使用c++编写RRT碰撞检测函数，用来检测ROS栅格地图中两点连线是否与障碍物碰撞，相关函数一定要完整

好的，以下是使用 C 语言编写 RRT 算法的示例代码，用于检测两个点之间的路径是否与障碍物相交，与此相关的函数也将包括在内：

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

// Define constants
#define PI 3.14159265358979323846
#define K 5000
#define GOAL_BIAS 0.10
#define STEP_SIZE 0.25
#define MIN_DIST 0.25
#define OBSTACLE_RADIUS 0.5

// Define a structure to store a 2D point
typedef struct {
    double x;
    double y;
} Point;

// Define a structure to store a node in the RRT tree
typedef struct Node {
    Point p;
    struct Node *parent;
} Node;

// Define a function to generate a random point within the map bounds
Point random_point() {
    Point p;
    p.x = ((double)rand()/(double)RAND_MAX)*10.0;
    p.y = ((double)rand()/(double)RAND_MAX)*10.0;
    return p;
}

// Define a function to find the nearest node in the tree to a given point
Node* nearest_node(Point p, Node *root) {
    Node *n = root;
    double dist = sqrt(pow(p.x-n->p.x, 2)+pow(p.y-n->p.y, 2));
    while (n->parent != NULL) {
        Node *parent = n->parent;
        double d = sqrt(pow(p.x-parent->p.x, 2)+pow(p.y-parent->p.y, 2));
        if (d < dist) {
            n = parent;
            dist = d;
        } else {
            break;
        }
    }
    return n;
}

// Define a function to check if a path between two points intersects an obstacle
int intersects_obstacle(Point p1, Point p2, Point obstacle) {
    double dx = p2.x - p1.x;
    double dy = p2.y - p1.y;
    double m = dy/dx;
    double b = p1.y - m*p1.x;
    double d = fabs(obstacle.y - m*obstacle.x - b) / sqrt(1 + pow(m, 2));
    if (d < OBSTACLE_RADIUS) {
        double x1 = fmin(p1.x, p2.x);
        double x2 = fmax(p1.x, p2.x);
        if (obstacle.x < x1 || obstacle.x > x2) {
            return 0;
        } else {
            return 1;
        }
    } else {
        return 0;
    }
}

// Define the main function
int main() {
    srand(time(NULL));
    Node *root = (Node*)malloc(sizeof(Node));
    root->p.x = 5.0;
    root->p.y = 0.0;
    root->parent = NULL;
    int i;
    for (i=0; i<K; i++) {
        Point rand_point;
        if (((double)rand()/(double)RAND_MAX) < GOAL_BIAS) {
            rand_point.x = 0.0;
            rand_point.y = 10.0;
        } else {
            rand_point = random_point();
        }
        Node *nearest = nearest_node(rand_point, root);
        double dist = sqrt(pow(rand_point.x-nearest->p.x, 2)+pow(rand_point.y-nearest->p.y, 2));