相机在 3d 中无法正确移动 space

Question

我目前正在研究移动 3d 相机 space。我希望它仅在 x 轴和 z 轴（水平）上移动。到目前为止，当相机的旋转全部为零时它正在正确移动，但是当我改变它的值时，相机开始表现得有点奇怪，向错误的方向移动。我正在使用 SFML，但我认为这是导致问题的数学问题。这很奇怪，因为我移动相机的代码与我之前编写的一个项目相同，但该项目运行正常。
这是限制旋转的代码：

camera.rot.x += movey;
if (glm::degrees(camera.rot.x) < -180.0f) camera.rot.x = glm::radians(180.0f) + camera.rot.x;
if (glm::degrees(camera.rot.x) > 180.0f) camera.rot.x = camera.rot.x + glm::radians(-180.0f);
camera.rot.y -= movex;
if (glm::degrees(camera.rot.y) < -180.0f) camera.rot.y = glm::radians(180.0f) + camera.rot.y;
if (glm::degrees(camera.rot.y) > 180.0f) camera.rot.y = camera.rot.y + glm::radians(-180.0f);

我用来移动相机的代码：

float x = sin(camera.rot.y) * camera.speed; float z = cos(camera.rot.y) * camera.speed;
if (sf::Keyboard::isKeyPressed(sf::Keyboard::W)) { camera.pos.x -= x; camera.pos.z -= z; }
if (sf::Keyboard::isKeyPressed(sf::Keyboard::S)) { camera.pos.x += x; camera.pos.z += z; }
if (sf::Keyboard::isKeyPressed(sf::Keyboard::A)) { camera.pos.x += z; camera.pos.z -= x; }
if (sf::Keyboard::isKeyPressed(sf::Keyboard::D)) { camera.pos.x -= z; camera.pos.z += x; }

如果有人能帮我解决这个问题，我将不胜感激。

对于任何想知道的人，这是我用来将 3d 坐标转换为屏幕坐标的代码：

glm::mat3 x(0.0f);
x[0][0] = 1.0f;
x[1][1] = cos(camera.rot.x);
x[1][2] = sin(camera.rot.x);
x[2][1] = -sin(camera.rot.x);
x[2][2] = cos(camera.rot.x);
glm::mat3 y(0.0f);
y[0][0] = cos(camera.rot.y);
y[0][2] = -sin(camera.rot.y);
y[1][1] = 1.0f;
y[2][0] = sin(camera.rot.y);
y[2][2] = cos(camera.rot.y);
glm::mat3 z(0.0f);
z[0][0] = cos(camera.rot.z);
z[0][1] = sin(camera.rot.z);
z[1][0] = -sin(camera.rot.z);
z[1][1] = cos(camera.rot.z);
z[2][2] = 1.0f;
glm::mat3 trans = x * y * z;
//trans is the perspective matrix
glm::vec3 e(SCREEN_WIDTH / 2, SCREEN_HEIGHT / 2, (float)tan(camera.fov / 2) * (float)(SCREEN_WIDTH / 2));
//e is the distance from the camera pinhole relate to the 'screen'
glm::mat3 ScreenTrans(0.0f);
ScreenTrans[0][0] = 1.0f;
ScreenTrans[0][2] = e.x / e.z;
ScreenTrans[1][1] = 1.0f;
ScreenTrans[1][2] = e.y / e.z;
ScreenTrans[2][2] = 1.0f / e.z;
//ScreenTrans is the matrix use to transform Camera space into Screen space
std::vector<glm::vec3> 3D_coords = Some3DPoints;
for (glm::vec3 coord: 3D_coords){
    glm::vec3 afterTrans = trans * coord;
    glm::vec3 cameraSpace = afterTrans - camera.pos;
    glm::vec3 2DScreenCoord = cameraSpace * ScreenTrans;
}

Answer 1

深入研究我的代码很长时间后，我发现问题出在我限制旋转的代码中，以及我如何获得“trans”矩阵。
首先，约束代码应该是：

camera.rot.x -= movey;
if (glm::degrees(camera.rot.x) < -90.0f) camera.rot.x = glm::radians(180.0f) + camera.rot.x;
if (glm::degrees(camera.rot.x) > 90.0f) camera.rot.x = camera.rot.x + glm::radians(-180.0f);
camera.rot.y += movex;
if (glm::degrees(camera.rot.y) < -180.0f) camera.rot.y = glm::radians(360.0f) + camera.rot.y;
if (glm::degrees(camera.rot.y) > 180.0f) camera.rot.y = camera.rot.y + glm::radians(-360.0f);

我计算错了值，把 rot.x 误认为是 y-axis，把 rot.y 误认为是 x-axis。
下一个是“trans”矩阵。应该是：

glm::mat3 trans = z * y * x;

应该首先处理 y-axis 的旋转，而不是 x-axis，否则你的 y-axis（相机 space）的旋转将永远是在 y-axis(世界 space).

相机在 3d 中无法正确移动 space

Camera not moving correctlly in 3d space

math

3d

trigonometry

3d-rendering