四元数旋转导致场景拉伸

Question

我已经修改了Vulkano、GLTF viewer example，以允许键盘和鼠标输入，将平移和旋转应用于场景。平移工作正常，但旋转会导致场景中的对象直接向上移动到相机并拉伸，直到它们看起来像垃圾，因为旋转接近 90 - 180 度。

这是旋转前场景的样子：

。

这是旋转大约 90 度的时候：

.

我正在使用 cgmath Quaternions 进行轮换。我以前没有使用过四元数，所以我想知道是否有人可以告诉我我是否正确使用它们，我怀疑这就是问题所在。

这就是我创建初始四元数的方式，使用我找到的方程式here：

let rotation_speed_deg = 0.01;
let rotation_speed = rotation_speed_deg * f32::consts::PI / 180.0;
let rotation_angle_deg = 0.0;
let rotation_angle = rotation_angle_deg * f32::consts::PI / 180.0;
let rotation_axis = Vector3::new(0.0, 1.0, 0.0);
let rotation_scalar = (rotation_angle / 2.0 as f32).cos();
let rotation_vec = Vector3::new(
    rotation_axis.x * (rotation_angle / 2.0 as f32).sin(),
    rotation_axis.y * (rotation_angle / 2.0 as f32).sin(),
    rotation_axis.z * (rotation_angle / 2.0 as f32).sin());
let mut rotation_quat = Quaternion::from_sv(rotation_scalar, rotation_vec);

然后我正在修改四元数以对鼠标输入应用旋转，如下所示：

let diff_x = position.0 - last_x;
if diff_x > 0.0 {
    // println!("turn right");
    rotation_quat.v.x += rotation_axis.x * ((rotation_angle + rotation_speed) / 2.0 as f32).sin();
    rotation_quat.v.y += rotation_axis.y * ((rotation_angle + rotation_speed) / 2.0 as f32).sin();
    rotation_quat.v.z += rotation_axis.z * ((rotation_angle + rotation_speed) / 2.0 as f32).sin();
    rotation_quat.s += ((rotation_angle + rotation_speed) / 2.0 as f32).cos();
} else if diff_x < 0.0 {
    // println!("turn left");
    rotation_quat.v.x += rotation_axis.x * ((rotation_angle - rotation_speed) / 2.0 as f32).sin();
    rotation_quat.v.y += rotation_axis.y * ((rotation_angle - rotation_speed) / 2.0 as f32).sin();
    rotation_quat.v.z += rotation_axis.z * ((rotation_angle - rotation_speed) / 2.0 as f32).sin();
    rotation_quat.s += ((rotation_angle - rotation_speed) / 2.0 as f32).cos();
}

last_x = position.0;

为了应用平移和旋转，我将矩阵相乘如下：

let fovy = Rad(60.0 * f32::consts::PI / 180.0);
let mut aspect = viewport_dimensions[0] as f32 / viewport_dimensions[1] as f32;
let near = 0.1;
let far = 100.0;
let mut proj = perspective(fovy, aspect, near, far);
let view = Matrix4::look_at(Point3::new(0.0, 1.0, -5.0), Point3::new(0.0, 1.0, 0.0), Vector3::new(0.0, -1.0, 0.0));
let trans_mat = Matrix4::from_translation(trans);
let rot_mat = Matrix4::from(rot);
builder = self.draw_node(node.index(), proj * view * trans_mat * rot_mat, viewport_dimensions, builder);

所以你可以看到，我将 proj * view * trans_mat * rot_mat 相乘......也许这是错误的顺序？

任何帮助将不胜感激。我没有很强的数学背景，而且多年来一直在努力自学 CG，所以我不知道还能去哪里。一些关于这类东西的阅读资源也将不胜感激。

Answer 1

拉伸的原因是因为我错误地组合了初始四元数和后续四元数。您不能只是将它们加在一起，但 * 运算符可以连接旋转。

所以我把代码的鼠标输入部分改成了这样，它可以工作了：

let diff_x = position.0 - last_x;
if diff_x > 0.0 {
    // println!("turn right");
    let rotation_scalar = ((rotation_angle + rotation_speed) / 2.0 as f32).cos();
    let rotation_vec = Vector3::new(
        rotation_axis.x * ((rotation_angle + rotation_speed) / 2.0 as f32).sin(),
        rotation_axis.y * ((rotation_angle + rotation_speed) / 2.0 as f32).sin(),
        rotation_axis.z * ((rotation_angle + rotation_speed) / 2.0 as f32).sin());
    let rotation_quat2 = Quaternion::from_sv(rotation_scalar, rotation_vec);
    rotation_quat = rotation_quat * rotation_quat2;
} else if diff_x < 0.0 {
    // println!("turn left");
    let rotation_scalar = ((rotation_angle - rotation_speed) / 2.0 as f32).cos();
    let rotation_vec = Vector3::new(
        rotation_axis.x * ((rotation_angle - rotation_speed) / 2.0 as f32).sin(),
        rotation_axis.y * ((rotation_angle - rotation_speed) / 2.0 as f32).sin(),
        rotation_axis.z * ((rotation_angle - rotation_speed) / 2.0 as f32).sin());
    let rotation_quat2 = Quaternion::from_sv(rotation_scalar, rotation_vec);
    rotation_quat = rotation_quat * rotation_quat2;
}
last_x = position.0;