四元数矩阵转化

//公式都是网上搜罗的，下面这些经过简单的测试，确认可用。

//ps: x,y,z,w 分别是四元素的四个值。

稍微修改下就可以用。

// 由旋转矩阵创建四元数
inline CQuaternion(const_Matrix4& m)
{
float tr, s, q[4];
int i, j, k;
int nxt[3] = {1, 2, 0 };
// 计算矩阵轨迹
tr = m._11 + m._22 + m._33;
// 检查矩阵轨迹是正还是负
if(tr>0.0f)
{
s = sqrt(tr + 1.0f);
this->w = s / 2.0f;
s = 0.5f / s;
this->x = (m._23 - m._32) * s;
this->y = (m._31 - m._13) * s;
this->z = (m._12 - m._21) * s;
}
else
{
// 轨迹是负
// 寻找m11 m22 m33中的最大分量
i = 0;
if(m.m[1][1]>m.m[0][0]) i = 1;
if(m.m[2][2]>m.m[i][i]) i = 2;
j = nxt[i];
k = nxt[j];
s = sqrt((m.m[i][i] - (m.m[j][j] + m.m[k][k])) + 1.0f); q[i] = s * 0.5f;
if( s!= 0.0f) s = 0.5f / s;
q[3] = (m.m[j][k] - m.m[k][j]) * s;
q[j] = (m.m[i][j] - m.m[j][i]) * s;
q[k] = (m.m[i][k] - m.m[k][i]) * s;
this->x = q[0];
this->y = q[1];
this->z = q[2];
this->w = q[3];
}
};
// 由欧拉角创建四元数
inline CQuaternion(const_Vector3& angle)
{
float cx = cos(angle.x/2);
float sx = sin(angle.x/2);
float cy = cos(angle.y/2);
float sy = sin(angle.y/2);
float cz = cos(angle.z/2);
float sz = sin(angle.z/2);
this->w = cx*cy*cz + sx*sy*sz;
this->x = sx*cy*cz - cx*sy*sz;
this->y = cx*sy*cz + sx*cy*sz;
this->z = cx*cy*sz - sx*sy*cz;
};
// 给定角度和轴创建四元数
inline CQuaternion(_Vector3 anxi, const float& angle) {
CVector3 t;
t.x = anxi.x;
t.y = anxi.y;
t.z = anxi.z;
t.Normalize();
float cosa = cos(angle);
float sina = sin(angle);
this->w = cosa;
this->x = sina * t.x;
this->y = sina * t.y;
this->z = sina * t.z;
};
// 由旋转四元数推导出矩阵
inline CMatrix4 GetMatrixLH()
{
CMatrix4 ret;
float xx = x*x;
float yy = y*y;
float zz = z*z;
float xy = x*y;
float wz = w*z;
float wy = w*y;
float xz = x*z;
float yz = y*z;
float wx = w*x;
ret._11 = 1.0f-2*(yy+zz);
ret._12 = 2*(xy-wz);
ret._13 = 2*(wy+xz);
ret._14 = 0.0f;
ret._21 = 2*(xy+wz);
ret._22 = 1.0f-2*(xx+zz);
ret._23 = 2*(yz-wx);
ret._24 = 0.0f;
ret._31 = 2*(xy-wy);
ret._32 = 2*(yz+wx);
ret._33 = 1.0f-2*(xx+yy);
ret._34 = 0.0f;
ret._41 = 0.0f;
ret._42 = 0.0f;
ret._43 = 0.0f;
ret._44 = 1.0f;
return ret;
};
inline CMatrix4 GetMatrixRH() {
CMatrix4 ret;
float xx = x*x;
float yy = y*y;
float zz = z*z;
float xy = x*y;
float wz = -w*z;
float wy = -w*y;
float xz = x*z;
float yz = y*z;
float wx = -w*x;
ret._11 = 1.0f-2*(yy+zz);
ret._12 = 2*(xy-wz);
ret._13 = 2*(wy+xz);
ret._14 = 0.0f;
ret._21 = 2*(xy+wz);
ret._22 = 1.0f-2*(xx+zz);
ret._23 = 2*(yz-wx);
ret._24 = 0.0f;
ret._31 = 2*(xy-wy);
ret._32 = 2*(yz+wx);
ret._33 = 1.0f-2*(xx+yy);
ret._34 = 0.0f;
ret._41 = 0.0f;
ret._42 = 0.0f;
ret._43 = 0.0f;
ret._44 = 1.0f;
return ret;
};
// 由四元数返回欧拉角（主要是这个dx api里没有提供）
inline CVector3 GetEulerAngle()
{
CVector3 ret;
float test = y*z + x*w;
if(test > 0.4999f)
{
ret.z = 2.0f * atan2(y, w);
ret.y = PIOver2;
ret.x = 0.0f;
return ret;
}
if(test < -0.4999f)
{
ret.z = 2.0f * atan2(y, w);
ret.y = -PIOver2;
ret.x = 0.0f;
return ret;
}
float sqx = x * x;
float sqy = y * y;
float sqz = z * z;
ret.z = atan2(2.0f * z * w - 2.0f * y * x, 1.0f - 2.0f * sqz - 2.0f * sqx);
ret.y = asin(2.0f * test);
ret.x = atan2(2.0f * y * w - 2.0f * z * x, 1.0f - 2.0f * sqy - 2.0f * sqx);
return ret;
};。