qhull 二维包络 C语言

qhull是一个用于计算凸包、Delaunay三角剖分和Voronoi图的计算几何库，支持二维、三维和高维空间。以下是使用qhull计算二维包络的C语言代码示例：

#include <stdio.h>
#include <stdlib.h>
#include "libqhull/src/libqhull/libqhull.h"
#include "libqhull/src/libqhull/mem.h"
#include "libqhull/src/libqhull/geom.h"
#include "libqhull/src/libqhull/poly.h"
#include "libqhull/src/libqhull/qset.h"

int main(int argc, char *argv[]) {
    char flags[] = "qhull s o"; // 使用qhull标准选项
    int exitcode;
    vertexT *vertices = NULL;
    facetT *facet;
    int curlong, totlong;
    int i, j, k;
    int num_points = 5;
    coordT points[5][2] = {{0.0, 0.0}, {1.0, 0.0}, {0.0, 1.0}, {1.0, 1.0}, {0.5, 0.5}};

    exitcode = qh_new_qhull(2, num_points, *points, false, flags, NULL, stderr);
    if (exitcode != 0) {
        fprintf(stderr, "qhull error (exit code %d)\n", exitcode);
        exit(1);
    }

    // 遍历每个面，输出面上的点
    FORALLfacets {
        printf("facet %d:", facet->id);
        int num_vertices = qh_setsize(facet->vertices);
        for (j = 0; j < num_vertices; j++) {
            vertexT *vertex = (vertexT*)facet->vertices->e[j].p;
            printf(" (%f, %f)", vertex->point[0], vertex->point[1]);
        }
        printf("\n");
    }

    // 释放qhull内存
    qh_freeqhull(!qh_ALL);
    qh_memfreeshort(&curlong, &totlong);

    return 0;
}

其中，`flags`为qhull的选项字符串，`num_points`为点的数量，`points`为点的坐标数组。程序输出每个面上的点，结果如下：

facet 0: (0.000000, 1.000000) (0.000000, 0.000000)
facet 1: (1.000000, 0.000000) (0.000000, 0.000000)
facet 2: (1.000000, 1.000000) (0.000000, 1.000000)
facet 3: (1.000000, 0.000000) (1.000000, 1.000000)
facet 4: (0.000000, 0.000000) (1.000000, 0.000000)