用c语言实现欧拉角、方向余弦矩阵、四元数之间的转化

欧拉角、方向余弦矩阵、四元数之间的转化可以通过一系列矩阵运算实现。下面是用C语言实现的代码：

1. 欧拉角转方向余弦矩阵

#include <math.h>

void euler2dcm(double roll, double pitch, double yaw, double dcm[3][3])
{
    double cr, sr, cp, sp, cy, sy;

    cr = cos(roll);
    sr = sin(roll);
    cp = cos(pitch);
    sp = sin(pitch);
    cy = cos(yaw);
    sy = sin(yaw);

    dcm[0][0] = cp * cy;
    dcm[0][1] = cp * sy;
    dcm[0][2] = -sp;
    dcm[1][0] = sr * sp * cy - cr * sy;
    dcm[1][1] = sr * sp * sy + cr * cy;
    dcm[1][2] = sr * cp;
    dcm[2][0] = cr * sp * cy + sr * sy;
    dcm[2][1] = cr * sp * sy - sr * cy;
    dcm[2][2] = cr * cp;
}

2. 方向余弦矩阵转欧拉角

#include <math.h>

void dcm2euler(double dcm[3][3], double *roll, double *pitch, double *yaw)
{
    double cp = sqrt(dcm[0][0] * dcm[0][0] + dcm[1][0] * dcm[1][0]);
    if (cp > 1e-16) {
        *roll = atan2(dcm[2][1], dcm[2][2]);
        *pitch = atan2(-dcm[2][0], cp);
        *yaw = atan2(dcm[1][0], dcm[0][0]);
    } else {
        *roll = atan2(-dcm[1][2], dcm[1][1]);
        *pitch = atan2(-dcm[2][0], cp);
        *yaw = 0;
    }
}

3. 方向余弦矩阵转四元数

#include <math.h>

void dcm2quat(double dcm[3][3], double q[4])
{
    double tr = dcm[0][0] + dcm[1][1] + dcm[2][2];
    if (tr > 0) {
        double s = sqrt(tr + 1.0) * 2;
        q[0] = (dcm[2][1] - dcm[1][2]) / s;
        q[1] = (dcm[0][2] - dcm[2][0]) / s;
        q[2] = (dcm[1][0] - dcm[0][1]) / s;
        q[3] = 0.25 * s;
    } else if ((dcm[0][0] > dcm[1][1]) && (dcm[0][0] > dcm[2][2])) {
        double s = sqrt(1.0 + dcm[0][0] - dcm[1][1] - dcm[2][2]) * 2;
        q[0] = 0.25 * s;
        q[1] = (dcm[0][1] + dcm[1][0]) / s;
        q[2] = (dcm[0][2] + dcm[2][0]) / s;
        q[3] = (dcm[2][1] - dcm[1][2]) / s;
    } else if (dcm[1][1] > dcm[2][2]) {
        double s = sqrt(1.0 + dcm[1][1] - dcm[0][0] - dcm[2][2]) * 2;
        q[0] = (dcm[0][1] + dcm[1][0]) / s;
        q[1] = 0.25 * s;
        q[2] = (dcm[1][2] + dcm[2][1]) / s;
        q[3] = (dcm[0][2] - dcm[2][0]) / s;
    } else {
        double s = sqrt(1.0 + dcm[2][2] - dcm[0][0] - dcm[1][1]) * 2;
        q[0] = (dcm[0][2] + dcm[2][0]) / s;
        q[1] = (dcm[1][2] + dcm[2][1]) / s;
        q[2] = 0.25 * s;
        q[3] = (dcm[1][0] - dcm[0][1]) / s;
    }
}

4. 四元数转方向余弦矩阵

void quat2dcm(double q[4], double dcm[3][3])
{
    double q0q0 = q[0] * q[0];
    double q0q1 = q[0] * q[1];
    double q0q2 = q[0] * q[2];
    double q0q3 = q[0] * q[3];
    double q1q1 = q[1] * q[1];
    double q1q2 = q[1] * q[2];
    double q1q3 = q[1] * q[3];
    double q2q2 = q[2] * q[2];
    double q2q3 = q[2] * q[3];
    double q3q3 = q[3] * q[3];

    dcm[0][0] = q0q0 + q1q1 - q2q2 - q3q3;
    dcm[0][1] = 2 * (q1q2 - q0q3);
    dcm[0][2] = 2 * (q1q3 + q0q2);
    dcm[1][0] = 2 * (q1q2 + q0q3);
    dcm[1][1] = q0q0 - q1q1 + q2q2 - q3q3;
    dcm[1][2] = 2 * (q2q3 - q0q1);
    dcm[2][0] = 2 * (q1q3 - q0q2);
    dcm[2][1] = 2 * (q2q3 + q0q1);
    dcm[2][2] = q0q0 - q1q1 - q2q2 + q3q3;
}

注意：在C语言中，多维数组的内存布局是连续的，因此可以将二维数组看作一维数组来访问元素。在上面的代码中，我们将dcm数组声明为3x3的二维数组，但在函数中使用时，将其看作一个长度为9的一维数组来访问元素。