Contour refers to the curve formed by adjacent points of equal height on a surface. Contour mode is a traditional form of geological surface expression. Before the emergence of computers, the geoscience community had always expressed geoscience surfaces using contours. The drawing method of expressing mountains with closed Contour line appeared on the Fangmatan wooden board map unearthed in Tianshui, Gansu Province at the end of the Warring States Period (239 BC) and on the silk Topographic map unearthed in Mawangdui, Changsha City at the Western Han Dynasty (186 BC) [17] [18] . However, this painting method has not been passed down and promoted. In 1728, Krucky of the Netherlands first used the isobath method to represent the depth and bed condition of rivers, and later applied it to represent the depth of the sea; In 1791, DuPontriel in France drew the first contour map; Subsequently, contour lines gradually began to be used in surveying topographic maps. The contour mapping method is a revolution in geological mapping. From then on, people can express the three-dimensional morphology of natural surfaces such as terrain, stratigraphic interfaces, and fault planes in a precise and measurable manner on a 2D map, as shown in Figure 1. Geological engineers can modify the shape of surfaces by modifying the shape of contour lines. So, it has unique advantages in coal exploration mapping. The contour drawing method also has some drawbacks, that is, when the surface is upright, the contour lines overlap with each other, and when the surface is inverted from positive to negative, the contour lines intersect with each other chaos. In a computer 3D drawing environment, although people can “see” the 3D shape of a surface by drawing 3D contour curves, it does not have the feeling of “surface continuity” and cannot achieve “color gradients” effect, as shown in Figure 2. Therefore, in the context of computer 3D geological modeling, the contour representation method ultimately gives way to the TIN method.

After the 1960s, computers began to be used for graphic display and rendering. People had found that the most effective way to display a 3D surface with a computer is to discretize the surface into many small triangle flat patches for display. The surface is represented by a collection of many small triangular flat patches embedded in an irregular triangular network. When displaying surfaces on a computer, setting different colors for the vertices of each small triangular

patch based on their elevation can achieve the color gradien effect, making people’s “feeling” of the 3D shape of the surface more realistic. TIN has the advantages that neither contour nor regular rectangular grid has. Therefore, TIN is the standard expression of free surface in computer graphics, 3D geographic information system and 3D geological modeling.

In the field of surveying and geographic information, it is generally believed that DEM is the abbreviation of Digital Elevation Model. The digital elevation model is a digital simulation of geospatial surfaces such as the ground, by limited terrain elevation data (i.e. the digital expression of terrain surface morphology) [19] . According to the definition, digital elevation models should not only include regular square grid network, but also include contour and TIN. The essence of the grid network method is to represent the elevation of a surface in the form of an ordered numerical array. The DEM data provided by the surveying and mapping industry is a digital elevation matrix data of a certain resolution. So, DEM, as an abbreviation for Digital Elevation Matrix, is more appropriate. DEM data is a type of grid data in which data points are equidistant in the abscissa and ordinate directions. It is not necessary to record the horizontal coordinates of each grid point, but only one point horizontal coordinate of lower left corner (or upper left corner) and the grid spacing in abscissa and ordinate direction. It is easy to calculate the abscissa and ordinate coordinates of each grid point. So, for every grid point only needs to record its elevation. For data points without elevation values, use −9999 instead. Dividing each rectangular grid of DEM data into two isosceles triangles along the diagonal, and then it can be converted into regular TIN data. The regular TIN is a special case of irregular TIN. DEM is suitable for expressing geological surfaces with huge amounts of data such as terrain, but it is not suitable for expressing geological surfaces that may appear nearly upright or inverted.

The fitting steps are: 1) obtaining the elevation from the endpoint of the contour line started or ended at the fault line, as shown in Figure 4; 2) Fit a 3D spline curve using these intersection points which obtained elevation from contour; 3) Assign elevations to other knots of the fault line based on the fitted 3D spline

curve. The more endpoints the contour line intersects with the fault line, the more accurate the fitted fault line elevation is.

In some cases, a fault line may not have been encountered any contour line, so another method should be used, which is to first triangulate based on the contour lines of the coal seam floor as the limiting line, and fit a rough reference surface—“refer-surface”. Since the fault line, the boundary line of the collapse column, and the boundary line of the coal free area are not used to build “refer-surface”, the fitted “refer-surface” is very rough. But, with this “refer-surface” as a reference, the elevation of each knot the fault line can be calculated by horizontal abscissa and ordinate coordinates of the knots.

The elevation accuracy of fault line which obtained by the first two methods may not be satisfactory and require editing, as shown in Figure 5. It can be modified in 3D environment, by generating a vertical profile that curves along the fault lines, then move the knots in the vertical profile, where knots only can move in vertical direction, can not move in horizontal direction, as shown in Figure 6.

Although it is possible to modify the elevation of a fault line in the 3D environment, its operation is not convenient enough, and people are still more accustomed to editing 3D curves in a 2D environment. So, another method is to project the 3D curved vertical profile onto a 2D vertical section. It is a reverse operation to translate 2D profile to 3D profile [11] . Modifying the elevation of knots of the fault line on the 2D section and then mapping the modifying into the 3D profile.

By comprehensively applying the above four methods, the fault line can be obtained basically satisfactory elevation accuracy. The accuracy of 3D modeling requires continuous iteration to approach accuracy. After the following semi-automatic partition triangulation, the step 2) “refer-surface” should be replaced by the partition triangulation surface. Then recalculating the elevation of each node on the intersection line of the sections will improve the modeling accuracy has been improved.

Users need to determine in advance how many partitions the entire area needs to be divided into based on the cutting situation of faults, collapsed column boundary lines and coal free boundary lines. Each partition is a surface patch, which is boundared by a ring consisted of fault line, collaped column boundary line and coal free zone boundary line. Then, for each partition, the user clicks to select the line features (including fault line, collapsed column boundary line, coal free boundary line, and the boundary line of the work area) consisted of the partition boundary ring. When clicking in anticlockwise order, the software will automatically cut and connect the line feature, and finally form the boundary ring of the surface patch. When clicked, select one layer at a time as an editable layer (note: not to edit or modify this layer here, but only to set the layer in the editing state as the selected layer), forming a closed boundary ring, as shown in Figure 7.

After the partition boundary ring is closed, the line features that fall into the partition boundary ring should be treated as limiting lines (as shown in Figure 8) or limiting rings in triagulation procedure.

The software will scans and identifies whether the fault line ring formed by the fault lines that fallen into the partition boundary ring is a normal fault ring or a reverse fault ring, and then treated separately.

A fault ring is formed by closing the fault lines on the upper and lower walls of a same fault. The algorithm for generating a fault ring from the fault line is as follows: 1) Scan all fault lines, record all the fault lines that fall into the boundary ring of the patch, and generate a set of fault lines to be matched; 2) Check the set of the fault lines one by one, match each fault line with all other fault line in the set. If one endpoint meets, check the other endpoint; If the other end also coincides, the intersection line connecting these two sections in a clockwise direction forms a fault ring; If the two endpoints on the other end do not coincide, check whether the other end of the intersection line of the two sections intersects with the patch boundary ring. If so, connecting the intersection line of these two sections clockwise with the intersecting boundary segment to form a fault ring. 3) For each fault ring formed, the two fault lines are removed from the set of intersection lines.

Based on whether exist contour lines of the coal seam floor between the fault rings, it can be determinated that the fault ring is a normal fault ring or a reverse fault ring. If exist one or more contour line in the fault ring, it indicates that the fault ring area is a duplicate area of coal seams, and the fault is a reverse fault (Figure 9, left); If not, it is a normal fault (Figure 9, right).

The interior of the normal fault ring is a blank area with missing coal seams, so triangulation is relatively simple. The processing of normal fault ring is to organize the sampling point of the normal fault ring in a clockwise direction as a inner boundary ring in triangulation. As shown in Figure 10.

The treatment method for boundary rings of collapsed columns and coal free areas is the same as that for normal fault rings.

The processing algorithm of reverse fault rings is very complex, it will be discussed detailly in next Chapter 5.

Firstly, an outer expanding ring is generated by off reverse fault ring a distance, such as 10 meters. The procedure is shown as Figure 11.

The outer expanding ring separates the reverse fault area from other part of the patch which is normal area without the duplicate area. For the normal area, it can be triangulation normally, as shown in Figure 12.

The duplicate area will be divided to two side, left side and right side. The two sides left side and right side all are contain diclicasd area. Left side and right side can be triangulated severally. As shown in Figure 13, Figure 14.

Remove the outer ring of the duplicate area and non original data with topological adjacency, locally reconstruct the triangular network, and generate the final set of research area triangular networks. As shown in Figure 15

Using the contour line’s own range as the outer boundary, Delaunay triangulation is carried out internally. Observing the results of the triangulation, the triangulated triangles can be divided into three types: Type I, where two edges in the triangle are constraint edges, that is, two edges are on the contour line; Type II, in a triangle, one edge is a constraint edge, that is, only one edge is on the contour line; Class III, unconstrained edges in a triangle, meaning that all three edges of the triangle are not on the contour line, as shown in Figure 16.

In the constructed Delaunay triangulation network, for type I triangles, the midpoint of the unconstrained edge in the triangle is connected to the triangle vertex relative to the unconstrained edge; For type II triangles, the midpoint of the two unconstrained edges of the triangle is connected; For type III triangles, the midpoint of the three sides of the triangle and the center of gravity of the triangle are connected. Finally, connect these connected line segments according to a certain topological relationship to form a whole, which is the desired central axis, as shown in Figure 17.

Add the extracted geolines in Figure 17 as constraints and reconstruct the triangulation network, as shown in Figure 18. Extracting geolines and using them as constraint lines will make the surface triangulation network more optimized.

The construction method of stratigraphic body is to use the boundary rings of the top interface and bottom interfaces of the stratigraphic body for constrained triangulation, forming a triangular network of the lateral torus of the stratigraphic body, as shown in Figure 21. After coloring the lateral torus, it is shown in Figure 22. After closed top, bottom, and side torus surfaces, it is shown in Figure 23.

Generally, there is no contour map of coal seam roof in the geological report of coal field exploration, but a contour map of coal seam thickness is provided, and there is basically no fault information on the contour map of coal seam thickness. Therefore, for the construction of coal seam body, the zoning boundary of the

coal seam floor surface can be used to overlay the coal seam thickness as the coal seam roof surface, and then the construction method is the same as that of the stratum body. The bifurcation, merger and pinch out expression of coal seams are the most important in the construction of coal seams 3D modelling [14] .