underground environment three-dimensional data model as the unified representation form, Nurbs parameter surface is used to represent the spatial objects;
(2) Several data interpolation encryption methods have been analyzed, and according to the interpolation results, it is proved that self-reflection fractal interpolation to borehole data has good results both in the horizontal and vertical direction, which is suitable for self-reflection fractal of strata itself, especially under the situation of the small data amount, and that the fractal interpolation can maintain the strata self-reflection fractal structure different from other, and the interpolation speed is also faster than others;
(3) The formation three-dimensional surface model has been build, based on Nurbs (non-uniform rational b-spline surface), and by the way of building and testing the unified Nurbs model of spatial points, polyline and polygon, the dissertation proposed to use three parameter Nurbs entity model to represent entities, enabling Nurbs surface model to represent the object's internal according the Nurbs unified representation form, except representing the object boundary;
(4) The Nurbs surface model is built, and the storage structure, along with the topology of various spatial object models are given;
(5) The main calculating method of Nurbs formation model are given, focused on the Nurbs calculating process and method of surface length, area and volume, and experiments are carried out to check the calculating results;
(6) The Nurbs modeling method of several special geological objects is given, and the modeling process and method of surface fractal texture, which can well represent the strata roughness and have excellent effects to represent strata surface, based on the analysis on the strata surface texture of the surface model;
The dissertation has built the underground environment three-dimensional data model, which is based on Nurbs and its overall structure, modeling process and calculating are also given. Through the experiments it is proved that this model, compared with other models, reveals characters of simplicity, low storage and efficient operation.
引文
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