【 OpenGL 】 Random Talk 1. The camera rotates around a point in the space by dragging the mouse

1. Preface

This is a problem I encountered recently , As shown in the title , I need to drag the mouse to rotate the camera around the point , The original idea was simple , similar Note 8 、 The camera As mentioned in , From the perspective of focusing on the central point , Distance to move the mouse xoffset and yoffset Convert to yaw and pitch horn , Then calculate the vector of the angle of view , Intersect with the sphere to get the current position of the camera , But there is a serious problem in the actual process , It is the fatal defect of Euler angle —— Omnidirectional lock , If pitch Angular excess ±90°, We will encounter various problems , When designing the first perspective, we can control pitch Angle in 90° To -90° Between , It doesn't affect our experience , But if we want to control the camera to rotate the sphere , It may be wrong to be lazy , So can there be other ways to achieve this effect ？ Of course there are , One is the quaternion , It can realize smooth interpolation transition of spherical rotation , But today I want to introduce another more intuitive implementation

2. Camera's spherical rotation

alike , We need to record the distance of each mouse movement xoffset and yoffset, How to use these two values ？

You can draw a diagram ：

among A and B Is the point before and after the camera moves ,O Point is the focus of our camera , So what we have to do now is obvious , Originally, the camera's viewing angle was a parallel circular surface , We think of it as a projection plane , While moving the camera , We are in OAB Move on the formed circular surface , Then our task is to make use of OA Get OB

First, we calculate OA vector , Find the current rotation radius

	void updateCameraVectors()
    {
    
        if (xoffset == 0 && yoffset == 0)
            return;
        glm::vec3 target, offset;
        target = Position - Front;
        double radius = glm::length(target);
        target = glm::normalize(target);

After that, we compare the current camera up with OA The right vector of the projection plane is obtained by cross multiplication of the vectors

        Right = glm::normalize(glm::cross(Up, target));

Second, use OA The vector and the obtained cross product get the upper vector of the projection plane

        Up = glm::normalize(glm::cross(target, Right));

Then we find the vector corresponding to the screen displacement on the projection plane AB（ Multiply the right vector and the upper vector of the projection plane by xy The displacement values are added ）

        offset = Up * yoffset + Right * xoffset ;

Then we convert the arc length of the displacement to OAB The radian of a circle is negative , Ensure that the relative rotation direction of the object is consistent with the direction of the mouse （ The camera rotation direction is opposite to the mouse displacement direction ）

        double len = glm::length(offset);
        double angle = -len / radius;
        offset = glm::normalize(offset);

Finally, we calculate the new target vector OB = (OAcos(OAB)+ABsin(OAB)), And multiply it by the length of the radius and add it to the focal point , So we can get the position of our camera

        double cr = cos(angle) * radius, sr = sin(angle) * radius;
        Position = Front + glm::vec3(target.x * cr + offset.x * sr, target.y * cr + offset.y * sr, target.z * cr + offset.z * sr);
	}

3. effect