CN107301678A - A kind of three-dimensional modeling method of geological mass - Google Patents
A kind of three-dimensional modeling method of geological mass Download PDFInfo
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Abstract
本发明公开了一种地质块体的三维建模方法,包括:给定待建模的地质块体模型和空间裂隙面的几何描述;对于地质块体模型,求取边界面、裂隙面形成的迹线并获得棱边;棱边正则化处理,利用边界算子并进行搜索后形成有向环,基于对有向环的属性判断及有向环间的包含关系判断形成有向面;有向面正则化处理,利用边界算子并进行搜索后形成有向壳,基于对有向壳的属性判断及有向壳间的包含关系判断形成有向体;对形成的各有向体进行块体拓扑性检查和块体体积总和检查。本发明不需引入任何人为假设且完全根据实际地质结构面特点,形成空间任意复杂的地质块体,在工程实践中具有重要的应用价值,对非连续介质力学数值方法的发展具有积极的理论意义。
The invention discloses a three-dimensional modeling method of a geological block, which includes: given a geological block model to be modeled and a geometric description of a spatial fissure surface; track and obtain edges; edge regularization processing, use boundary operators and search to form directed rings, and form directed surfaces based on the judgment of the attributes of directed rings and the inclusion relationship between directed rings; directed Surface regularization processing, using boundary operators and searching to form directed shells, based on the judgment of the attributes of directed shells and the judgment of the inclusion relationship between directed shells to form directed bodies; block the formed directed bodies Topology checks and block volume sum checks. The present invention does not need to introduce any artificial assumptions and is completely based on the characteristics of the actual geological structural surface to form geological blocks with arbitrary complex space, which has important application value in engineering practice and has positive theoretical significance for the development of numerical methods of discontinuous medium mechanics .
Description
技术领域technical field
本发明涉及一种基于三维地质建模技术实现的地质块体,特别是复杂地质块体的三维建模方法,属于岩体工程的非连续介质力学数值计算与分析技术领域。The invention relates to a geological block realized based on a three-dimensional geological modeling technology, in particular to a three-dimensional modeling method for a complex geological block, and belongs to the technical field of numerical calculation and analysis of discontinuous medium mechanics in rock mass engineering.
背景技术Background technique
岩体介质在其形成和演变的整个地质历史时期中,经受各种复杂而不均衡的地质作用后,形成一个复杂的地质形体。从宏观地质结构上讲,岩体可以看成是由若干空间地质结构面切割而成的块体系统。During the entire geological history period of its formation and evolution, the rock mass medium forms a complex geological shape after undergoing various complex and uneven geological actions. From the perspective of macroscopic geological structure, rock mass can be regarded as a block system cut by several spatial geological structure planes.
目前,离散元法、不连续变形分析等非连续介质力学方法,均是以离散块体系统为研究对象,将岩体视为若干空间结构面所切割而成的复杂空间岩块集合体。但是,由于自然界的地形地质条件非常复杂,即使对岩体地形地质条件进行简化,也不可能像处理二维问题那样进行手工的块体剖分,因此有必要建立一种复杂地质块体的三维建模方法。At present, methods of discontinuous medium mechanics such as discrete element method and discontinuous deformation analysis all take the discrete block system as the research object, and regard the rock mass as a complex spatial rock block aggregate cut by several spatial structural planes. However, due to the very complex topographic and geological conditions in nature, even if the topographic and geological conditions of the rock mass are simplified, it is impossible to manually divide the blocks like dealing with two-dimensional problems. Therefore, it is necessary to establish a three-dimensional model of complex geological blocks. modeling method.
P.M.Warburton于1983年提出了一种应用无限大平面进行块体剖分的方法,但是这种方法不能表示岩体复杂的块体形态,而且生成的块体只能局限于凸体,这一点与实际工程中地质块体的具体情况不相符合。后来很多学者开始假定裂隙面为有限尺寸的空间多边形(或圆形)来研究复杂地质块体的三维建模问题,分别从代数拓扑同调论、矢体以及有向图理论三个方面出发,虽然出发角度不同,但基本上实现的是一般性质的地质块体的三维建模问题。In 1983, P.M.Warburton proposed a method of block subdivision using an infinite plane, but this method cannot represent the complex block shape of the rock mass, and the generated blocks can only be limited to convex bodies, which is different from The specific conditions of geological blocks in actual engineering do not match. Later, many scholars began to study the three-dimensional modeling of complex geological blocks by assuming that the fracture surface is a finite-sized spatial polygon (or circle), starting from the three aspects of algebraic topological homology, vector and directed graph theory, although The starting angles are different, but basically what is realized is the 3D modeling of geological blocks of general nature.
从实际实施中可以发现,上述众多方法,要么仅给出了严谨的数学理论而未给出可编程实现的具体算法,要么引入若干人工干预项或缺乏必要的正则化处理,进而导致复杂块体建模过程不完备,要么就是未提出完备、且具有可操作性的判定准则来验证复杂地质块体三维建模的完备性和准确性。From the actual implementation, it can be found that many of the above methods either only give rigorous mathematical theories but do not give specific algorithms for programmable realization, or introduce some artificial intervention items or lack necessary regularization processing, resulting in complex blocks. The modeling process is incomplete, or a complete and operable judgment criterion has not been proposed to verify the completeness and accuracy of 3D modeling of complex geological blocks.
由此可见,研究出一种可解决地质块体,特别是复杂地质块体在三维建模方面所出现的上述诸多不足,是目前亟需解决的问题。It can be seen that it is an urgent problem to be solved to develop a method that can solve the above-mentioned problems in 3D modeling of geological blocks, especially complex geological blocks.
发明内容Contents of the invention
本发明的目的在于提供一种地质块体的三维建模方法,其可快速、准确地针对地质块体,尤其是复杂地质块体进行三维建模,构建出的三维模型可真实反映地质块体的实际构造。The purpose of the present invention is to provide a three-dimensional modeling method for geological blocks, which can quickly and accurately perform three-dimensional modeling on geological blocks, especially complex geological blocks, and the constructed three-dimensional model can truly reflect the geological blocks actual structure.
为了实现上述目的,本发明采用了以下技术方案:In order to achieve the above object, the present invention adopts the following technical solutions:
一种地质块体的三维建模方法,其特征在于,它包括步骤:A three-dimensional modeling method of a geological block is characterized in that it comprises the steps of:
1)给定待建模的地质块体模型和空间裂隙面的几何描述;1) Given the geological block model to be modeled and the geometric description of the spatial fracture surface;
2)对于待建模的地质块体模型,求取其上边界面与边界面之间、裂隙面与裂隙面之间以及边界面与裂隙面之间形成的迹线,进而获得边界面和裂隙面上形成的棱边;2) For the geological block model to be modeled, obtain the traces formed between the upper boundary surface and the boundary surface, between the fracture surface and the fracture surface, and between the boundary surface and the fracture surface, and then obtain the boundary surface and the fracture surface the edge formed on
3)棱边经正则化处理后,利用边界算子并根据环路搜索准则进行搜索后形成有向环,基于对有向环的属性判断以及有向环间的包含关系判断形成有向面;3) After the edge is regularized, use the boundary operator and search according to the loop search criteria to form a directed ring, and form a directed surface based on the judgment of the attributes of the directed ring and the inclusion relationship between the directed rings;
4)有向面经正则化处理后,利用边界算子并根据空间壳搜索准则进行搜索后形成有向壳,基于对有向壳的属性判断以及有向壳间的包含关系判断形成有向体;4) After the directed surface is regularized, use the boundary operator and search according to the space shell search criteria to form a directed shell, and form a directed body based on the judgment of the attributes of the directed shell and the inclusion relationship between the directed shells ;
5)对形成的各有向体经块体拓扑性检查和块体体积总和检查,判断形成的各有向体是否可构成待建模的地质块体模型:若可构成,则三维建模成功并结束。5) Check the topology of each formed directed body and check the sum of block volume to judge whether each formed directed body can constitute the geological block model to be modeled: if it can be formed, the 3D modeling is successful and end.
本发明的优点是:The advantages of the present invention are:
本发明将地质块体视为有向复合形,基于闭曲面的拓扑性质,经正则化处理,利用边界算子并结合相应搜索准则后进行相关包含判断实现了三维块体建模,建模效率高,所建模型的准确性与完备性高,建模成功率高。The invention regards the geological block as a directed composite shape, based on the topological properties of the closed surface, after regularization processing, using the boundary operator and combining with the corresponding search criteria to carry out relevant inclusion judgments to realize the three-dimensional block modeling, the modeling efficiency High, the accuracy and completeness of the built model are high, and the modeling success rate is high.
附图说明Description of drawings
图1是本发明三维建模方法的实施流程图。Fig. 1 is a flow chart of the implementation of the three-dimensional modeling method of the present invention.
图2是裂隙面的初始形态图。Figure 2 is the initial shape diagram of the fracture surface.
图3是环路搜索最大右转角准则的说明示意图。FIG. 3 is an explanatory schematic diagram of the maximum right-turn angle criterion for loop search.
图4a、图4b分别是内环、外环示意图。Figure 4a and Figure 4b are schematic diagrams of the inner ring and the outer ring, respectively.
图5是空间壳搜索最大右转角准则的说明示意图。Fig. 5 is an explanatory schematic diagram of searching for a maximum right-turn angle criterion in a space shell.
图6a、图6b分别是外壳、内壳示意图。Figure 6a and Figure 6b are schematic diagrams of the outer shell and the inner shell, respectively.
图7是有限元模型实例图。Fig. 7 is an example diagram of the finite element model.
图8、图9、图10是裂隙面修正得到的多边形(粗实线所示)示意图。Fig. 8, Fig. 9 and Fig. 10 are schematic diagrams of polygons (indicated by thick solid lines) corrected by fracture surfaces.
图11是棱边正则化处理后的结果示意图。Fig. 11 is a schematic diagram of the result after edge regularization processing.
图12a是形成有向环1(内环)的环路搜索说明图。Fig. 12a is an explanatory diagram of a loop search forming a directed loop 1 (inner loop).
图12b是形成有向环2(内环)的环路搜索说明图。Fig. 12b is an explanatory diagram of a loop search forming a directed loop 2 (inner loop).
图12c是形成有向环3(外环)的环路搜索说明图。Fig. 12c is an explanatory diagram of a loop search forming a directed loop 3 (outer loop).
图12d是形成有向环4(内环)的环路搜索说明图。Fig. 12d is an explanatory diagram of a loop search forming a directed loop 4 (inner loop).
图13a是形成有向壳1(粗实线所示内壳)的空间壳搜索说明图。Fig. 13a is an explanatory diagram of searching for a space shell formed with an orientation shell 1 (inner shell indicated by a thick solid line).
图13b是形成有向壳2(粗实线所示内壳)的空间壳搜索说明图。Fig. 13b is an explanatory view of searching for a space shell formed with a directed shell 2 (inner shell indicated by a thick solid line).
图13c是形成有向壳3(粗实线所示内壳)的空间壳搜索说明图。Fig. 13c is an explanatory view of searching for a space shell formed with a directed shell 3 (inner shell indicated by a thick solid line).
具体实施方式detailed description
作为三维块体,可从拓扑信息和几何信息来进行表征,其中:几何信息是指三维块体的空间位置,由其角点空间坐标来表示;拓扑信息是指各组成元素之间的相互关系,组成元素为有向体、有向壳、有向面、有向环、有向边和角点。As a three-dimensional block, it can be characterized from topological information and geometric information, among which: geometric information refers to the spatial position of the three-dimensional block, which is represented by the spatial coordinates of its corner points; topological information refers to the relationship between the constituent elements, The constituent elements are directed volumes, directed shells, directed faces, directed rings, directed edges and corners.
对于三维块体,其可视为一有向体,该有向体是由一个内壳和若干个外壳所组成,它是一个三维空间R3的非空、有界、连续、封闭的子集,其边界是若干个有向壳的并集。有向壳则是由若干有向面围成的有限空间,它是三维空间R3中非空、有界、连续、封闭的子集,其边界是若干个有向面的并集。有向面是三维空间R3中由一个内环和若干个外环组成的非空、有界、连续、封闭的子集,其边界是若干个有向环的并集。有向环则是由若干个有序、有向边组成的空间平面上的封闭边界,环中各边不能自交,相邻两条有向边共用一个角点。有向边具有两个角点,并且具有方向性。角点为不共线的有向边的交点或不共面的有向面的交点。For a three-dimensional block, it can be regarded as a directed body, which is composed of an inner shell and several outer shells, and it is a non-empty, bounded, continuous, and closed subset of a three-dimensional space R3 , whose boundary is the union of several directed shells. A directed shell is a finite space enclosed by several directed faces. It is a non-empty, bounded, continuous and closed subset of the three-dimensional space R 3 , and its boundary is the union of several directed faces. A directed surface is a non-empty, bounded, continuous and closed subset composed of an inner ring and several outer rings in the three-dimensional space R 3 , and its boundary is the union of several directed rings. A directed ring is a closed boundary on a space plane composed of several ordered and directed edges. Each edge in the ring cannot intersect itself, and two adjacent directed edges share a corner point. A directed edge has two corners and has directionality. A corner is the intersection of non-collinear directed edges or the intersection of non-coplanar directed faces.
如图1所示,本发明提出的地质块体的三维建模方法包括如下步骤:As shown in Figure 1, the three-dimensional modeling method of geological block that the present invention proposes comprises the following steps:
1)给定待建模的地质块体模型和空间裂隙面的几何描述;1) Given the geological block model to be modeled and the geometric description of the spatial fracture surface;
2)对于待建模的地质块体模型,求取其上边界面与边界面之间、裂隙面与裂隙面之间以及边界面与裂隙面之间形成的迹线,进而获得边界面和裂隙面上形成的棱边;2) For the geological block model to be modeled, obtain the traces formed between the upper boundary surface and the boundary surface, between the fracture surface and the fracture surface, and between the boundary surface and the fracture surface, and then obtain the boundary surface and the fracture surface the edge formed on
3)棱边经正则化处理后,利用边界算子并根据环路搜索准则进行搜索后形成有向环,基于对有向环的属性判断以及有向环间的包含关系判断形成有向面;3) After the edge is regularized, use the boundary operator and search according to the loop search criteria to form a directed ring, and form a directed surface based on the judgment of the attributes of the directed ring and the inclusion relationship between the directed rings;
4)有向面经正则化处理后,利用边界算子并根据空间壳搜索准则进行搜索后形成有向壳,基于对有向壳的属性判断以及有向壳间的包含关系判断形成有向体;4) After the directed surface is regularized, use the boundary operator and search according to the space shell search criteria to form a directed shell, and form a directed body based on the judgment of the attributes of the directed shell and the inclusion relationship between the directed shells ;
5)对形成的各有向体经块体拓扑性检查和块体体积总和检查,判断形成的各有向体是否可构成待建模的地质块体模型:若可构成,则三维建模成功并结束;若不可构成,则三维建模失败,重新开始。5) Check the topology of each formed directed body and check the sum of block volume to judge whether each formed directed body can constitute the geological block model to be modeled: if it can be formed, the 3D modeling is successful and end; if it cannot be constructed, the 3D modeling fails and starts again.
在步骤1)中:In step 1):
待建模的地质块体模型为任意空间、呈凹或凸状的单连通多面体,待建模的地质块体模型的几何描述可采用分段线性复合形来表达,其包括两部分:一部分是几何信息,以角点空间坐标来表示;另一部分是拓扑信息,以组成待建模的地质块体模型的各边界面上的封闭环路(按逆时针走向)的点序列来表示;The geological block model to be modeled is a concave or convex simply connected polyhedron in any space. The geometric description of the geological block model to be modeled can be expressed by a piecewise linear compound, which includes two parts: one part is Geometric information, represented by the spatial coordinates of the corner points; the other part is topological information, represented by the point sequence of the closed loop (going counterclockwise) on each boundary surface of the geological block model to be modeled;
在假设裂隙面的初始形态为内接于圆形的正多边形(如图2)的基础上,根据裂隙面的延伸是否受到其它裂隙面的约束来进行修正:若受到约束,则根据与其它裂隙面的相交线段,将裂隙面的初始形态修正为相应不规则多边形;反之若不受约束,则裂隙面直接采用初始形态来表示。On the basis of assuming that the initial shape of the fracture surface is a regular polygon inscribed in a circle (as shown in Figure 2), it is corrected according to whether the extension of the fracture surface is constrained by other fracture surfaces: The initial shape of the fracture surface is corrected to the corresponding irregular polygon; otherwise, if it is not constrained, the fracture surface is directly represented by the initial shape.
在本发明中,对裂隙面初始形态的修正是本领域的熟知技术,在此不再详述。In the present invention, the correction of the initial shape of the fracture surface is a well-known technique in the art, and will not be described in detail here.
在实际设计中,步骤2)包括如下步骤:In actual design, step 2) includes the following steps:
2-1)对边界面与边界面之间、裂隙面与裂隙面之间、裂隙面与边界面之间进行求交运算来获取相交线段,记为迹线;2-1) Intersection calculations are performed between boundary surfaces and boundary surfaces, between crack surfaces and crack surfaces, and between crack surfaces and boundary surfaces to obtain intersecting line segments, which are recorded as traces;
2-2)对迹线进行两两相交运算,获取边界面、裂隙面上形成的棱边。2-2) Perform pairwise intersection operations on the traces to obtain the edges formed on the boundary surfaces and fracture surfaces.
在实际设计中,步骤3)包括如下步骤:In actual design, step 3) includes the following steps:
3-1)对棱边进行正则化处理(公知技术),以删除各裂隙面和各边界面上的孤立棱边和“悬空”棱边;3-1) regularize the edges (known technology), to delete the isolated edges and "dangling" edges on each fracture surface and each boundary surface;
3-2)将棱边视为有向边,对每个有向边利用边界算子(公知技术),并根据环路搜索最大右转角准则(还可采用其它形式的环路搜索准则)进行空间环路搜索,形成空间环路,记为有向环;3-2) Treat the edge as a directed edge, use a boundary operator (known technology) for each directed edge, and search the maximum right-turn angle criterion according to the loop (other forms of loop search criteria can also be used) Carry out space loop search to form a space loop, which is recorded as a directed ring;
3-3)判断3-2)产生的有向环的属性:每个有向环为内环还是外环,以形成内环集合和外环集合,其中,内环为有内侧域的有向环(如图4a),外环为有外侧域的有向环(如图4b);3-3) Determine the attributes of the directed ring generated in 3-2): whether each directed ring is an inner ring or an outer ring, to form an inner ring set and an outer ring set, wherein the inner ring is a directed ring with an inner domain Ring (as shown in Figure 4a), the outer ring is a directed ring with an outer domain (as shown in Figure 4b);
3-4)选取每个外环的外侧域内的任意一点作为其特征点;3-4) select any point in the outer domain of each outer ring as its feature point;
3-5)对内环集合中的所有内环进行如下遍历,来获得内环与外环相互之间的包含关系:基于内环集合中的一内环,对外环集合中的所有外环进行遍历操作,通过各外环的特征点是否属于此内环来判断此内环与各外环之间的包含关系,此可视为点与多面边形之间包含关系判断;3-5) Perform the following traversal on all the inner rings in the inner ring set to obtain the mutual inclusion relationship between the inner ring and the outer ring: based on an inner ring in the inner ring set, execute all the outer rings in the outer ring set The traversal operation judges the inclusion relationship between the inner ring and each outer ring by whether the feature points of each outer ring belong to the inner ring, which can be regarded as the inclusion relationship judgment between points and polygons;
3-6)鉴于有向面是由一个内环且仅有一个内环以及若干个外环组成的特点,根据内环与外环互相之间的包含关系,在各裂隙面、各边界面上生成有向面。3-6) In view of the fact that the oriented surface is composed of an inner ring and only one inner ring and several outer rings, according to the inclusion relationship between the inner ring and the outer ring, on each crack surface and each boundary surface Generate directed faces.
在本发明中,步骤3-2)中的环路搜索最大右转角准则是指:In the present invention, the loop search maximum right-turn angle criterion in step 3-2) refers to:
A)以任一边界面或裂隙面上的任一有向边及此有向边上任一角点分别作为当前有向边、当前角点,然后沿右手握拳,大拇指朝向当前搜索的有向面(边界面或裂隙面)的法向矢量所指方向时其余四指所指方向,以当前角点为中心旋转(视为反时针旋转,如图3所示)当前有向边,来找到与当前有向边构成最大角度的有向边,从而把找到的此有向边作为新的当前有向边以及把找到的此有向边上异于前一环路搜索所使用角点的角点作为新的当前角点,以进行下一环路搜索,如此继续进行环路搜索,直至找不到构成最大角度的有向边,从而形成有向环;A) Take any oriented edge on any edge or crack surface and any corner point on this oriented edge as the current oriented edge and current corner point respectively, then make a fist along the right hand, with the thumb facing the currently searched oriented surface ( The normal vector of the boundary surface or fracture surface) In the direction pointed by the other four fingers, rotate around the current corner point (considered as a counterclockwise rotation, as shown in Figure 3) the current directed edge to find the directed edge that forms the largest angle with the current directed edge , so that the found directed edge is used as the new current directed edge and the corner point on the found directed edge that is different from the corner point used in the previous loop search is used as the new current corner point for the next step Loop search, continue loop search in this way until no directed edge forming the maximum angle can be found, thus forming a directed ring;
B)重复执行步骤A),直至当前搜索的边界面或裂隙面上的所有有向边被全部遍历(换句话说,若当前搜索的是边界面,那么则通过重复执行步骤A)来对此边界面上的所有有向边全部遍历搜索完,若当前搜索的是裂隙面,那么则通过重复执行步骤A)来对此裂隙面上的所有有向边全部遍历搜索完);B) Repeat step A) until all the directed edges on the currently searched boundary surface or fracture surface are traversed (in other words, if the current search is a boundary surface, then by repeatedly executing step A) to solve this problem All directed edges on the boundary surface have been traversed and searched, if the current search is a cracked surface, then step A) is repeated to complete all directed edges on the cracked surface);
C)重复执行步骤B)、C),直至所有边界面和所有裂隙面全部被执行过环路搜索,整个环路搜索结束。C) Steps B) and C) are repeated until all boundary surfaces and all fracture surfaces have been subjected to the loop search, and the entire loop search ends.
在本发明中,在环路搜索过程中遵循的最大右转角准则进一步说明如下:In the present invention, the maximum right-turn angle criterion followed in the loop search process is further described as follows:
如图3,设定有向边所在空间环路的下一条有向边可能为n为大于1的正整数,设定与之间形成的右转夹角为θi:As shown in Figure 3, set the directed edge The next directed edge of the space loop may be n is a positive integer greater than 1, set and The right turn angle formed between is θ i :
若 like
若 like
上式中:In the above formula:
为所有有向边所在有向面(当前搜索的有向面)的法向矢量。 is the normal vector of the directed face where all directed edges are located (directed face currently searched).
按照上式1)和2)求出各个可能的有向边与之间形成的右转夹角(沿右手握拳,大拇指朝向法向矢量所指方向时其余四指所指方向,以角点O为中心旋转所构成的夹角)θi,从而确定最大右转角θmax=max(θ1,θ2,…,θn)=θk,则将θk,即θmax所对应的有向边作为下一环路搜索的当前有向边。Calculate each possible directed edge according to the above formulas 1) and 2) and The right turn angle formed between (fist along the right hand, thumb facing the normal vector The pointed direction is the direction pointed by the other four fingers, and the angle formed by rotating with the corner point O as the center) θ i , so as to determine the maximum right turning angle θ max =max(θ 1 , θ 2 ,..., θ n )= θ k , then θ k , that is, the directed edge corresponding to θ max The current directed edge to search for next loop.
如图3,图中示出的有向边与之间构成了最大右转角,从而有向边为下一环路搜索的当前有向边,而将有向边上异于角点O的另一角点作为下一环路搜索的当前角点。As shown in Figure 3, the directed edge shown in the figure and form the maximum right-turn angle, so that the directed edge is the current directed edge searched for the next cycle, and the directed edge Another corner point different from the corner point O is used as the current corner point of the next loop search.
在实际设计中,有向环属性的判定准则为:In the actual design, the judgment criterion of the directed ring attribute is:
根据有向环的有向面积的正负来判断:According to the directed area of the directed ring to judge whether it is positive or negative:
当时,有向环为内环;when , the directed ring is the inner ring;
当时,有向环为外环;when , the directed ring is the outer ring;
其中:有向环的有向面积采用下式3)求出:Where: the directed area of the directed ring Use the following formula 3) to find:
上式3)中:In formula 3):
为有向环的有向面积; is the directed area of the directed ring;
n为组成有向环的角点个数,n为大于1的正整数;n is the number of corner points forming a directed ring, and n is a positive integer greater than 1;
xk、yk分别为组成有向环的第k个角点的横、纵坐标。x k , y k are respectively the abscissa and ordinate of the kth corner point forming the directed ring.
在实际设计中,步骤4)包括如下步骤:In actual design, step 4) includes the following steps:
4-1)对有向面进行正则化处理(公知技术),以删除孤立有向面和“悬空”有向面;4-1) Carry out regularization processing (known technology) to directed face, to delete isolated directed face and " dangling " directed face;
4-2)对每个有向面利用边界算子(公知技术),并根据空间壳搜索最大右转角准则(还可采用其它形式的空间壳搜索准则)进行空间壳搜索,形成有向壳;4-2) Utilize the boundary operator (known technology) for each directional surface, and carry out the space shell search according to the space shell search maximum right-turn angle criterion (other forms of space shell search criteria can also be used) to form a directed shell ;
4-3)判断4-2)产生的有向壳的属性:每个有向壳是内壳还是外壳,以形成内壳集合和外壳集合,其中,内壳为有内侧域的有向壳(如图6b),外壳为有外侧域的有向壳(如图6a);4-3) Determine the properties of the directed shell produced in 4-2): whether each directed shell is an inner shell or an outer shell to form an inner shell set and an outer shell set, wherein the inner shell is a directed shell with an inner domain ( As shown in Figure 6b), the shell is a directed shell with an outer domain (as shown in Figure 6a);
4-4)选取每个外壳的外侧域内的任意一点作为其特征点;4-4) Select any point in the outer domain of each shell as its feature point;
4-5)对内壳集合中的所有内壳进行如下遍历,来获得内壳与外壳相互之间的包含关系:基于内壳集合中的一内壳,对外壳集合中的所有外壳进行遍历操作,通过各外壳的特征点是否属于此内壳来判断此内壳与各外壳之间的包含关系,此可视为点与多面边体之间包含关系判断;4-5) Perform the following traversal on all the inner shells in the inner shell set to obtain the inclusion relationship between the inner shell and the outer shell: based on an inner shell in the inner shell set, perform a traversal operation on all the outer shells in the outer shell set , judge the inclusion relationship between the inner shell and each outer shell by whether the feature points of each outer shell belong to the inner shell, which can be regarded as the inclusion relationship judgment between the point and the polyhedron;
4-6)鉴于有向体是由一个内壳且仅有一个内壳以及若干个外壳组成的特点,根据内壳与外壳相互之间的包含关系,生成有向体。4-6) In view of the fact that the directed body is composed of one inner shell and only one inner shell and several outer shells, the directed body is generated according to the inclusion relationship between the inner shell and the outer shell.
在本发明中,步骤4-2)中的空间壳搜索最大右转角准则是指:In the present invention, the space shell search maximum right-turn angle criterion in step 4-2) refers to:
A)以任一有向面及其上任一有向边分别作为当前有向面、当前有向边,然后沿右手握住当前有向边,大拇指朝向当前有向边所指方向时其余四指所指方向旋转(视为反时针旋转),来找到与当前有向面拥有公共的当前有向边且构成最大角度的有向面,从而把找到的此有向面作为新的当前有向面以及把找到的此有向面上异于前一空间壳搜索所使用有向边的有向边作为新的当前有向边,以进行下一空间壳搜索,如此继续进行空间壳搜索,直至被空间壳搜索过的有向面上的所有有向边被全部遍历以及找不到构成最大角度的有向面,从而形成有向壳;A) Take any oriented surface and any oriented edge above it as the current oriented surface and current oriented edge respectively, then hold the current oriented edge with the right hand, and when the thumb faces the direction pointed by the current oriented edge, the other four Refers to the direction of rotation (considered as anti-clockwise rotation), to find the directed face that has the common current directed edge and forms the largest angle with the current directed face, so that the found directed face is used as the new current directed face and take the oriented edge on this oriented surface that is different from the oriented edge used in the previous space shell search as the new current oriented edge to carry out the next space shell search, and continue the space shell search in this way until All oriented edges on the oriented surface searched by the space shell are traversed and no oriented surface forming the largest angle can be found, thus forming a directed shell;
B)重复执行步骤A),直至所有有向面及各有向面上的所有有向边被全部遍历,整个空间壳搜索结束。B) Step A) is repeated until all directed faces and all directed edges on each directed face are traversed, and the search for the entire space shell ends.
在本发明中,在空间壳搜索过程中遵循的最大右转角准则进一步说明如下:In the present invention, the maximum right-turn angle criterion followed in the space shell search process is further described as follows:
如图5,设定空间已搜索到有向面以的某有向边作为当前有向边,与拥有公共边的下一个有向面可能为n为大于1的正整数,设定与之间形成的右转夹角(沿右手握住公共边大拇指朝向公共边所指方向时其余四指所指方向旋转所构成的夹角)为θi:As shown in Figure 5, the set space has searched for the directed surface by a directed edge of As the current directed edge, with has a common edge The next directed face of may be n is a positive integer greater than 1, set and The right turn angle formed between (hold the common side along the right hand thumbs towards common side The angle formed by the rotation of the other four fingers in the pointed direction) is θ i :
若 like
若 like
上式中:In the above formula:
为的外法向矢量; for The outer normal vector of ;
为的外法向矢量。 for The outer normal vector of .
按照上式4)和5)求出各个可能的有向面与之间形成的右转夹角θi,从而确定最大右转角θmax=max(θ1,θ2,…,θn)=θk,则将θk,即θmax所对应的有向面作为下一空间壳搜索的当前有向面,而有向面上异于有向边的任一有向边作为下一空间壳搜索的当前有向边。According to the above formulas 4) and 5), each possible directional surface can be obtained and The right-turn angle θ i formed between them, so as to determine the maximum right-turn angle θ max = max (θ 1 , θ 2 ,..., θ n ) = θ k , then θ k , that is, the directional noodle as the current oriented face to be searched for in the next space shell, and the oriented face up is different from the directed edge Any directed edge of is used as the current directed edge for the next space shell search.
如图5,图中示出的有向面与之间构成了最大右转角,从而有向面作为下一空间壳搜索的当前有向面,进而选择有向面上除有向边之外的任一有向边作为下一空间壳搜索的当前有向边。As shown in Figure 5, the oriented face shown in the figure and The maximum right-turn angle is formed between them, so that the directed face as the current oriented face for the next space shell search, and then select the oriented face divide by directed edge Any directed edge other than is used as the current directed edge for the next space shell search.
在实际设计中,有向壳属性的判定准则为:In actual design, the criteria for judging directed shell properties are:
根据有向壳的有向体积的正负来判断:Directed volume according to directed shell to judge whether it is positive or negative:
当时,有向壳为内壳;when , the directed shell is the inner shell;
当时,有向壳为外壳;when , the directed shell is the shell;
其中:有向壳的有向体积采用下式6)求出:where: the directed volume of the directed shell Adopt following formula 6) to obtain:
上式6)中:In formula 6):
为有向壳的有向体积; is the directed volume of the directed shell;
s为组成有向壳的有向面个数;s is the number of directed faces that make up the directed shell;
n(i)为组成第i个有向面的角点个数;n(i) is the number of corner points forming the i-th directed surface;
为第i个有向面上的第k个角点的三维坐标。 is the three-dimensional coordinates of the kth corner point on the i-th directed surface.
在实际设计中,步骤5)包括如下步骤:In actual design, step 5) includes the following steps:
5-1)对每个有向体基于是否满足下式7)来进行块体拓扑性检查,以保证块体搜索准确性:5-1) Check the block topology for each directed body based on whether it satisfies the following formula 7) to ensure the accuracy of block search:
Nv+Nf-Ne=2·(Nb-Nh) 7)N v +N f -N e =2·(N b -N h ) 7)
上式7)中:In formula 7):
Nv为组成有向体的角点总数;N v is the total number of corner points that make up the directed body;
Nf为组成有向体的有向面总数;N f is the total number of directed faces that make up the directed body;
Ne为组成有向体的棱边(有向边)总数;N e is the total number of edges (directed edges) forming the directed body;
Nb为组成有向体的有向壳总数;N b is the total number of directed shells that make up the directed body;
Nh为组成有向体的孔洞总数。N h is the total number of holes that make up the directed body.
在实际实施时,若有向体满足式7),则其建模成功,反之,建模失败,重新开始。In actual implementation, if the directed body satisfies Equation 7), its modeling is successful; otherwise, modeling fails and starts again.
5-2)对所有有向体的总和基于是否满足下式8)来进行块体体积总和检查,以保证块体搜索的完备性:5-2) Check the sum of block volume based on whether the sum of all directed bodies satisfies the following formula 8) to ensure the completeness of block search:
∑iV(Bi)=V(T) 8)∑ i V(B i )=V(T) 8)
上式中:In the above formula:
V(Bi)为第i个有向体Bi的体积,i为大于1的正整数;V(B i ) is the volume of the i-th directed body B i , i is a positive integer greater than 1;
V(T)为待建模的地质块体模型T的体积。V(T) is the volume of the geological block model T to be modeled.
在实际实施时,若所有有向体总和满足式8),则三维建模成功并结束,实现了对整个地质块体模型的三维建模目的,反之,三维建模失败,重新开始。In actual implementation, if the sum of all directed bodies satisfies formula 8), the 3D modeling is successful and ends, and the purpose of 3D modeling of the entire geological block model is realized; otherwise, the 3D modeling fails and starts again.
下面将以图7所示有限元模型为例,来说明本发明的具体实施过程:The following will take the finite element model shown in Figure 7 as an example to illustrate the specific implementation process of the present invention:
图7示出的有限元模型为规则形体的简单地质块体,目的在于阐述本发明实施过程,实际建模中所涉及到的地质块体通常为较复杂的地质块体。The finite element model shown in Fig. 7 is a simple geological block with a regular shape, and its purpose is to illustrate the implementation process of the present invention. The geological blocks involved in actual modeling are usually relatively complex geological blocks.
第一步,假设待建模的地质块体模型为任意空间单连通多面体(凸或凹),其几何描述采用分段线性复合形来表达,具体数据结构包括两部分:一部分是几何信息,以角点空间坐标来表示,如表1所示;另一部分是拓扑信息,以组成模型的各边界面上的封闭环路(按逆时针走向)的点序列来表示,如表2所示。In the first step, it is assumed that the geological block model to be modeled is a simple connected polyhedron (convex or concave) in any space, and its geometric description is expressed by a piecewise linear composite. The specific data structure includes two parts: one part is geometric information, and The space coordinates of the corner points are represented as shown in Table 1; the other part is topological information, which is represented by the point sequence of the closed loop (going counterclockwise) on each boundary surface of the model, as shown in Table 2.
表1待建模的地质块体模型的几何信息Table 1 Geometric information of the geological block model to be modeled
表2待建模的地质块体模型的拓扑信息Table 2 Topological information of the geological block model to be modeled
裂隙面最终修正所采用的多边形参见图8~图10所示。The polygons used in the final correction of the fracture surface are shown in Figures 8 to 10.
第二步,通过边界面与边界面之间、裂隙面与裂隙面之间、边界面与裂隙面之间求交来获取相交线段,即迹线,然后通过迹线之间的求交来获取棱边。The second step is to obtain the intersecting line segment, that is, the trace, by intersecting between the boundary surface and the boundary surface, between the fissure surface and the fissure surface, and between the boundary surface and the fissure surface, and then obtain it by intersecting the traces Edge.
第三步,对棱边进行完正则化处理后得到图11所示结果。在图11、图12a至图12d中,通过圆圈内数字来表示角点编号。In the third step, the results shown in Figure 11 are obtained after regularizing the edges. In Fig. 11, Fig. 12a to Fig. 12d, the numbers of the corner points are indicated by the numbers in the circles.
然后,利用边界算子并根据环路搜索最大右转角准则来进行空间环路搜索,得到若干有向环。图12a至图12d示出了搜索出来的其中四个有向环。Then, the space loop search is carried out by using the boundary operator and according to the maximum right-turn angle criterion of the loop search, and several directed loops are obtained. Figures 12a to 12d show four of the searched directed rings.
然后,判断有向环的属性,其中,图12a、图12b、图12d示出的有向环被判断为内环,图12c示出的有向环被判断为外环。Then, the attributes of the directed rings are judged, wherein the directed rings shown in Fig. 12a, Fig. 12b, and Fig. 12d are judged as inner rings, and the directed rings shown in Fig. 12c are judged as outer rings.
然后,判断内环与外环相互之间的包含关系,从而形成有向面。Then, determine the inclusion relationship between the inner ring and the outer ring to form a directed surface.
第四步,对有向面进行正则化处理。正则化处理后得到的结果可参考图13a来理解。在图13a至图13c中,通过圆圈内数字来表示角点编号。The fourth step is to regularize the directed surface. The results obtained after regularization processing can be understood with reference to Figure 13a. In Fig. 13a to Fig. 13c, the corner point numbers are indicated by the numbers inside the circles.
然后,利用边界算子并根据空间壳搜索最大右转角准则来进行空间壳搜索,得到若干有向壳。图13a至图13c示出了搜索出来的全部三个有向壳(粗实线示出)。Then, the space shell search is carried out by using the boundary operator and according to the maximum right-turn angle criterion of the space shell search, and several directed shells are obtained. Figures 13a to 13c show all three directed shells (indicated by thick solid lines) that are searched.
然后,判断有向壳的属性,图13a至图13c示出的有向壳全部被判断为内壳。从而内壳与外壳相互之间的包含关系判断省略,三个内壳直接形成有向体。Then, the attributes of the directed shells are judged, and the directed shells shown in Fig. 13a to Fig. 13c are all judged as inner shells. Therefore, the determination of the inclusion relationship between the inner shell and the outer shell is omitted, and the three inner shells directly form an directed body.
第五步,对图13a至图13c示出的有向体进行块体拓扑性检查和块体体积总和检查,从而判断出最终搜索得到的三个有向体的准确性和完备性,完成三维建模任务。The fifth step is to perform a block topology check and a block volume sum check on the directed bodies shown in Figures 13a to 13c, so as to judge the accuracy and completeness of the three directed bodies obtained in the final search, and complete the three-dimensional modeling tasks.
表3块体拓扑性检查和块体体积总和检查结果Table 3 Block topology check and block volume sum check results
从上表3可见,最终形成的各有向体通过了块体拓扑性检查和块体体积总和检查,这些有向体可以较好地组合构成图7所示的待建模的地质块体模型,三维建模成功。It can be seen from Table 3 above that the finally formed directed bodies have passed the block topology check and block volume sum check, and these directed bodies can be well combined to form the geological block model to be modeled as shown in Figure 7 , 3D modeling is successful.
本发明从地质块体的拓扑特性——单纯形及单纯复合形的概念出发,将地质块体视为有向复合形,基于闭曲面的拓扑性质,引入必要的正则化处理,利用边界算子并结合相应搜索规则,实现了完全满足完备性和准确性要求的三维块体建模方法,对岩体工程具有重要实践价值,对非连续介质力学数值方法的发展具有积极的理论意义。The present invention starts from the topological characteristics of geological blocks—the concepts of simplex and simplex complex, and regards geological blocks as directed complex shapes. Based on the topological properties of closed surfaces, it introduces necessary regularization processing and uses boundary operators to Combined with the corresponding search rules, a three-dimensional block modeling method that fully meets the requirements of completeness and accuracy is realized, which has important practical value for rock mass engineering and positive theoretical significance for the development of numerical methods for discontinuous medium mechanics.
由于本发明具有坚实的数学理论基础,因此形成的地质块体,特别是复杂地质块体能够满足准确性与完备性要求,这为以离散块体系统为研究对象的非连续介质力学数值分析方法提供了一种正确、便捷的前处理方法,对非连续介质力学数值分析方法的发展起到了促进作用。另外,本发明优点还在于不需引入任何人为假设且完全根据实际地质结构面特点,形成空间任意复杂的地质块体,在工程实践中具有重要的应用价值,特别是在岩体工程中遇到复杂关键块体情况下可以准确产生复杂地质块体的三维模型,对岩体工程加固措施的制定和实施具有重要参考价值。Because the present invention has a solid mathematical theoretical foundation, the formed geological blocks, especially complex geological blocks, can meet the requirements of accuracy and completeness. It provides a correct and convenient pretreatment method, which promotes the development of numerical analysis methods of discontinuous medium mechanics. In addition, the advantage of the present invention is that it does not need to introduce any artificial assumptions and is completely based on the characteristics of the actual geological structural plane to form a geological block with an arbitrary complex space, which has important application value in engineering practice, especially in rock mass engineering. In the case of complex key blocks, the 3D model of complex geological blocks can be accurately generated, which has important reference value for the formulation and implementation of rock mass engineering reinforcement measures.
以上所述是本发明较佳实施例及其所运用的技术原理,对于本领域的技术人员来说,在不背离本发明的精神和范围的情况下,任何基于本发明技术方案基础上的等效变换、简单替换等显而易见的改变,均属于本发明保护范围之内。The above are the preferred embodiments of the present invention and the technical principles used therein. For those skilled in the art, without departing from the spirit and scope of the present invention, any technical solution based on the present invention, etc. Obvious changes such as effective conversion and simple replacement all fall within the protection scope of the present invention.
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