ArcBall+glm 实现射线拾取Ray Picking

在做一个基于qt和opengl的网格变形实验，用户交互方面需要实现射线拾取，框架本身是使用ArcBall实现鼠标拖拽旋转的。探索了几天，使用glm实现了射线拾取

1 射线拾取原理

射线拾取的原理很多博客也讲过了，主要就是：以当前眼睛位置（摄像机位置）为起点，以眼睛位置（摄像机位置）指向鼠标点选位置所对应的世界坐标 的方向为方向，生成一条射线，再判断射线与网格中的各个三角形是否相交。
个人认为重点是得到眼睛位置（摄像机位置）和鼠标点选位置所对应的世界坐标

2 实现步骤

2.1 生成射线

1. 眼睛位置

  vec3 eyepos = eye_distance_*eye_direction_;;            //视点坐标与观察点坐标
    //ptr_arcball_是轨迹球，GetInvertedBallMatrix()是得到旋转四元数构成的矩阵的逆矩阵
    glm::mat4 invertM = glm::make_mat4(ptr_arcball_->GetInvertedBallMatrix());
    glm::mat3 invertM_3 = glm::mat3(invertM); //取前三行&前三列
    glm::vec3 eyepos_glm = glm::vec3(eyepos[0],eyepos[1],eyepos[2]);
    glm::vec3 cameraPos = invertM_3 * eyepos_glm;

2. 鼠标点选位置对应的世界坐标

    // Get the matrix matView & matProj
    glm::mat4 matView = glm::make_mat4(ptr_arcball_->GetBallMatrix());//ptr_arcball_是轨迹球，GetBallMatrix()是得到旋转四元数构成的矩阵
    glm::mat4 matProj = glm::perspective(3.141592f / 2.0f, GLfloat(WIDTH / HEIGHT), 1.0f, 100.0f);

    vec3 mouse_coord = convert(x,y,width(),height());

    // x y z w  4D裁剪坐标 Z取1,至最远处,即z离相机100,即为(0,0-50)
    glm::vec4 ray_clip = glm::vec4(mouse_coord[0], mouse_coord[1], 1.0f, 1.0f);
    glm::vec4 ray_eye = glm::inverse(matProj) * ray_clip;   // 转为视觉坐标
    glm::vec4 ray_world = glm::inverse(matView) * ray_eye;  // 转为世界坐标

    ray_world.x /= ray_world.w;
    ray_world.y /= ray_world.w;
    ray_world.z /= ray_world.w;

    glm::vec3 ray_wordXYZ = glm::vec3(ray_world);

3 CastRay总体函数

void RenderWidget::CastRay(int x, int y, Ray &pickingRay)
{
    vec3 eyepos = eye_distance_*eye_direction_;;            //视点坐标与观察点坐标
    //ptr_arcball_是轨迹球，GetInvertedBallMatrix()是得到旋转四元数构成的矩阵的逆矩阵
    glm::mat4 invertM = glm::make_mat4(ptr_arcball_->GetInvertedBallMatrix());
    glm::mat3 invertM_3 = glm::mat3(invertM); //取前三行&前三列
    glm::vec3 eyepos_glm = glm::vec3(eyepos[0],eyepos[1],eyepos[2]);
    glm::vec3 cameraPos = invertM_3 * eyepos_glm;


    /*glm::vec3 cameraTarg = glm::vec3(0.0f, 0.0f, 0.0f);
    glm::vec3 cameraUp = glm::vec3(0.0f, 1.0f, 0.0f);
    glm::mat4 matView = glm::lookAt(cameraPos, cameraTarg, cameraUp);*/

    // Get the matrix matView & matProj
    glm::mat4 matView = glm::make_mat4(ptr_arcball_->GetBallMatrix());
    glm::mat4 matProj = glm::perspective(3.141592f / 2.0f, GLfloat(WIDTH / HEIGHT), 1.0f, 100.0f);

    vec3 mouse_coord = convert(x,y,width(),height());

    // x y z w  4D裁剪坐标 Z取1,至最远处,即z离相机100,即为(0,0-50)
    glm::vec4 ray_clip = glm::vec4(mouse_coord[0], mouse_coord[1], 1.0f, 1.0f);
    glm::vec4 ray_eye = glm::inverse(matProj) * ray_clip;   // 转为视觉坐标
    glm::vec4 ray_world = glm::inverse(matView) * ray_eye;  // 转为世界坐标

    ray_world.x /= ray_world.w;
    ray_world.y /= ray_world.w;
    ray_world.z /= ray_world.w;

    glm::vec3 ray_wordXYZ = glm::vec3(ray_world);
    glm::vec3 ray_dir = glm::normalize(ray_wordXYZ - cameraPos);

    //画射线
    vec3 p1 = {cameraPos.x, cameraPos.y, cameraPos.z};
    vec3 p2 = {ray_wordXYZ.x, ray_wordXYZ.y, ray_wordXYZ.z};
    near_point_.push_back(p1);
    far_point_.push_back(p2);

    // 构造射线
    vec3 ray_pos = {cameraPos[0],cameraPos[1],cameraPos[2]};
    pickingRay.pos = ray_pos;
    vec3 ray_ = {ray_dir.x, ray_dir.y, ray_dir.z};
    pickingRay.dir = ray_;

}

里面用到的convert函数，是把屏幕坐标转（x，y）换到-1到1之间

vec3 RenderWidget::convert(int x, int y, int nWinWidth, int nWinHeight)
{
    vec3 coord;
    if(nWinWidth>=nWinHeight)
    {
        coord[0]=( float(x)/nWinWidth-0.5f )*2*(nWinWidth/nWinHeight);
        coord[1]=-(float(y)/nWinHeight-0.5f)*2;
    }
    else
    {
        coord[0]=(float(x)/nWinWidth-0.5f)*2;
        coord[1]=-(float(y)/nWinHeight-0.5f)*2*(nWinHeight/nWinWidth);
    }
    coord[2] = 0;
    return coord;
}

2.2 判断三角形与射线相交与否

这里我参考了https://blog.csdn.net/charlee44/article/details/104348131的第二个方法
代码如下：

bool RenderWidget::IntersectTriangle(const vec3& pos, const vec3& dir,
    vec3& v0, vec3& v1, vec3& v2, float &t, float &u, float &v)//
{
    // E1
    vec3 E1 = v1 - v0;
    // E2
    vec3 E2 = v2 - v0;
    // P
    vec3 P = dir.cross(E2);
    // determinant
    float det = E1.dot(P);
    // keep det > 0, modify T accordingly
    vec3 T;//Vector3
    if( det >0 )
    {
        T = pos - v0;
    }
    else
    {
        T = v0 - pos;
        det = -det;
    }
    // If determinant is near zero, ray lies in plane of triangle
    if( det < 0.0001f )
        return false;
    // Calculate u and make sure u <= 1
    u = T.dot(P);
    if( u < 0.0f || u > det )
        return false;
    // Q
    vec3 Q = T.cross(E1);
    // Calculate v and make sure u + v <= 1
    v = dir.dot(Q);
    if( v < 0.0f || u + v > det )
        return false;
    // Calculate t, scale parameters, ray intersects triangle
    t = E2.dot(Q);
    float fInvDet = 1.0f / det;
    t *= fInvDet;
    u *= fInvDet;
    v *= fInvDet;
    return true;
}

2.3 遍历网格中所有三角形判断与射线的相交

这个比较简单，就是遍历，然后循环判断，加一个深度值z的判断，就是一条射线可能会跟三维模型又不止一个交点，要判断一下选离摄像机最近的那个，这里用IntersectTriangle里面的t值来表示

void RenderWidget::RayPicking(QPoint point)
{
    CastRay(point.x(), point.y(), picking_ray_);

    float intersect_t = 1000.0f;
    int select_id = -1;
    std::vector<vec3> tri_v(3);
    //遍历面
    for (MyMesh::FaceIter f_it = mesh_.faces_begin(); f_it != mesh_.faces_end(); ++f_it)
    {
        int i = 0;
        for (MyMesh::FaceVertexIter fv_it = mesh_.fv_iter(*f_it); fv_it.is_valid(); ++fv_it) {

            auto vertex = mesh_.point(*fv_it);
            tri_v[i] = {vertex.data()[0],vertex.data()[1],vertex.data()[2]};
            i++;
        }

        //相交判断
        float t = 0, u = 0, v = 0;
        bool is_intersect = IntersectTriangle(picking_ray_.pos,picking_ray_.dir,tri_v[0],tri_v[1],tri_v[2],t ,u ,v);

        if(is_intersect)
        {
            std::cout<<"t:"<<t<<std::endl;
            if(t < intersect_t)
            {
                intersect_t = t;
                select_id = f_it.handle().idx();

                is_draw_selected_tri_ = true;
            }
        }
    }

    selected_face_id_.push_back(select_id);

}