NX二次开发，C++ 写一个OBB算法，获取最小包容盒

OBB（Oriented Bounding Box）算法是将一个物体用一个最小的有向矩形框住，这个矩形是由物体坐标系下的三个轴向量和物体中心点唯一确定的。以下是一个简单的 C++ 实现，需要自己实现向量、矩阵等相关计算函数：

#include <vector>
#include <algorithm>

// 3D向量结构体
struct Vector3 {
    float x, y, z;
    Vector3(float x = 0, float y = 0, float z = 0) : x(x), y(y), z(z) {}
};

// 矩阵结构体
struct Matrix3x3 {
    Vector3 col1, col2, col3;
    Matrix3x3(Vector3 col1 = Vector3(), Vector3 col2 = Vector3(), Vector3 col3 = Vector3())
        : col1(col1), col2(col2), col3(col3) {}
};

// 计算两个向量的点积
float Dot(const Vector3& a, const Vector3& b) {
    return a.x * b.x + a.y * b.y + a.z * b.z;
}

// 计算两个向量的叉积
Vector3 Cross(const Vector3& a, const Vector3& b) {
    return Vector3(
        a.y * b.z - a.z * b.y,
        a.z * b.x - a.x * b.z,
        a.x * b.y - a.y * b.x
    );
}

// 计算向量长度的平方
float LengthSq(const Vector3& v) {
    return Dot(v, v);
}

// 计算两个向量之间的距离
float Distance(const Vector3& a, const Vector3& b) {
    return std::sqrt(LengthSq(a - b));
}

// 计算单位向量
Vector3 Normalize(const Vector3& v) {
    float len = std::sqrt(LengthSq(v));
    if (len > 0.0f)
        return Vector3(v.x / len, v.y / len, v.z / len);
    return v;
}

// 计算矩阵乘法
Matrix3x3 operator*(const Matrix3x3& a, const Matrix3x3& b) {
    return Matrix3x3(
        Vector3(Dot(a.col1, Vector3(b.col1.x, b.col2.x, b.col3.x)), Dot(a.col2, Vector3(b.col1.x, b.col2.x, b.col3.x)), Dot(a.col3, Vector3(b.col1.x, b.col2.x, b.col3.x))),
        Vector3(Dot(a.col1, Vector3(b.col1.y, b.col2.y, b.col3.y)), Dot(a.col2, Vector3(b.col1.y, b.col2.y, b.col3.y)), Dot(a.col3, Vector3(b.col1.y, b.col2.y, b.col3.y))),
        Vector3(Dot(a.col1, Vector3(b.col1.z, b.col2.z, b.col3.z)), Dot(a.col2, Vector3(b.col1.z, b.col2.z, b.col3.z)), Dot(a.col3, Vector3(b.col1.z, b.col2.z, b.col3.z)))
    );
}

// 计算矩阵乘以向量
Vector3 operator*(const Matrix3x3& a, const Vector3& v) {
    return Vector3(Dot(a.col1, v), Dot(a.col2, v), Dot(a.col3, v));
}

// 计算物体的 OBB 包围盒
void ComputeOBB(const std::vector<Vector3>& points, Matrix3x3& orientation, Vector3& halfExtents, Vector3& center) {
    // 计算点云的中心点
    center = Vector3();
    for (const auto& p : points)
        center += p;
    center /= static_cast<float>(points.size());

    // 计算协方差矩阵
    Matrix3x3 covMat;
    for (const auto& p : points) {
        Vector3 delta = p - center;
        covMat.col1.x += delta.x * delta.x;
        covMat.col1.y += delta.x * delta.y;
        covMat.col1.z += delta.x * delta.z;
        covMat.col2.x += delta.y * delta.x;
        covMat.col2.y += delta.y * delta.y;
        covMat.col2.z += delta.y * delta.z;
        covMat.col3.x += delta.z * delta.x;
        covMat.col3.y += delta.z * delta.y;
        covMat.col3.z += delta.z * delta.z;
    }
    covMat.col1 /= static_cast<float>(points.size());
    covMat.col2 /= static_cast<float>(points.size());
    covMat.col3 /= static_cast<float>(points.size());

    // 计算协方差矩阵的特征值和特征向量
    Matrix3x3 eigenVecs;
    Vector3 eigenVals;
    // TODO: 使用特征值分解计算特征值和特征向量
    // ...

    // 将特征向量作为包围盒的方向向量
    orientation = eigenVecs;

    // 计算包围盒的半径
    halfExtents.x = std::sqrt(eigenVals.x);
    halfExtents.y = std::sqrt(eigenVals.y);
    halfExtents.z = std::sqrt(eigenVals.z);
}

注：以上代码只是一个简单的示例，实际使用时需要按需自行实现向量、矩阵等相关计算函数。