Research On Mesh Generation And Surface Reconstruction For Complex Models

Discretization is the basis of numerical calculation for the study area,and grid generation technology is an important way to discretize the study area,which has many applications in numerical simulation,computer graphics and other fields.At the same time,mesh generation can also be used as the expression of surface reconstruction and the basis of surface interpolation and fitting.As an important link of reverse engineering,surface reconstruction has a wide range of applications in the fields of medical imaging,cultural relic restoration,aerospace equipment and so on.In the face of the modeling problem of single feature,the conventional methods of mesh generation and surface reconstruction can express it well.However,the existing mesh generation and surface reconstruction methods are difficult to accurately express the features of geological models when facing complex geological models.The reason is that the cost of acquiring geological data in the process of geological exploration is very high,so the quantity of acquired data is sparse and the distribution is irregular.In addition,there are many characteristics and constraints on the target geological surface,which increase the difficulty of mesh generation and surface reconstruction in complex geological model.In order to solve the above problems,the main work content and innovation points completed in this thesis are as follows:1.This thesis proposes a trend grid generation method,which can be used to diffuse the sparse seed points along the trend direction,so that the interpolated data have better geological trend characteristics.When the target geological surface contains multiple geological trends and the original data is too sparse,the method in this thesis can solve the problem that the existing mesh interpolation method cannot take into account every trend and the trend characteristics obtained do not conform to the geological law.2.Based on the existing methods,this thesis develops a stable minimum curvature meshing method with tension,and meanwhile deals with the fault constraint processing method in surface reconstruction.In the engineering application of geological surface reconstruction,there are many geological features such as faults besides sparse data.For the reconstruction of the surface can not only adjust the fitting degree,also can effectively deal with constraint region,based on the existing stable minimum curvature grid method,presents a stable through the mathematical deduction of belt tension minimum curvature difference iterative format,complete algorithm optimization,targeted treatment fault constraint region at the same time,the reconstruction of fault surface more effective expression constraint area.3.In this thesis,the trend grid generation method and the minimum curvature surface reconstruction method with stable tension are integrated into the existing software system with basic functions.In addition to the above algorithms,the system can also carry out basic human-computer interaction operation.At present,the integrated algorithm has been successfully applied to the geological data processing software of cooperative research institutions.Summary of work: Based on the traditional grid generation idea,this thesis proposes a trend grid generation method which can effectively express the characteristics of geological trends and publishes the corresponding patent.Based on the existing surface reconstruction methods,a stable minimum curvature differential iterative scheme with tension is developed,and the virtual point method is used to effectively deal with the constraints of geological faults.Finally,the method proposed in this thesis is integrated into the software system of cooperative institutions and applied.