🚀概述
在GIS（地理信息科学）中，地形有两种表达方式，一种是格网DEM，一种是不规则三角网TIN。一般情况下规则格网DEM用的比较多，因为可以将高程当作像素，将其存储为图片类型的数据（例如.tif）。但是规则格网存储的数据量大，按规则取点，并不能最大程度的保证地形特征，所以很多情况下需要将其表达为不规则三角网，也就是TIN。
🌈详论
1️⃣数据准备
下载SRTM30的DEM数据，找到美国大峡谷附近的地形，通过UTM投影，将其转换成30米的平面坐标的DEM（.tif格式）。通过Global Mapper打开，显示的效果如下：
2️⃣转换算法
格网DEM本身也可以看作是一个三角网，每个方格由两个三角形组成，N个方格据组成了一个地形格网。所以在参考文献一中提到了一种保留重要点法，将格网DEM中认为不重要的点去除掉，剩下的点构建成不规则三角网即可。那么怎么直到有的点重要，有的点不重要呢？参考文献一中提到了一种约束：
可以看到这类似于图像处理中的滤波操作，通过比较每个高程点与周围的平均高差，如果大于一个阈值，则为重要点，否则为不重要点。其中的关键点就是求空间点与直线的距离，具体算法可参看这篇文章《空间点与直线距离算法》。
3️⃣TIN构建
经过保留重要点法过滤之后，剩下的点就要进行构网了。一般来说最好构建成Delaunay三角网（因为Delaunay三角网具有很多最优特性）。Delaunay三角网的构建算法也挺复杂，不过可以通过计算几何算法库CGAL来构建。
查阅CGAL的文档，发现CGAL居然已经有了GIS专题，里面有许多与地形处理相关的示例。其中一个示例就是通过点集生成了Delaunay三角网，并且生成了.ply文件。.ply文件正好是一种三维数据格式，能够被很多三维软件打开。
4️⃣具体实现
解决了两个关键算法，具体实现就很简单了：引入GDAL数据来处理地形数据（.tif），遍历每个像素点（高程点）做滤波操作，通过CGAL来构建TIN：
#include <iostream>#include <string>#include <Vec3.hpp>#include <threeCGAL.h>#include <gdal_priv.h>#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>#include <CGAL/Projection_traits_xy_3.h>#include <CGAL/Delaunay_triangulation_2.h>#include <CGAL/Triangulation_vertex_base_with_info_2.h>#include <CGAL/Triangulation_face_base_with_info_2.h>#include <CGAL/boost/graph/graph_traits_Delaunay_triangulation_2.h>#include <CGAL/boost/graph/copy_face_graph.h>#include <CGAL/Point_set_3.h>#include <CGAL/Surface_mesh.h>#include <CGAL/Polygon_mesh_processing/border.h>#include <CGAL/Polygon_mesh_processing/remesh.h>using Kernel = CGAL::Exact_predicates_inexact_constructions_kernel;using Projection_traits = CGAL::Projection_traits_xy_3<Kernel>;using Point_2 = Kernel::Point_2;using Point_3 = Kernel::Point_3;using Segment_3 = Kernel::Segment_3;// Triangulated Irregular Networkusing TIN = CGAL::Delaunay_triangulation_2<Projection_traits>;using namespace std;int main(int argc, char *argv[]){GDALAllRegister();string demPath = "D:/Work/DEM2TIN/DEM.tif";string tinPath = "D:/Work/DEM2TIN/Tin.ply";GDALDataset* img = (GDALDataset *)GDALOpen(demPath.c_str(), GA_ReadOnly);if (!img){cout << "Can't Open Image!" << endl;return 1;}int imgWidth = img->GetRasterXSize();//图像宽度int imgHeight = img->GetRasterYSize();//图像高度int bandNum = img->GetRasterCount();//波段数//int depth = GDALGetDataTypeSize(img->GetRasterBand(1)->GetRasterDataType()) / 8;//图像深度int depth = sizeof(float);//图像深度double padfTransform[6];img->GetGeoTransform(padfTransform);double dx = padfTransform[1];double startx = padfTransform[0] + 0.5 * dx;double dy = -padfTransform[5];double starty = padfTransform[3] - imgHeight * dy + 0.5 * dy;//申请bufint bufWidth = imgWidth;int bufHeight = imgHeight;size_t imgBufNum = (size_t)bufWidth * bufHeight * bandNum;size_t imgBufOffset = (size_t)bufWidth * (bufHeight - 1) * bandNum;float *pblock = new float[imgBufNum];//读取img->RasterIO(GF_Read, 0, 0, bufWidth, bufHeight, pblock + imgBufOffset, bufWidth, bufHeight,GDT_Float32, bandNum, nullptr, bandNum*depth, -bufWidth * bandNum*depth, depth);CGAL::Point_set_3<Point_3> points;double zThreshold = 5;//for (int yi = 0; yi < imgHeight; yi++){for (int xi = 0; xi < imgWidth; xi++){//将四个角点的约束加入，保证与DEM范围一致if ((xi == 0 && yi == 0) || (xi == imgWidth - 1 && yi == 0) ||(xi == imgWidth - 1 && yi == imgHeight - 1) || (xi == 0 && yi == imgHeight - 1)){double gx1 = startx + dx * xi;double gy1 = starty + dy * yi;size_t m11 = (size_t)(imgWidth)* yi + xi;tinyCG::Vec3d P(gx1, gy1, pblock[m11]);points.insert(Point_3(P.x(), P.y(), P.z()));}else{double gx0 = startx + dx * (xi - 1);double gy0 = starty + dy * (yi - 1);double gx1 = startx + dx * xi;double gy1 = starty + dy * yi;double gx2 = startx + dx * (xi + 1);double gy2 = starty + dy * (yi + 1);size_t m00 = (size_t)imgWidth * (yi - 1) + xi - 1;size_t m01 = (size_t)imgWidth * (yi - 1) + xi;size_t m02 = (size_t)imgWidth * (yi - 1) + xi + 1;size_t m10 = (size_t)imgWidth* yi + xi - 1;size_t m11 = (size_t)imgWidth* yi + xi;size_t m12 = (size_t)imgWidth* yi + xi + 1;size_t m20 = (size_t)imgWidth * (yi + 1) + xi - 1;size_t m21 = (size_t)imgWidth * (yi + 1) + xi;size_t m22 = (size_t)imgWidth * (yi + 1) + xi + 1;tinyCG::Vec3d P(gx1, gy1, pblock[m11]);double zMeanDistance = 0;int counter = 0;if(m00 < imgBufNum && m22 < imgBufNum){tinyCG::Vec3d A(gx0, gy0, pblock[m00]);tinyCG::Vec3d E(gx2, gy2, pblock[m22]);zMeanDistance = zMeanDistance + tinyCG::threeCGAL::CalDistancePointAndLine(P, A, E);counter++;}if (m02 < imgBufNum && m20 < imgBufNum){tinyCG::Vec3d C(gx2, gy0, pblock[m02]);tinyCG::Vec3d G(gx0, gy2, pblock[m20]);zMeanDistance = zMeanDistance + tinyCG::threeCGAL::CalDistancePointAndLine(P, C, G);counter++;}if (m01 < imgBufNum && m21 < imgBufNum){tinyCG::Vec3d B(gx1, gy0, pblock[m01]);tinyCG::Vec3d F(gx1, gy2, pblock[m21]);zMeanDistance = zMeanDistance + tinyCG::threeCGAL::CalDistancePointAndLine(P, B, F);counter++;}if (m12 < imgBufNum && m10 < imgBufNum){tinyCG::Vec3d D(gx2, gy1, pblock[m12]);tinyCG::Vec3d H(gx0, gy1, pblock[m10]);zMeanDistance = zMeanDistance + tinyCG::threeCGAL::CalDistancePointAndLine(P, D, H);counter++;}zMeanDistance = zMeanDistance / counter;if (zMeanDistance > zThreshold){points.insert(Point_3(P.x(), P.y(), P.z()));}}}}delete[] pblock;pblock = nullptr;GDALClose(img);// Create DSMTIN dsm (points.points().begin(), points.points().end());using Mesh = CGAL::Surface_mesh<Point_3>;Mesh dsm_mesh;CGAL::copy_face_graph (dsm, dsm_mesh);std::ofstream dsm_ofile (tinPath, std::ios_base::binary);CGAL::set_binary_mode (dsm_ofile);CGAL::write_ply (dsm_ofile, dsm_mesh);dsm_ofile.close();return 0;}
5️⃣实验结果
将最终生成的三维模型文件.ply通过MeshLab打开，渲染效果如下：
通过Global Mapper还可以看到具体的三角构网效果：
📚参考
DEM模型之间的相互转换代码地址1
代码地址2 提取码:x0wt
