本部分的实现代码，见 07_Camera

关于摄像机的实现，实际上就是调整观察矩阵的问题。为了确定观察矩阵，需要确认四个信息：

  • 摄像机的位置
  • 摄像机的前方
  • 摄像机的右方
  • 摄像机的上方。

这四个信息构成了 观察矩阵 ，也可称为 LookAt 矩阵。

 LookAt =[RxRyRz0UxUyUz0DxDyDz00001]∗[100−Px010−Py001−Pz0001]\text { LookAt }=\left[\begin{array}{cccc} R_x & R_y & R_z & 0 \\ U_x & U_y & U_z & 0 \\ D_x & D_y & D_z & 0 \\ 0 & 0 & 0 & 1 \end{array}\right] *\left[\begin{array}{cccc} 1 & 0 & 0 & -P_x \\ 0 & 1 & 0 & -P_y \\ 0 & 0 & 1 & -P_z \\ 0 & 0 & 0 & 1 \end{array}\right]

其中RR表示摄像机的右方，UU表示摄像机的上方，DD表示摄像机的前方，PP表示摄像机的位置。

需要注意的是，虽然说观察矩阵是为了表现摄像机。但因为观察矩阵最后是与 Model 矩阵相乘的，因此观察矩阵要表达的变换是与摄像机要表达的变换相反的，例如摄像机后退三米相当于场景前进三米。也因此，LookAt 矩阵中，旋转矩阵是经过了转置的，位移矩阵是取了负的。

GLM 中提供了 LookAt 函数的接口，调用如下：

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glm::mat4 view(1.0f);
view = glm::lookAt(glm::vec3(0.0f, 0.0f, 3.0f), glm::vec3(0.0f, 0.0f, 0.0f), glm::vec3(0.0f, 1.0f, 0.0f));

lookAt 函数需要三个向量：

  • 摄像机的位置
  • 摄像机的目标
  • 摄像机的上方。

前两个参数可以确定摄像机的前方，通过摄像机的前方和第三个参数摄像机的上方，可以叉乘获得摄像机的右方。

#键盘控制摄像机位置

可通过函数 glfwGetKey 获取键盘按键信息。在绘制循环函数中去检查输入信息，并根据输入信息对摄像机的位置进行调整，再根据摄像机的位置调整观察矩阵，即能满足键盘控制摄像机位置的效果：

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while (!glfwWindowShouldClose(window))
{
    processInput(window);
    ...
    glm::mat4 view(1.0f);
    view = glm::lookAt(cameraPos, cameraPos + cameraFront, cameraUp);
    ...
}

...

float lastFrameTime = 0.0f;
float currFrameTime = 0.0f;
float deltaTime = 0.0f;
void processInput(GLFWwindow *window)
{
    currFrameTime = glfwGetTime();
    deltaTime = currFrameTime - lastFrameTime;
    lastFrameTime = currFrameTime;

    float cameraSpeed = 2.5f * deltaTime;
    if (glfwGetKey(window, GLFW_KEY_W) == GLFW_PRESS)
        cameraPos += cameraSpeed * cameraFront;
    if (glfwGetKey(window, GLFW_KEY_S) == GLFW_PRESS)
        cameraPos -= cameraSpeed * cameraFront;
    if (glfwGetKey(window, GLFW_KEY_A) == GLFW_PRESS)
        cameraPos -= glm::normalize(glm::cross(cameraFront, cameraUp)) * cameraSpeed;
    if (glfwGetKey(window, GLFW_KEY_D) == GLFW_PRESS)
        cameraPos += glm::normalize(glm::cross(cameraFront, cameraUp)) * cameraSpeed;

    if (glfwGetKey(window, GLFW_KEY_ESCAPE) == GLFW_PRESS)
        glfwSetWindowShouldClose(window, true);
}

#鼠标控制摄像机角度

首先需要了解摄像机角度的定义，对于摄像机有三个术语 pitch, yaw, roll分别描述绕着x,y,zx,y,z三个轴的旋转：

pitch, yaw, roll

通量来说，只需要修改 pitch 角和 yaw 角度即可。可使用鼠标的水平平移来修改 yaw 角度，鼠标的前进后退来修改 pitch 角度。

通过 pitch 和 yaw 角度，可以计算出摄像机的前方向。根据前方向，和世界坐标的上方向(0,1,0)(0,1,0)，可以计算出摄像机的右方向。再根据摄像机的前方向，摄像机的右方向，可求得摄像机的上方向。

首先只考虑 yaw 角度，根据示意图，可以很快的计算出 yaw 角度对于摄像机前方向的贡献：

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glm::vec3 direction;
direction.x = cos(glm::radians(yaw)); // Note that we convert the angle to radians first
direction.z = sin(glm::radians(yaw));

然后计算 pitch 角度。想想物体躺在 X 轴上，pitch 角度为θ\theta，y 轴上分量为 sin⁡θ\sin\theta，x 轴上分量为cos⁡θ\cos\theta。同理，当物体躺在 Z 轴上时，y 轴上分量为 sin⁡θ\sin\theta，z 轴上分量为cos⁡θ\cos\theta。示意图代码如下：

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direction.x = cos(glm::radians(yaw)) * cos(glm::radians(pitch));
direction.y = sin(glm::radians(pitch));
direction.z = sin(glm::radians(yaw)) * cos(glm::radians(pitch));

结合可得：

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glm::vec3 direction;
direction.x = cos(glm::radians(yaw)) * cos(glm::radians(pitch));
direction.y = sin(glm::radians(pitch));
direction.z = sin(glm::radians(yaw)) * cos(glm::radians(pitch));
cameraFront = glm::normalize(direction);

为了保证初始的cameraFront指向-z方向，yaw的初始值应该取-90°

在获得了 cameraFront 后，可利用叉乘获得 cameraRight 和 cameraUp

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cameraRight = glm::normalize(glm::cross(cameraFront, WorldUp)); // normalize the vectors, because their length gets closer to 0 the more you look up or down which results in slower movement.

cameraUp = glm::normalize(glm::cross(cameraRight, cameraFront));

可以通过函数 glfwSetCursorPosCallback 设置鼠标移动的回调，并在回调中根据鼠标的移动，调整 yaw 和 pitch 角，并进一步更新摄像机的三个方向信息。并且可以通过函数 glfwSetMouseButtonCallback 设置仅当鼠标右键按下时，才对鼠标的移动进行操作。

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glfwSetCursorPosCallback(window, mouse_callback);
glfwSetMouseButtonCallback(window, mouse_button_Callback);

bool firstMouse = true;
double lastX = 0.0, lastY = 0.0;
double mouseSensitivity = 0.05;
float yaw = -90.0f;
float pitch = 0.0f;
bool ClickDown = false;

void mouse_callback(GLFWwindow *window, double xpos, double ypos)
{
    if (!ClickDown)
        return;

    if (firstMouse)
    {
        lastX = xpos;
        lastY = ypos;
        firstMouse = false;
    }

    float xoffset = (xpos - lastX) * mouseSensitivity;
    float yoffset = (lastY - ypos) * mouseSensitivity; // reversed since y-coordinates go from bottom to top

    lastX = xpos;
    lastY = ypos;

    yaw += xoffset;
    pitch += yoffset;

    if (pitch > 89.0f)
        pitch = 89.0f;
    if (pitch < -89.0f)
        pitch = -89.0f;

    glm::vec3 front;
    front.x = cos(glm::radians(yaw)) * cos(glm::radians(pitch));
    front.y = sin(glm::radians(pitch));
    front.z = sin(glm::radians(yaw)) * cos(glm::radians(pitch));
    cameraFront = glm::normalize(front);
    // also re-calculate the Right and Up vector
    glm::vec3 cameraRight = glm::normalize(glm::cross(cameraFront, glm::vec3(0, 1, 0))); // normalize the vectors, because their length gets closer to 0 the more you look up or down which results in slower movement.
    cameraUp = glm::normalize(glm::cross(cameraRight, cameraFront));
}

void mouse_button_Callback(GLFWwindow *window, int key, int action, int mode)
{
    if (key == GLFW_MOUSE_BUTTON_RIGHT)
    {
        if (action == GLFW_PRESS)
        {
            ClickDown = GL_TRUE;
        }
        else if (action == GLFW_RELEASE)
        {
            ClickDown = GL_FALSE;
        }
    }
}

在上述代码中变量 firstMouse 是为了避免程序一开始因为 lastX, lastY 初始值为 0 导致的跳变。同时为了避免颠倒情况，将 pitch 的范围限制在 −89∼89-89 \sim 89的范围内。

#结果与源码

此时即可以通过键盘的 WASD 控制摄像机的位置，通过按下鼠标右键并移动鼠标控制摄像机的角度。

Result