NURBS-based 3D graphical modeling and visualization of geological

NURBS-based 3D Graphical modeling and Visualization of Geological Structures Denghua Zhonga, Mingchao Lia, Gang Wangb, Huang Weia a School of Civil Engineering, Tianjin University, Tianjin 300072, China [email protected], [email protected], [email protected] b Chengdu Hydroelectric Investigation & Design Institute, Chengdu 610072, China [email protected]

Abstract 3D computer modeling and visualization of geological structures is currently a topical research area. Most of common methods to be able to reconstruct 3D geological models require enough raw data and storage space. But in fact the known data sets are discrete and sparse. This paper presents a novel approach to modeling geological structures in 3D with all data from investigations and interpretations. NURBS technique is improved to build the VisualGeo system as 3D geological modeling environment. Following the object-oriented and classified modeling method, all kinds of geological structures could be simulated and the whole 3D geological model was set up systematically by graphical operations and texture mapping. Finally an example was given to display the constructed models and some visualizations of geologic analysis. The successful application and popularization in practice of the system indicate that it will have much applied importance. Keywords: 3D graphic modeling, geological structures, NURBS, visualization

1. Introduction Complex geological structures bring great difficulties to the design and construction of many hydroelectric, underground and geotechnical projects. Graphic representations allow more people to understand a project better. The geologists have gotten used to presenting geologic information by graphics. However, they commonly utilize the traditional ways, which are limit to plans, profile maps or projections [10]. This discontinuous 2D manner has been hard to satisfy the demands of spatial analysis. Then, 3D

geological models will enable them to add graphical visualization to the limit database, and help designers to obtain effective geologic information more easily. The development for computer graphical modeling and visualization of geological structures in 3D is an important research field in recent years. Modeling methods have been proposed in some research publications. For example, DSI method [7], Bézier construction tools [2], volume visualization techniques [8], lag insertion and local reconstruction of faults [12]. Whereas all of these have gained some achievements, there are no perfect tools or easy-to-handle solutions up to now. This is due to the geometric irregularity and discontinuity in geological surfaces and volumes, and insufficient sampling density in 3D modeling [3]. Complex geologic bodies are a kind of special and professional graphic objects [5], so these methods require voluminous information to build models, and are usually restricted by storage capacity and analytical speed. To solve these problems, a new approach is presented for modeling geological structures, which not only constructs 3D models from multi-source data, but also effectively overcomes those limitations in engineering geology, and greatly improves the flexibility in practical modeling. This paper is organized as follows: first, an overview summarizes some aspects of 3D geological modeling and holds up the general framework of our method. Next, is a detailed description of the proposed approach. Those sections are followed by a case study that indicates the practicability of this method. Finally, conclusions are provided.

2. Creating 3D geological models There are two critical problems required to be solved in creating 3D geological models: one is

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determination and disposal of modeling data sources, and another is choosing the modeling method according to data sources and application goal. Generally, the geologic data are discrete and nonuniform in spatial distribution. If the studied region is large-scale, it is not possible to build geological objects just from raw data sets. Then a series of interpreted sections by geologists can be added to improve the structural model towards a more real solution. Therefore, it will be good and necessary to create a geometric model that approximates real geologic bodies from sparse control data and adequate 2D sections in an interpretive environment that combines flexible interpolation functions along with a powerful 2D/3D editing and graphics display engine. After data sources are possessed, the modeling method is a more important problem to be faced. Geometric models in 3D can be broken down into three categories fully from various approaches: surface models, volume models and hybrid models, not excepting geological structures [5]. Surface modeling method is the major way of realizing 3D geological model for practical application, because they have some obvious advantages in the computer implementation and visualization. In engineering geology, geologists analyze reliable information from drills and stulms to extrapolate 3D characters of geological objects through 2D sections. Our solution is illustrated in Figure 1. Here NURBS technique [9] is imported and improved by geologic features to create the reliable 3D geometric models. A prototype modeling system, VisualGeo, is built to realize these processes and construct the complete and photo realistic 3D models, which are easy to edit, modify and analyze interactively in 3D environment.

3. NURBS tool and geological surfaces NURBS are industry standard tools for the representation and design of geometry. In this research, NURBS tool is utilized to model 3D geometric bodies of geological structures. This approach is very efficient, which means lower computational memory requirements and faster data processing. It supports space uniqueness and geometry inalterability for representing geological structures. NURBS tools mathematically represent complex geological structures with smooth continuous curves and surfaces based on only a few control points that can be easily manipulated. For a more detailed discussion on the NURBS technique, the interested reader is referred to references [4, 9, 14]. Then, geological surfaces can be reconstructed easily using NURBS tools. The main steps of realization are as follows: (1) Derive curvilinear vectors of a surface in u, v parametric directions, according to points from drill cores and curves from interpreted sections; (2) Determine control points of each vector by the back-calculating the actual data twice in u, v directions in turn; (3) Fit and construct the NURBS surface by interpolating control points and adjusting the weights; (4) Clip the surface boundary, and shade or render it using the specified colors or textures.

4. Geometric modeling of geological structures The structural bodies of 3D geometric modeling include digital terrain, horizons, overburden layers, veins, faults, interlayer dip-offset belts, and deep fissures. With systematic, object-oriented and class thoughts, these structures can be reduced to terrain class, horizon class including horizons, overburden layers and fault class consisting of faults, veins, dipoffset belts, deep fissures.

4.1. NURBS model of 3D digital terrain

Figure 1. System flow chart of 3D geological modeling and visualization

Terrain is the most visible feature of geologic configurations. 3D Digital Terrain Model (DTM) is the receptor of all operations during the whole reconstruction of geologic bodies. It should have the demands of small memory space, accuracy and easy graphic manipulation. Traditionally both of regular grid models with low precision and triangulated irregular network (TIN) models with large storage [6] can not meet these needs for geological modeling.


NURBS tool can fill the role integrating with TIN model. Based on topographic contours, the algorithm is described as follows: (1) Set up initial contours. If the contours are too sparse, new lines can be added by interpolation. (2) Define TIN model. Based on the established contours, a DTM can be defined in TIN format using Delaunay algorithm provided in GIS [13]. (3) Reconstruct NURBS model. Adequate contours of continuous distribution are extracted from TIN model by given interval. With the collected control information, NURBS model can be generated. This computation procedure was found very efficient. The size of the NURBS model based on the TIN model decreases considerably from a 101 MB level to a 102 KB level. And the accuracy test by checkpoint method [6] shows its accuracy is high enough to come up to the need of geological modeling.

linear and discontinuous. They should be constructed as solids directly because of their small thickness. For a single fault, by drill data and path lines of interpretation map, NURBS surfaces can be performed with 3D extrapolated fault net. If the result is discontinuous, the initial interpretation is required to modify until a satisfying solution. Finally, a fault body can be set up stitching the determined NURBS surfaces. Supposing that there are two interlaced faults, f1 and f2, the construction process may be more complicated: (1) Analyze respective historical origin and determine their precedence relationship. If f1 has misplaced, the formation of f2 should be prior to that of f1. (2) Construct the body of f2, then f1 is divided into two sections to make based on their scatter data, successively. (3) Match together all sections of two faults in space using Boolean operation.

4.2. Structural modeling of horizon class

4.4. Visualization of the geometric model

Bedding surfaces of horizons are important reference planes for researching tectonic deformation and its influence on the engineering design. Although spatial shapes of the horizons are solids geometrically, they can be constructed by set operations between geomorphic profile and separation planes of bed, due to their wide distribution and large thickness. The essential is the modeling for separation plane of bed with their actual structural features. For a single stratal surface, the realization of NURBS structure has been given above. Each body is enclosed by six boundary surfaces of top and bottom, front and back, left and right. In fact, a horizon body is formed by Boolean operations among NURBS surfaces of top, bottom and topographic body. Immediate surfaces of adjacent horizons must be coincident. In general, there are four different connections between adjacent horizons: inclusion, overlay, intersection, and multilayer intersections. It is difficult to match together these immediate surfaces if we make up them through different data of adjacent horizons respectively. A simple method of trimming-overlap is able to sew stratal surfaces of adjacent horizons.

When all kinds of geological structures are simulated using NURBS tool, the whole geological model can be reconstructed by geometric operations. To meet a demand of the visualization, the geometric model should be rendered with different colors or textures. Considering that textures of rock appearance need not be too fine, a special algorithm is adopted here. Namely, true display effects of concavo-convex textures may be created via disturbing normal directions of surfaces [1]. A perturbation function attached to normal directions of the original surface makes smooth and slow changes become acute and brevity, and then the coarse vision of the surface can be seen by illumination.

4.3. Structural modeling of fault class Faults are a kind of the widest geological structures in the lithosphere, and break the continuity of geologic bodies. The join of faults make 3D geological modeling complicated [11]. Mathematically, faults are geometric discontinuities and can be disposed as a hyperlink between both sides of a horizon which are

5. Application We have implemented the proposed methods in Visual C++ 6.0 and the OpenGL graphics library on a PC platform. Geological structures and models in 3D can be reconstructed and edited in the integrated VisualGeo system. We can zoom, move, rotate and strip 3D models, and perform space analysis, space query, and so on. The system has been applied to 3D geological modeling of a large-scale hydropower project in Sichuan, China. Figure 2 exhibits the geological model in the whole region of interest. To understand interior conditions and spatial relationships of geological structures more directly, Figure 3 gives several visualizations of 3D geologic analysis associated with the engineering.


scene. This approach can reduce the amount of computational memory and improve the analytical speed. During the modeling process, the integrated VisualGeo system allows geologists to modify or edit models by an interactive editor on the basis of their experience. All these establish a stable foundation for further development and applications. All together, 3D geological modeling is a challenging topic in geology and it has yet to research into theories and practical applications in depth.

References Figure 2. Example of application in Sichuan, China

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(a) 3D view along dam axis of rock-mass quality classification in dam area

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[7] [8]

[9] [10] (b) Eight digital drills of 30 m diameter

Figure 3. Visualizations of geologic analysis [11]

6. Conclusions 3D geological models have attracted more attention in many fields. The traditional methods are both cumbersome and restrictive. In the approach presented here data from geological exploration and interpretation could be used to build the model and visualize their spatial distributions. NURBS technique and the object-oriented class modeling are designed semi-automatically to build geometric models in a 3D

[12]

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