请帮我用c++代码实现采用四元数进行点云配准矩阵求解的代码

好的，以下是c语言实现采用四元数进行点云配准矩阵求解的代码示例：

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

typedef struct _point {
    double x;
    double y;
    double z;
} Point;

typedef struct _quaternion {
    double w;
    double x;
    double y;
    double z;
} Quaternion;

void normalize(Quaternion* q) {
    double norm = sqrt(q->w * q->w + q->x * q->x + q->y * q->y + q->z * q->z);
    q->w /= norm;
    q->x /= norm;
    q->y /= norm;
    q->z /= norm;
}

Quaternion conjugate(Quaternion q) {
    Quaternion result;
    result.w = q.w;
    result.x = -q.x;
    result.y = -q.y;
    result.z = -q.z;
    return result;
}

Quaternion multiply(Quaternion q1, Quaternion q2) {
    Quaternion result;
    result.w = q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z;
    result.x = q1.w * q2.x + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y;
    result.y = q1.w * q2.y - q1.x * q2.z + q1.y * q2.w + q1.z * q2.x;
    result.z = q1.w * q2.z + q1.x * q2.y - q1.y * q2.x + q1.z * q2.w;
    normalize(&result);
    return result;
}

Quaternion fromRotationMatrix(double r[3][3]) {
    Quaternion q;
    double trace = r[0][0] + r[1][1] + r[2][2];
    if (trace > 0) {
        double s = 0.5 / sqrt(trace + 1.0);
        q.w = 0.25 / s;
        q.x = (r[2][1] - r[1][2]) * s;
        q.y = (r[0][2] - r[2][0]) * s;
        q.z = (r[1][0] - r[0][1]) * s;
    } else {
        if (r[0][0] > r[1][1] && r[0][0] > r[2][2]) {
            double s = 2.0 * sqrt(1.0 + r[0][0] - r[1][1] - r[2][2]);
            q.w = (r[2][1] - r[1][2]) / s;
            q.x = 0.25 * s;
            q.y = (r[0][1] + r[1][0]) / s;
            q.z = (r[0][2] + r[2][0]) / s;
        } else if (r[1][1] > r[2][2]) {
            double s = 2.0 * sqrt(1.0 + r[1][1] - r[0][0] - r[2][2]);
            q.w = (r[0][2] - r[2][0]) / s;
            q.x = (r[0][1] + r[1][0]) / s;
            q.y = 0.25 * s;
            q.z = (r[1][2] + r[2][1]) / s;
        } else {
            double s = 2.0 * sqrt(1.0 + r[2][2] - r[0][0] - r[1][1]);
            q.w = (r[1][0] - r[0][1]) / s;
            q.x = (r[0][2] + r[2][0]) / s;
            q.y = (r[1][2] + r[2][1]) / s;
            q.z = 0.25 * s;
        }
    }
    return q;
}

void computeRotationMatrix(double r[3][3], Quaternion q) {
    double qw = q.w, qx = q.x, qy = q.y, qz = q.z;
    double xx = qx * qx, xy = qx * qy, xz = qx * qz, xw = qx * qw;
    double yy = qy * qy, yz = qy * qz, yw = qy * qw;
    double zz = qz * qz, zw = qz * qw;

    r[0][0] = 1.0 - 2.0 * (yy + zz);
    r[0][1] = 2.0 * (xy - zw);
    r[0][2] = 2.0 * (xz + yw);
    r[1][0] = 2.0 * (xy + zw);
    r[1][1] = 1.0 - 2.0 * (xx + zz);
    r[1][2] = 2.0 * (yz - xw);
    r[2][0] = 2.0 * (xz - yw);
    r[2][1] = 2.0 * (yz + xw);
    r[2][2] = 1.0 - 2.0 * (xx + yy);
}

void transformPoint(Point* p, double r[3][3], double t[3]) {
    double x = r[0][0] * p->x + r[0][1] * p->y + r[0][2] * p->z + t[0];
    double y = r[1][0] * p->x + r[1][1] * p->y + r[1][2] * p->z + t[1];
    double z = r[2][0] * p->x + r[2][1] * p->y + r[2][2] * p->z + t[2];
    p->x = x;
    p->y = y;
    p->z = z;
}

void computePointCloudTransformation(Point* src, Point* dst, int n,
                                     double r[3][3], double t[3]) {
    Point centroidSrc = {0, 0, 0};
    Point centroidDst = {0, 0, 0};
    for (int i = 0; i < n; ++i) {
        centroidSrc.x += src[i].x;
        centroidSrc.y += src[i].y;
        centroidSrc.z += src[i].z;
        centroidDst.x += dst[i].x;
        centroidDst.y += dst[i].y;
        centroidDst.z += dst[i].z;
    }
    centroidSrc.x /= n;
    centroidSrc.y /= n;
    centroidSrc.z /= n;
    centroidDst.x /= n;
    centroidDst.y /= n;
    centroidDst.z /= n;

    double H[3][3] = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
    for (int i = 0; i < n; ++i) {
        Point p = {src[i].x - centroidSrc.x, src[i].y - centroidSrc.y,
                   src[i].z - centroidSrc.z};
        Point q = {dst[i].x - centroidDst.x, dst[i].y - centroidDst.y,
                   dst[i].z - centroidDst.z};
        H[0][0] += p.x * q.x;
        H[0][1] += p.x * q.y;
        H[0][2] += p.x * q.z;
        H[1][0] += p.y * q.x;
        H[1][1] += p.y * q.y;
        H[1][2] += p.y * q.z;
        H[2][0] += p.z * q.x;
        H[2][1] += p.z * q.y;
        H[2][2] += p.z * q.z;
    }

    Quaternion rotation = fromRotationMatrix(H);
    computeRotationMatrix(r, rotation);

    Quaternion tquat;
    tquat.x = t[0];
    tquat.y = t[1];
    tquat.z = t[2];
    tquat.w = 0;
    tquat = multiply(conjugate(rotation), multiply(tquat, rotation));
    t[0] = tquat.x;
    t[1] = tquat.y;
    t[2] = tquat.z;

    for (int i = 0; i < n; ++i) {
        transformPoint(&src[i], r, t);
    }
}

int main() {
    // example usage with two sets of three points
    Point src[] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
    Point dst[] = {{9, 8, 7}, {6, 5, 4}, {3, 2, 1}};

    double r[3][3] = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}};
    double t[3] = {0, 0, 0};

    computePointCloudTransformation(src, dst, 3, r, t);

    printf("Rotation matrix:\n");
    for (int i = 0; i < 3; ++i) {
        for (int j = 0; j < 3; ++j) {
            printf("%lf ", r[i][j]);
        }
        printf("\n");
    }

    printf("Translation vector:\n");
    for (int i = 0; i < 3; ++i) {
        printf("%lf ", t[i]);
    }
    printf("\n");

    return 0;
}

希望这份代码可以对您有所帮助。