qt复杂多边形的三角剖分

Qt中可以使用QPolygonF类表示多边形，但是Qt并没有提供直接的多边形三角剖分的函数。不过可以使用第三方库来进行剖分。

以下是使用Triangle库进行多边形三角剖分的步骤：

1. 下载Triangle库，并将其添加到Qt项目中。

2. 将QPolygonF转换为Triangle库支持的数据格式。Triangle库支持的数据格式是一个简单的结构体，包含点的坐标和一个标记（这里不需要）。

struct triangulateio
{
    double *pointlist;
    int *pointmarkerlist;
    int *pointattributelist;
    int numberofpoints;
    int numberofpointattributes;
    double *segmentlist;
    int *segmentmarkerlist;
    int numberofsegments;
    double *holelist;
    int numberofholes;
    int *regionlist;
    int numberofregions;
    int *edgelist;
    int *edgemarkerlist;
    double *normlist;
    int numberofedges;
};

triangulateio in, out;
memset(&in, 0, sizeof(triangulateio));
memset(&out, 0, sizeof(triangulateio));

// 设置输入点的数量和坐标
in.numberofpoints = polygon.size();
in.pointlist = (double*)malloc(in.numberofpoints * 2 * sizeof(double));
for (int i = 0; i < in.numberofpoints; ++i)
{
    in.pointlist[i * 2] = polygon[i].x();
    in.pointlist[i * 2 + 1] = polygon[i].y();
}

// 设置输入线段的数量和顶点索引
in.numberofsegments = polygon.size();
in.segmentlist = (double*)malloc(in.numberofsegments * 2 * sizeof(double));
for (int i = 0; i < in.numberofsegments; ++i)
{
    in.segmentlist[i * 2] = i;
    in.segmentlist[i * 2 + 1] = (i + 1) % polygon.size();
}

3. 调用Triangle库的函数进行三角剖分。

char options[] = "pQ";
triangulate(options, &in, &out, nullptr);

4. 将剖分结果转换为Qt中的数据格式。

QPolygonF triangles;
for (int i = 0; i < out.numberoftriangles; ++i)
{
    int i1 = out.trianglelist[i * 3];
    int i2 = out.trianglelist[i * 3 + 1];
    int i3 = out.trianglelist[i * 3 + 2];

    QPointF p1(out.pointlist[i1 * 2], out.pointlist[i1 * 2 + 1]);
    QPointF p2(out.pointlist[i2 * 2], out.pointlist[i2 * 2 + 1]);
    QPointF p3(out.pointlist[i3 * 2], out.pointlist[i3 * 2 + 1]);

    triangles << p1 << p2 << p3;
}

完整代码如下：

#include <QApplication>
#include <QPolygonF>
#include <QDebug>

#include "triangle.h"

int main(int argc, char *argv[])
{
    QApplication a(argc, argv);

    // 定义一个多边形
    QPolygonF polygon;
    polygon << QPointF(0, 0) << QPointF(100, 0) << QPointF(150, 50)
            << QPointF(100, 100) << QPointF(0, 100);

    // 将多边形转换为Triangle库支持的数据格式
    triangulateio in, out;
    memset(&in, 0, sizeof(triangulateio));
    memset(&out, 0, sizeof(triangulateio));

    // 设置输入点的数量和坐标
    in.numberofpoints = polygon.size();
    in.pointlist = (double*)malloc(in.numberofpoints * 2 * sizeof(double));
    for (int i = 0; i < in.numberofpoints; ++i)
    {
        in.pointlist[i * 2] = polygon[i].x();
        in.pointlist[i * 2 + 1] = polygon[i].y();
    }

    // 设置输入线段的数量和顶点索引
    in.numberofsegments = polygon.size();
    in.segmentlist = (double*)malloc(in.numberofsegments * 2 * sizeof(double));
    for (int i = 0; i < in.numberofsegments; ++i)
    {
        in.segmentlist[i * 2] = i;
        in.segmentlist[i * 2 + 1] = (i + 1) % polygon.size();
    }

    // 调用Triangle库的函数进行三角剖分
    char options[] = "pQ";
    triangulate(options, &in, &out, nullptr);

    // 将剖分结果转换为Qt中的数据格式
    QPolygonF triangles;
    for (int i = 0; i < out.numberoftriangles; ++i)
    {
        int i1 = out.trianglelist[i * 3];
        int i2 = out.trianglelist[i * 3 + 1];
        int i3 = out.trianglelist[i * 3 + 2];

        QPointF p1(out.pointlist[i1 * 2], out.pointlist[i1 * 2 + 1]);
        QPointF p2(out.pointlist[i2 * 2], out.pointlist[i2 * 2 + 1]);
        QPointF p3(out.pointlist[i3 * 2], out.pointlist[i3 * 2 + 1]);

        triangles << p1 << p2 << p3;
    }

    // 输出三角形数量
    qDebug() << "Number of triangles:" << out.numberoftriangles;

    return a.exec();
}