iOS OpenGL ES 2.0 四元数旋转 Slerp 到 XYZ 位置

Question

我正在学习四元数教程：http://www.raywenderlich.com/12667/how-to-rotate-a-3d-object-using-touches-with-opengl 并尝试将地球仪旋转到某个 XYZ 位置。我有一个初始四元数并在地球表面生成一个随机 XYZ 位置。我将该 XYZ 位置传递给以下函数。这个想法是用 GLKMatrix4MakeLookAt 生成一个lookAt向量，并从lookAt矩阵定义slerp步骤的结束四元数。

- (void)rotateToLocationX:(float)x andY:(float)y andZ:(float)z {

    // Turn on the interpolation for smooth rotation
    _slerping = YES; // Begin auto rotating to this location
    _slerpCur = 0;
    _slerpMax = 1.0;
    _slerpStart = _quat;

    // The eye location is defined by the look at location multiplied by this modifier
    float modifier = 1.0;

    // Create a look at vector for which we will create a GLK4Matrix from
    float xEye = x;
    float yEye = y;
    float zEye = z;
    //NSLog(@"%f %f %f %f %f %f",xEye, yEye, zEye, x, y, z);
    _currentSatelliteLocation = GLKMatrix4MakeLookAt(xEye, yEye, zEye, 0, 0, 0, 0, 1, 0);
    _currentSatelliteLocation = GLKMatrix4Multiply(_currentSatelliteLocation,self.effect.transform.modelviewMatrix);

    // Turn our 4x4 matrix into a quat and use it to mark the end point of our interpolation
    //_currentSatelliteLocation = GLKMatrix4Translate(_currentSatelliteLocation, 0.0f, 0.0f, GLOBAL_EARTH_Z_LOCATION);
    _slerpEnd = GLKQuaternionMakeWithMatrix4(_currentSatelliteLocation);

    // Print info on the quat
    GLKVector3 vec = GLKQuaternionAxis(_slerpEnd);
    float angle = GLKQuaternionAngle(_slerpEnd);
    //NSLog(@"%f %f %f %f",vec.x,vec.y,vec.z,angle);

    NSLog(@"Quat end:");
    [self printMatrix:_currentSatelliteLocation];
    //[self printMatrix:self.effect.transform.modelviewMatrix];

}

插值有效，我得到了一个平滑的旋转，但是结束位置从来不是我输入的 XYZ - 我知道这一点，因为我的地球是一个球体，我正在从 Lat Lon 计算 XYZ。我想在旋转后从地球表面的纬度/经度位置直接向下看向地球中心的“lookAt”矢量。我认为这可能与向上向量有关，但我已经尝试了所有有意义的方法。

我做错了什么 - 如何定义一个最终四元数，当我完成旋转时，它会向下看一个向量到地球表面的 XYZ？谢谢！

Answer 1

以下是你的意思吗： 你的地球中心是 (0, 0, 0)，半径是 R，起始位置是 (0, 0, R)，你的最终位置是 (0, R, 0)，所以将地球绕 X 轴旋转 90 度? 如果是这样，只需将lookat功能的眼睛位置设置为您的最终位置，将参数设置为地球中心。

m_target.x = 0.0f;
m_target.y = 0.0f;
m_target.z = 1.0f;

m_right.x = 1.0f;
m_right.y = 0.0f;
m_right.z = 0.0f;

m_up.x = 0.0f;
m_up.y = 1.0f;
m_up.z = 0.0f;
void CCamera::RotateX( float amount )
{
    Point3D target = m_target;
    Point3D up = m_up;

    amount = amount / 180 * PI;

    m_target.x = (cos(PI / 2 - amount) * up.x) + (cos(amount) * target.x);
    m_target.y = (cos(PI / 2 - amount) * up.y) + (cos(amount) * target.y);
    m_target.z = (cos(PI / 2 - amount) * up.z) + (cos(amount) * target.z);

    m_up.x = (cos(amount) * up.x) + (cos(PI / 2 + amount) * target.x);
    m_up.y = (cos(amount) * up.y) + (cos(PI / 2 + amount) * target.y);
    m_up.z = (cos(amount) * up.z) + (cos(PI / 2 + amount) * target.z);

    Normalize(m_target);
    Normalize(m_up);
}

void CCamera::RotateY( float amount )
{
    Point3D target = m_target;
    Point3D right = m_right;

    amount = amount / 180 * PI;

    m_target.x = (cos(PI / 2 + amount) * right.x) + (cos(amount) * target.x);
    m_target.y = (cos(PI / 2 + amount) * right.y) + (cos(amount) * target.y);
    m_target.z = (cos(PI / 2 + amount) * right.z) + (cos(amount) * target.z);

    m_right.x  = (cos(amount) * right.x) + (cos(PI / 2 - amount) * target.x);
    m_right.y  = (cos(amount) * right.y) + (cos(PI / 2 - amount) * target.y);
    m_right.z  = (cos(amount) * right.z) + (cos(PI / 2 - amount) * target.z);

    Normalize(m_target);
    Normalize(m_right);
}

void CCamera::RotateZ( float amount )
{
    Point3D right = m_right;
    Point3D up = m_up;

    amount = amount / 180 * PI;

    m_up.x = (cos(amount) * up.x) + (cos(PI / 2 - amount) * right.x);
    m_up.y = (cos(amount) * up.y) + (cos(PI / 2 - amount) * right.y);
    m_up.z = (cos(amount) * up.z) + (cos(PI / 2 - amount) * right.z);

    m_right.x = (cos(PI / 2 + amount) * up.x) + (cos(amount) * right.x);
    m_right.y = (cos(PI / 2 + amount) * up.y) + (cos(amount) * right.y);
    m_right.z = (cos(PI / 2 + amount) * up.z) + (cos(amount) * right.z);

    Normalize(m_right);
    Normalize(m_up);
}

void CCamera::Normalize( Point3D &p )
{
    float length = sqrt(p.x * p.x + p.y * p.y + p.z * p.z);
    if (1 == length || 0 == length)
    {
        return;
    }

    float scaleFactor = 1.0 / length;
    p.x *= scaleFactor;
    p.y *= scaleFactor;
    p.z *= scaleFactor;
}

Answer 2

这个问题的答案是下面的 rotateTo 函数和 Ray 教程 (http://www.raywenderlich.com/12667/how-to-rotate-a-3d-object-using-touches-with-opengl) 中对代码的更改的组合。正如那篇文章中的一位 cmets 所说，在 GLKQuaternion Q_rot = GLKQuaternionMakeWithAngleAndVector3Axis(angle * 2.0, axis); 中乘以 2.0 的任意因子。删除“2”并使用以下函数创建 _slerpEnd - 之后地球将平滑旋转到指定的 XYZ。

// Rotate the globe using Slerp interpolation to an XYZ coordinate
- (void)rotateToLocationX:(float)x andY:(float)y andZ:(float)z {

    // Turn on the interpolation for smooth rotation
    _slerping = YES; // Begin auto rotating to this location
    _slerpCur = 0;
    _slerpMax = 1.0;
    _slerpStart = _quat;

    // Create a look at vector for which we will create a GLK4Matrix from
    float xEye = x;
    float yEye = y;
    float zEye = z;
    _currentSatelliteLocation = GLKMatrix4MakeLookAt(xEye, yEye, zEye, 0, 0, 0, 0, 1, 0);

    // Turn our 4x4 matrix into a quat and use it to mark the end point of our interpolation
    _slerpEnd = GLKQuaternionMakeWithMatrix4(_currentSatelliteLocation);

}