## 3 Delaunay-TCOGIM Algorithm
### Steps of the Delaunay-TCOGIM Algorithm  
The specific steps of the Delaunay-TCOGIM algorithm are as follows:  
Figure 2: There are four main steps in the Bowyer-Watson algorithm: (**a**) inserting the discrete point p; (**b**) making the outer circle of the triangle containing the point p; (**c**) deleting the contained triangle; and (**d**) connecting the triangle vertices to the point p.  
1. Boundary discretization: The initial input data of the algorithm is a series of point sets obtained by discretizing the boundary edges and contour lines after topographic map recognition. According to the basic idea of the algorithm in this article, in the first one-dimensional mesh division, the mesh boundaries and contour lines are divided into discrete points and line segments and then transformed into boundary nodes, boundary edges, and discrete point sets. The obtained data includes all the necessary mesh data needed for subsequent mesh division. 2. Construct the initial triangle mesh: Based on the preceding mesh data, determine the center point of the target area, the maximum height (y-axis direction), and the maximum width (x-axis direction), multiply the maximum value of the two by a coefficient greater than 1, and then use the center point of the target area as the center and this length as the length of the side of the box to construct a square, the Delaunay box. The coordinates of the box's four vertices serve as the initial nodes of the Delaunay mesh; the rectangle and any diagonal serve as the initial mesh boundary; and the two triangles serve as the initial triangle mesh. 3. Construction of the initial Delaunay mesh: After constructing a sufficiently large enclosing box, the B-W algorithm described in Section II divides the mesh into its initial subdivisions. Use this enclosing box to turn the meshing problem into a convex envelopment problem with discrete points of the curves in the mesh boundary region and the four vertices of the enclosing box. To do this, start the enclosing box as two triangles with divisions at all discrete points. Then, the discrete points are used as insertion points for the B-W algorithm to build the Delaunay triangle. 4. Identify the inner region of the boundary: The Delaunay mesh obtained through the above description is a triangular mesh containing the Delaunay enveloping box. However, the boundary of the delineated region cannot be shown very intuitively in the mesh of the Delaunay enveloping box, and only the triangular mesh of the inner region need to be constructed for practical application. For this problem, we are identifying the region boundaries by using a coloring algorithm to differentiate between the internal and external components of the region [21] and removing the triangles and Delaunay enclosing boxes outside the mesh region. The following steps are the precise sequence of the coloring algorithm: Step 1. Assign v = \(-1\) to each triangle mesh cell. Step 2. Find the triangle mesh cell containing vertices, assign it a color, i.e., v = c (define c = 0), and store it in stack S. Step 3. If stack S is not empty, one of the triangle mesh cell e is taken out of the stack. Step 4. Traverse the three adjacent cells of the triangle mesh cell e for the following reasons: (1) If the value of the visited triangle cell is not \(-1\), then this triangle cell contains colored vertices. Return to Step 4. (2) If the value of the visited triangle cell is \(-1\), proceed directly to Step 5. Step 5. Determine the common edge of the visited triangle cell and cell e using the following method: (1) Assign a color to the visited triangle mesh, i.e., v = c, and store it in stack S if the joint edge of the visited triangle cell and cell e is not a region boundary edge. (2) If the joint edge of the visited triangle cell and cell e is a region boundary edge, proceed to Step 4 to traverse the neighboring cells. Step 6. Make c = c + 1 and clear stack S. If there is still a cell with v = \(-1\), proceed to Step 3. Otherwise, exit. The value of c is the number of region components.