英文:
How does GLM achieve quaternion crossing and normalization?
问题
我正在尝试跟随TheCherno的Rust光线追踪系列（目前在第6集），但我遇到了一个数学难题。我不确定如何处理这段代码：
if (delta.x != 0.0f || delta.y != 0.0f)
{
let pitchDelta = delta.y * GetRotationSpeed();
let yawDelta = delta.x * GetRotationSpeed();
let q = glm::normalize(glm::cross(glm::angleAxis(-pitchDelta, rightDirection),
glm::angleAxis(-yawDelta, glm::vec3(0.0f, 1.0f, 0.0f))));
m_ForwardDirection = glm::rotate(q, m_ForwardDirection);
moved = true;
}
GLM如何允许交叉和规范化四元数？我对这个概念是新手，但从数学上看似乎不太对劲。我正在尝试使用cgmath库在Rust中重写这段代码，但是这两个GLM函数没有对应物。我尝试找到源代码并自己实现这些函数，但除了在古老文档中没有提到之外，我找不到任何提及。
英文:
I'm trying to follow TheCherno's ray tracing series in Rust (Currently on Episode 6), but I've run into a mathematical roadblock. I'm uncertain what to do about this bit of code:
if (delta.x != 0.0f || delta.y != 0.0f)
{
float pitchDelta = delta.y * GetRotationSpeed();
float yawDelta = delta.x * GetRotationSpeed();
glm::quat q = glm::normalize(glm::cross(glm::angleAxis(-pitchDelta, rightDirection),
glm::angleAxis(-yawDelta, glm::vec3(0.f, 1.0f, 0.0f))));
m_ForwardDirection = glm::rotate(q, m_ForwardDirection);
moved = true;
}
How does GLM allow for crossing and normalizing quaternions? I'm new to the concept, but it doesn't seem mathematically sound. I'm trying to rewrite this code in Rust with the cgmath crate, but there is no counterpart to these two GLM functions. I've tried finding the source code and implementing the functions myself, but I can't find any mention apart from in the ancient documentation.
答案1
得分: 0
So anyway, this code is terrible, so don't feel too bad for not understanding it 
Ok, so what we have here is pretty poor usage of quats tbh. The code is generating two quaternions, one for the rotation around the x axis (I assume), and one around the y axis.
auto qr_xaxis = glm::angleAxis(-pitchDelta, rightDirection);
auto qr_yaxis = glm::angleAxis(-yawDelta, glm::vec3(0.f, 1.0f, 0.0f));
cross in GLM is actually just multiply - naming it cross is very wrong indeed! Effectively all this is doing is combining the X and Y axis rotations into a single rotation:
glm::quat q = qr_xaxis * qr_yaxis;
For reasons unknown, the author has decided that normalizing the result here is a good idea. There shouldn't be any need to normalize that quat here, because by definition qr_xaxis and qr_yaxis are already normalized, and the quat product of two unit quaternions is always a unit quaternion.
Finally, it's rotating m_ForwardDirection by the combined quat.
m_ForwardDirection = glm::rotate(q, m_ForwardDirection);
Honestly, I'm not entirely sure what this code is trying to do, but I will say that the original author's understanding of how quaternions work is clearly not great. I'd treat his tutorial series with a large dose of salt as a result...
英文:
So anyway, this code is terrible, so don't feel too bad for not understanding it
Ok, so what we have here is pretty poor usage of quats tbh. The code is generating two quaternions, one for the rotation around the x axis (I assume), and one around the y axis.
auto qr_xaxis = glm::angleAxis(-pitchDelta, rightDirection);
auto qr_yaxis = glm::angleAxis(-yawDelta, glm::vec3(0.f, 1.0f, 0.0f);
cross in GLM is actually just multiply - naming it cross is very wrong indeed! Effectively all this is doing is combining the X and Y axis rotations into a single rotation:
glm::quat q = qr_xaxis * qr_yaxis;
For reasons unknown, the author has decided that normalising the result here is a good idea. There shouldn't be any need to normalise that quat here, because by definition qr_xaxis and qr_yaxis are already normalised, and the quat product of two unit quaternions is always a unit quaternion.
Finally, its rotating m_ForwardDirection by the combined quat.
m_ForwardDirection = glm::rotate(q, m_ForwardDirection);
Honestly, I'm not entirely sure what this code is trying to do, but I will say that the original authors understanding of how quaternions work, is clearly not great. I'd treat his tutorial series with a large dose of salt as a result...
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