RANSAC算法来拟合圆形模型C++

RANSAC（Random Sample Consensus）算法是一种基于统计原理的模型拟合方法，可以用于拟合圆形模型。以下是一个用C++实现RANSAC算法拟合圆形模型的示例代码：

#include <iostream>
#include <vector>
#include <random>
#include <cmath>

// 定义圆形结构体
struct Circle {
    double x;  // 圆心x坐标
    double y;  // 圆心y坐标
    double r;  // 半径
};

// 计算两点之间的距离
double distance(double x1, double y1, double x2, double y2) {
    return std::sqrt(std::pow(x2 - x1, 2) + std::pow(y2 - y1, 2));
}

// 计算点到圆心的距离
double distance(double x, double y, Circle circle) {
    return std::sqrt(std::pow(x - circle.x, 2) + std::pow(y - circle.y, 2));
}

// RANSAC算法拟合圆形模型
Circle ransac(std::vector<std::pair<double, double>> points, int iterations, double threshold) {
    std::random_device rd;
    std::mt19937 gen(rd());
    std::uniform_int_distribution<> dis(0, points.size() - 1);

    Circle best_circle = {0, 0, 0};
    int best_count = 0;

    for (int i = 0; i < iterations; i++) {
        // 随机选择三个点
        int idx1 = dis(gen);
        int idx2 = dis(gen);
        int idx3 = dis(gen);

        // 计算圆形参数
        double x1 = points[idx1].first;
        double y1 = points[idx1].second;
        double x2 = points[idx2].first;
        double y2 = points[idx2].second;
        double x3 = points[idx3].first;
        double y3 = points[idx3].second;
        double a = x1 - x2;
        double b = y1 - y2;
        double c = x1 - x3;
        double d = y1 - y3;
        double e = (std::pow(x1, 2) - std::pow(x2, 2)) + (std::pow(y1, 2) - std::pow(y2, 2));
        double f = (std::pow(x1, 2) - std::pow(x3, 2)) + (std::pow(y1, 2) - std::pow(y3, 2));
        double delta = a * d - b * c;
        if (delta == 0) {
            continue;
        }
        double x0 = (d * e - b * f) / (2 * delta);
        double y0 = (a * f - c * e) / (2 * delta);
        double r = distance(x0, y0, x1, y1);

        // 统计点数
        int count = 0;
        for (std::pair<double, double> point : points) {
            if (distance(point.first, point.second, x0, y0) <= threshold) {
                count++;
            }
        }

        // 更新最优圆形
        if (count > best_count) {
            best_circle.x = x0;
            best_circle.y = y0;
            best_circle.r = r;
            best_count = count;
        }
    }

    return best_circle;
}

int main() {
    // 生成随机点
    std::vector<std::pair<double, double>> points;
    std::random_device rd;
    std::mt19937 gen(rd());
    std::uniform_real_distribution<> dis(-10, 10);
    for (int i = 0; i < 100; i++) {
        double x = dis(gen);
        double y = dis(gen);
        if (std::pow(x, 2) + std::pow(y, 2) <= 25) {  // 在圆内的点
            points.push_back({x, y});
        }
    }

    // RANSAC拟合圆形模型
    Circle circle = ransac(points, 1000, 1);

    // 输出结果
    std::cout << "Best circle: (" << circle.x << ", " << circle.y << "), r = " << circle.r << std::endl;

    return 0;
}

该代码通过随机选择三个点计算圆形参数，并统计在圆内的点数。重复此过程若干次后，选取点数最多的圆形作为最优圆形。