Java 在 1 个轴上旋转四元数？
声明：本页面是StackOverFlow热门问题的中英对照翻译，遵循CC BY-SA 4.0协议，如果您需要使用它，必须同样遵循CC BY-SA许可，注明原文地址和作者信息，同时你必须将它归于原作者（不是我）：StackOverFlow
原文地址: http://stackoverflow.com/questions/4436764/
Warning: these are provided under cc-by-sa 4.0 license. You are free to use/share it, But you must attribute it to the original authors (not me):
StackOverFlow
rotating a quaternion on 1 axis?
提问by William
I have a model rotated by a quaternion. I can only set the rotation, I can't add or subtract from anything. I need to get the value of an axis, and than add an angle to it (maybe a degree or radian?) and than re-add the modified quaternion.
我有一个由四元数旋转的模型。我只能设置旋转，不能加减任何东西。我需要获取轴的值，然后为其添加一个角度（可能是度数或弧度？），然后重新添加修改后的四元数。
How can I do this? (answer on each axis).
我怎样才能做到这一点？（在每个轴上回答）。
采纳答案by sje397
You can multiply two quaternions together to produce a third quaternion that is the result of the two rotations. Note that quaternion multiplication is not commutative, meaning order matters (if you do this in your head a few times, you can see why).
您可以将两个四元数相乘以产生作为两次旋转结果的第三个四元数。请注意，四元数乘法不是可交换的，这意味着顺序很重要（如果你在头脑中这样做几次，你就会明白为什么）。
You can produce a quaternion that represents a rotation by a given angle around a particular axis with something like this (excuse the fact that it is c++, not java):
您可以生成一个四元数，表示围绕特定轴按给定角度旋转，类似这样的东西（请原谅它是 c++，而不是 java）：
Quaternion Quaternion::create_from_axis_angle(const double &xx, const double &yy, const double &zz, const double &a)
{
// Here we calculate the sin( theta / 2) once for optimization
double factor = sin( a / 2.0 );
// Calculate the x, y and z of the quaternion
double x = xx * factor;
double y = yy * factor;
double z = zz * factor;
// Calcualte the w value by cos( theta / 2 )
double w = cos( a / 2.0 );
return Quaternion(x, y, z, w).normalize();
}
So to rotate around the x axis for example, you could create a quaternion with createFromAxisAngle(1, 0, 0, M_PI/2)and multiply it by the current rotation quaternion of your model.
例如，要绕 x 轴旋转，您可以创建一个四元数createFromAxisAngle(1, 0, 0, M_PI/2)并将其乘以模型的当前旋转四元数。
回答by Greg
Made a runable code from sje397's post for testing other details later, thought I would share. Eventually using C the reason for no Quaternion class.
从 sje397 的帖子中制作了一个可运行的代码，用于稍后测试其他细节，我想我会分享。最终使用 C 是没有 Quaternion 类的原因。
#include <iostream>
#include <math.h>
using namespace std;
struct float4{
float x;
float y;
float z;
float w;
};
float4 make_float4(float x, float y, float z, float w){
float4 quat = {x,y,z,w};
return quat;
}
float dot(float4 a)
{
return (((a.x * a.x) + (a.y * a.y)) + (a.z * a.z)) + (a.w * a.w);
}
float4 normalize(float4 q)
{
float num = dot(q);
float inv = 1.0f / (sqrtf(num));
return make_float4(q.x * inv, q.y * inv, q.z * inv, q.w * inv);
}
float4 create_from_axis_angle(const float &xx, const float &yy, const float &zz, const float &a)
{
// Here we calculate the sin( theta / 2) once for optimization
float factor = sinf( a / 2.0f );
float4 quat;
// Calculate the x, y and z of the quaternion
quat.x = xx * factor;
quat.y = yy * factor;
quat.z = zz * factor;
// Calcualte the w value by cos( theta / 2 )
quat.w = cosf( a / 2.0f );
return normalize(quat);
}
int main()
{
float degrees = 10.0f;
float4 quat = create_from_axis_angle(1, 0, 0, degrees*(3.14159f/180.0f));
cout << "> (" << quat.x << ", " <<quat.y << ", " <<quat.z << ", " <<quat.w << ")" << endl;
return 0;
}
Output
输出
(0.0871557, 0, 0, 0.996195)
(0.0871557, 0, 0, 0.996195)
