LWJGL-使用四元数和转换矩阵在6DOF相机中实现“滚动"的问题 [英] LWJGL - Problems implementing 'roll' in a 6DOF Camera using quaternions and a translation matrix
问题描述
我在这个问题上花了几周时间，似乎找不到合适的解决方案，需要一些建议.
I've spent a couple weeks on this issue and can't seem to find a proper solution and need some advice.
我正在使用LWJGL/Java创建Camera类，并正在使用四元数来处理轴承(偏航)，俯仰和横滚旋转.我希望这款相机能够处理3D空间中所有6度的运动并滚动.方位角，俯仰角和横滚都是四元数.我将它们乘以一个变化"四元数，然后从中创建一个翻译矩阵.我将其放入浮动缓冲区，然后将Modelview矩阵乘以包含旋转矩阵的缓冲区.
I'm working on creating a Camera class using LWJGL/Java, and am using Quaternions to handle bearing (yaw), pitch and roll rotations. I'd like this camera to handle all 6 degrees of movement in 3D space, and roll. Bearing, Pitch and Roll are all quaternions. I multiply them into a 'change' quaternion, and create a translation matrix from that. I put that in a float buffer, and multiply the modelview matrix by my buffer containing the rotation matrix.
我可以使方位角和俯仰角旋转正常工作，但是当我实施侧滚时，我遇到了问题.主要是，绕Z轴旋转(滚动)似乎不起作用.每当我滚动"相机时，它似乎绕全局Z轴而不是本地相机方向轴滚动.通常，我可以根据四元数的乘积顺序得到3个中的2个，但是我不能让它们一起工作.
I can get the bearing and pitch rotations to work properly, but when I implement roll, I'm running into issues. Mainly, rotating around the Z-axis (rolling) doesn't seem to work. When ever I "roll" the camera, it seems to roll around the global Z axis instead of the local camera direction axis. I can usually get 2 of the 3 to work depending on the order I multiply the quaternions, but I can't get them working together.
由于它们都是独立工作的，因此我假设定向方法存在问题，我将它们组合起来并构建了旋转矩阵.我在粘贴整个类时遇到问题，所以这里是与轮换有关的方法和声明:
Since they all work independently, I'm assuming there's something wrong with my orientation method where I combine them and build a rotation matrix. I'm having problems pasting the whole class in, so here are the methods and declarations relating to rotation:
private final static float DEGTORAD = (float)(Math.PI/180);
//Eye - position of the camera in the 3D world.
private Vector3f eye;
//Camera axis vectors, calculated each time reorient() is called.
//Initialized to global x, y, and z axis initially.
private Vector3f up;
private Vector3f right;
private Vector3f direction;
//Angles of rotation (in degrees)
private float pitchAngle;
private float bearingAngle;
private float rollAngle;
private Quaternion pitch;
private Quaternion bearing;
private Quaternion roll;
private FloatBuffer viewMatrixBuffer = BufferUtils.createFloatBuffer(16);
private Quaternion currentOrientation;
...
/**
* Change the bearing (yaw)
* @param bearing delta in degrees
*/
public void bearing(float bearingDelta){
bearingAngle += bearingDelta;
if(bearingAngle > 360){
bearingAngle -= 360;
}else if(bearingAngle < 0){
bearingAngle += 360;
}
bearing.setFromAxisAngle(new Vector4f(0f, 1f, 0f, bearingAngle * DEGTORAD));
bearing.normalise();
}
/**
* Change the pitch
* @param pitch delta in degrees
*/
public void pitch(float pitchDelta){
pitchAngle += pitchDelta;
if(pitchAngle > 360){
pitchAngle -= 360;
}else if(pitchAngle < 0){
pitchAngle += 360;
}
pitch.setFromAxisAngle(new Vector4f(1f, 0f, 0f, pitchAngle * DEGTORAD));
pitch.normalise();
}
/**
* @param initialRoll
*/
public void roll(float initialRoll) {
rollAngle += initialRoll;
if(rollAngle > 360){
rollAngle -= 360;
}else if(rollAngle < 0){
rollAngle += 360;
}
roll.setFromAxisAngle(new Vector4f(0, 0, 1, rollAngle * DEGTORAD));
roll.normalise();
}
/**
* Change direction to focus on a certain point in the world
* @param eye
*/
public void lookThrough(){
reorient();
GL11.glMultMatrix(viewMatrixBuffer);
}
public void reorient(){
//Multiply in order: bearing, pitch, roll. Non-commutative!
Quaternion change = new Quaternion();
Quaternion.mul(bearing, pitch, change);
Quaternion.mul(roll, change, change);
// orient the camera...
Matrix4f rotationMatrix = getRotationMatrix(change);
//Get the looking direction
direction.x = rotationMatrix.m20;
direction.y = rotationMatrix.m21;
direction.z = rotationMatrix.m22;
//Set the position
rotationMatrix.m30 = eye.x;
rotationMatrix.m31 = eye.y;
rotationMatrix.m32 = eye.z;
rotationMatrix.m33 = 1;
rotationMatrix.invert();
rotationMatrix.store(viewMatrixBuffer);
viewMatrixBuffer.rewind();
Vector3f.cross(new Vector3f(0,1,0), direction, null).normalise(right);
Vector3f.cross(right, direction, null).normalise(up);
}
Vector3f，Quaternion和Matrix4f都是LWJGL类，不是定制的.
Vector3f, Quaternion, and Matrix4f are all LWJGL classes, not custom made.
所以我的问题是，给定3个代表轴承，俯仰和横滚的四元数，如何修改ModelView矩阵以准确表示这些旋转?
So my question is, given 3 Quaternions representing Bearing, Pitch and Roll, how do I modify the ModelView matrix to accurately represent these rotations?
我觉得这非常接近.请参阅RiverC注释中的Gist链接.旋转了许多度之后，视图会跳很多圈，然后在滚动时恢复正常.它的要旨在那里，但仍然略有偏离.
I feel that this is very close. See the Gist link in RiverC's comment. After rotating so many degrees, the view jumps around a lot before coming back to normal when rolling. The gist of it is there, but it's still slightly off.
推荐答案
您正在以错误的顺序进行乘法.
You're doing the multiplications in the wrong order.
对于两次旋转q1和q2，如果q2跟在q1之后(因为旋转通常是非相交的)，则将q2 * q1乘以
For two rotations q1 and q2, if q2 is to follow q1 (since rotations are generally non-communitive) you multiply q2*q1.
在万向节式系统(例如FPS控件)中，优先级顺序始终为偏航，俯仰，横滚.这将建议以下数学:
In a gimbal style system such as controls for a FPS, the priority order is always yaw, pitch, roll. This would suggest the following math:
roll * pitch * yaw
从Java角度讲，我建议不要为每次更新都创建新的四元数
As a java point, I would suggest not creating new Quaternions for every update but anyway
change = Quaternion.mul(Quaternion.mul(roll, pitch, change), yaw, change);
如果您查看代码，则第四个四元数将被结果覆盖，因此无需在每帧/每次更新时都对其进行重置或重新创建.
If you look at the code, the third Quaternion will just be overwritten with the result, so no need to reset it or recreate it each frame / update.
这种轮换顺序的事情令人困惑，但是如果您查看有关四元数的Wiki页面，这是一般规则.
This rotational order thing is confusing, but if you look at the Wiki page on Quaternions, it's the general rule.
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