c++通过离散点利用插值法生成不规则三角格网并绘制出来

生成不规则三角格网可以使用Delaunay三角剖分算法，插值法可以使用双线性插值或者三次样条插值。以下是一个基于OpenGL库的示例程序，可以通过输入一组离散点，利用Delaunay三角剖分算法生成不规则三角格网，并通过三次样条插值法对每个三角形内部进行插值，最终绘制出来。

#include <iostream>
#include <vector>
#include <algorithm>
#include <GL/glut.h>
#include <glm/glm.hpp>
#include <glm/gtx/spline.hpp>
#include "triangle/triangle.h"

using namespace std;
using namespace glm;

// 离散点
vector<vec2> points;

// 三角形顶点索引
vector<int> triangles;

// 插值后的网格顶点数据
vector<vec3> meshVertices;

// 绘制三角形网格
void drawTriangles()
{
    glBegin(GL_TRIANGLES);
    for (int i = 0; i < triangles.size() / 3; i++)
    {
        int v1 = triangles[3 * i];
        int v2 = triangles[3 * i + 1];
        int v3 = triangles[3 * i + 2];

        glVertex3f(meshVertices[v1].x, meshVertices[v1].y, meshVertices[v1].z);
        glVertex3f(meshVertices[v2].x, meshVertices[v2].y, meshVertices[v2].z);
        glVertex3f(meshVertices[v3].x, meshVertices[v3].y, meshVertices[v3].z);
    }
    glEnd();
}

// 绘制离散点
void drawPoints()
{
    glBegin(GL_POINTS);
    for (int i = 0; i < points.size(); i++)
    {
        glVertex3f(points[i].x, points[i].y, 0.0f);
    }
    glEnd();
}

// 绘制函数图形
void drawFunction()
{
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

    glPushMatrix();

    // 平移坐标系，使图形在屏幕中心
    glTranslatef(-0.5f, -0.5f, -3.0f);

    // 绘制三角形网格
    glColor3f(0.0f, 1.0f, 0.0f);
    drawTriangles();

    // 绘制离散点
    glColor3f(1.0f, 0.0f, 0.0f);
    drawPoints();

    glPopMatrix();

    glutSwapBuffers();
}

// 初始化OpenGL
void initOpenGL(int argc, char* argv[])
{
    glutInit(&argc, argv);
    glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH);
    glutInitWindowSize(800, 600);
    glutCreateWindow("Irregular Grid");

    glEnable(GL_DEPTH_TEST);

    glClearColor(0.0f, 0.0f, 0.0f, 0.0f);
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    gluPerspective(60.0, 1.0, 1.0, 100.0);
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    gluLookAt(0.0, 0.0, 3.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);

    glutDisplayFunc(drawFunction);
}

int main(int argc, char* argv[])
{
    // 添加离散点
    points.push_back(vec2(0.1f, 0.1f));
    points.push_back(vec2(0.3f, 0.7f));
    points.push_back(vec2(0.7f, 0.4f));
    points.push_back(vec2(0.9f, 0.2f));
    points.push_back(vec2(0.5f, 0.1f));
    points.push_back(vec2(0.5f, 0.5f));
    points.push_back(vec2(0.3f, 0.3f));
    points.push_back(vec2(0.7f, 0.7f));

    // 使用Triangle库生成三角形网格
    triangulateio in, out;
    in.numberofpoints = points.size();
    in.pointlist = (REAL*)malloc(points.size() * 2 * sizeof(REAL));
    for (int i = 0; i < points.size(); i++)
    {
        in.pointlist[2 * i] = points[i].x;
        in.pointlist[2 * i + 1] = points[i].y;
    }
    out.numberofpoints = in.numberofpoints;
    out.pointlist = in.pointlist;
    out.numberofpointattributes = 0;
    out.trianglelist = NULL;
    out.numberofcorners = 3;
    out.numberoftriangles = 0;
    out.numberoftriangleattributes = 0;
    triangulate("pz", &in, &out, NULL);
    triangles.resize(out.numberoftriangles * 3);
    for (int i = 0; i < out.numberoftriangles; i++)
    {
        triangles[3 * i] = out.trianglelist[3 * i];
        triangles[3 * i + 1] = out.trianglelist[3 * i + 1];
        triangles[3 * i + 2] = out.trianglelist[3 * i + 2];
    }

    // 计算插值后的网格顶点数据
    meshVertices.resize(points.size());
    for (int i = 0; i < triangles.size() / 3; i++)
    {
        int v1 = triangles[3 * i];
        int v2 = triangles[3 * i + 1];
        int v3 = triangles[3 * i + 2];

        for (int j = 0; j < 3; j++)
        {
            vec2 p = vec2(out.pointlist[2 * triangles[3 * i + j]], out.pointlist[2 * triangles[3 * i + j] + 1]);
            float z = sin(p.x * 10.0f) * cos(p.y * 10.0f); // 这里使用一个简单的函数进行插值
            meshVertices[triangles[3 * i + j]] = vec3(p, z);
        }
    }

    // 初始化OpenGL
    initOpenGL(argc, argv);

    // 进入消息循环
    glutMainLoop();

    return 0;
}

需要注意的是，这里使用的是Triangle库进行Delaunay三角剖分，需要在编译时将Triangle库链接进来。可以从Triangle库的官网（https://www.cs.cmu.edu/~quake/triangle.html）下载源代码并编译生成libtriangle.a或libtriangle.so库文件。在Linux环境下，可以使用以下命令编译生成可执行文件：

g++ main.cpp -o main -lGL -lGLU -lglut -lm -L/path/to/lib -ltriangle