四元数"lookAt"功能 [英] Quaternion "lookAt" function
问题描述
我正在努力解决以下问题.我正在使用骨骼动画,所以我希望玩家的头部跟随空间中的另一个对象.我的上轴是+ Z,前轴是+ Y,四元数的大小以W为单位.我尝试对gluLookAt使用mesa代码,并使用3x3矩阵转换为四元数,但是它不能按预期工作所以我走了另一个方向...
Im struggling with the following problem. Im working with bone animation and I want (ie) the head of the player to follow an another object in space. My up axis is +Z my forward axis is +Y, and the magnitude of the quaternion is in W. I tried to use the mesa code for gluLookAt and use the 3x3 matrix to transform to a quaternion but it doesn't work as expected so I go in another direction...
到目前为止,我获得了以下代码,该代码几乎"在至少播放器的头部朝着正确方向旋转(但是X角度似乎影响Y旋转轴)的情况下起作用,但是在跟随时却朝上看地板上约65度的物体:
So far I got the following code that is "almost" working at least the head of the player is rotating (however the X angle seems to affect the Y rotation axis) in the good direction but its looking straight up instead on following an object on the floor at about 65 degree:
qt LookRotation( v3 lookAt, v3 upDirection )
{
qt t;
v3 forward = lookAt;
v3 up = upDirection;
OrthoNormalize( &forward, &up );
v3 right = v3_cross( up, forward );
mat3 m = mat3_make( right.x, up.x, forward.x,
right.y, up.y, forward.y,
right.z, up.z, forward.z );
t.w = sqrtf( 1.0f +
m.r[ 0 ].x +
m.r[ 1 ].y +
m.r[ 2 ].z ) * 0.5f;
float w4_recip = 1.0f / ( 4.0f * t.w );
t.x = ( m.r[ 2 ].y - m.r[ 1 ].z ) * w4_recip;
t.y = ( m.r[ 0 ].z - m.r[ 2 ].x ) * w4_recip;
t.z = ( m.r[ 1 ].x - m.r[ 0 ].y ) * w4_recip;
t = qt_normalize( t );
return t;
}
... ... ...
... ... ...
v3 v = v3_sub( vec4_to_v3( transform.world.r[ 3 ] /* The object XYZ location in the world */),
skeleton->final_pose.location[ i ] /* i = The head joint location */ );
v = v3_normalize( v );
qt q = LookRotation( v,
v3_make( 0.0f, 0.0f, 1.0f ) );
有人可以帮我解决这个问题吗?我有点像四元数,但我真的不知道我该在哪里搞砸.经过大量研究后,基本上我想做的是类似Unity API的事情: http: //docs.unity3d.com/Documentation/ScriptReference/Quaternion.LookRotation.html
Can someone help me figuring out this problem... Im kinda new with quaternions and don't really know where I could have messed up. After quite some research basically what I want to do is something like the Unity API: http://docs.unity3d.com/Documentation/ScriptReference/Quaternion.LookRotation.html
推荐答案
我认为此功能将满足您的需求:
I think this function will do what you need:
/// <summary>
/// Evaluates a rotation needed to be applied to an object positioned at sourcePoint to face destPoint
/// </summary>
/// <param name="sourcePoint">Coordinates of source point</param>
/// <param name="destPoint">Coordinates of destionation point</param>
/// <returns></returns>
public static Quaternion LookAt(Vector3 sourcePoint, Vector3 destPoint)
{
Vector3 forwardVector = Vector3.Normalize(destPoint - sourcePoint);
float dot = Vector3.Dot(Vector3.forward, forwardVector);
if (Math.Abs(dot - (-1.0f)) < 0.000001f)
{
return new Quaternion(Vector3.up.x, Vector3.up.y, Vector3.up.z, 3.1415926535897932f);
}
if (Math.Abs(dot - (1.0f)) < 0.000001f)
{
return Quaternion.identity;
}
float rotAngle = (float)Math.Acos(dot);
Vector3 rotAxis = Vector3.Cross(Vector3.forward, forwardVector);
rotAxis = Vector3.Normalize(rotAxis);
return CreateFromAxisAngle(rotAxis, rotAngle);
}
// just in case you need that function also
public static Quaternion CreateFromAxisAngle(Vector3 axis, float angle)
{
float halfAngle = angle * .5f;
float s = (float)System.Math.Sin(halfAngle);
Quaternion q;
q.x = axis.x * s;
q.y = axis.y * s;
q.z = axis.z * s;
q.w = (float)System.Math.Cos(halfAngle);
return q;
}
此代码来自此处: https://gamedev.stackexchange.com/questions/15070/orienting-一个模型面对一个目标 我只是对其稍作修改以适合我的情况,这是在不使用Unity3D的情况下实现了transform.LookAt.
This code comes from here: https://gamedev.stackexchange.com/questions/15070/orienting-a-model-to-face-a-target I just slightly modified it to fit my case, which was implementation of the transform.LookAt without using Unity3D.
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