opengl es 从零开始系列9动画基础和关键帧动画(4)

不过是比Vector 3D多加了一个GLfloat，经常把它当成w字段。所以对我们来说一个四元数就象这样：typedef struct { GLfloat x; GLfloat y; GLfloat z; GLfloat w;} Quaternion3D;Normalizing a Quaternion 四元数归一化这个十分简单。四元数代表空间里的一个方向，就像Vector3Ds，实际距离的值并不在意，并且在进行一些计算之前／之后使他们正常下降到1.0。完成这些我们可以这样做：static inline void Quaternion3DNormalize(Quaternion3D

*quaternion){ GLfloat magnitude; magnitude =

sqrtf((quaternion->x * quaternion->x) + (quaternion->y * quaternion->y) + (quaternion->z * quaternion->z) + (quaternion->w * quaternion->w)); quaternion->x /= magnitude; quaternion->y /= magnitude; quaternion->z /= magnitude;

quaternion->w /= magnitude;}Creating a Quaternion from a Rotation matrix 从一个旋转矩阵中创建一个四元数 如果我们没法在四元数同其他的对象转换过程中保存旋转角度信息的话，四元数对我们来说还是没用的。首先我们从一个旋转矩阵中创建一个四元数。代码如下： static inline Quaternion3D Quaternion3DMakeWithMatrix3D(Matrix3D matrix){ Quaternion3D quat; GLfloat trace, s; trace

= matrix[0] + matrix[5] + matrix[10]; if (trace > 0.0f) { s = sqrtf(trace + 1.0f); quat.w = s * 0.5f; s = 0.5f / s; quat.x = (matrix[9] - matrix[6]) * s; quat.y = (matrix[2] - matrix[8]) * s; quat.z = (matrix[4] - matrix[1]) * s; } else { NSInteger biggest; enum {A,E,I}; if (matrix[0] > matrix[5]) if (matrix[10] > matrix[0]) biggest = I; else biggest = A; else if (matrix[10] > matrix[0]) biggest = I; else biggest = E; switch (biggest) { case A: s = sqrtf(matrix[0] - (matrix[5] + matrix[10]) + 1.0f);

if (s > QUATERNION_TRACE_ZERO_TOLERANCE) { quat.x = s * 0.5f; s = 0.5f / s; quat.w = (matrix[9] - matrix[6]) * s; quat.y = (matrix[1] + matrix[4]) * s; quat.z = (matrix[2] +

matrix[8]) * s; break; } s = sqrtf(matrix[10] - (matrix[0] + matrix[5]) + 1.0f); if (s > QUATERNION_TRACE_ZERO_TOLERANCE) { quat.z = s * 0.5f; s = 0.5f / s; quat.w = (matrix[4] -

matrix[1]) * s; quat.x = (matrix[8] + matrix[2]) * s; quat.y = (matrix[9] +

matrix[6]) * s; break; } s = sqrtf(matrix[5] - (matrix[10] + matrix[0]) + 1.0f); if (s > QUATERNION_TRACE_ZERO_TOLERANCE) { quat.y = s * 0.5f; s = 0.5f / s; quat.w = (matrix[2] - matrix[8]) * s; quat.z = (matrix[6] + matrix[9]) * s; quat.x = (matrix[4] +

matrix[1]) * s; break; break; case E: = sqrtf(matrix[5] - (matrix[10] + matrix[0]) + 1.0f); if (s > QUATERNION_TRACE_ZERO_TOLERANCE) { quat.y = s * 0.5f; s = 0.5f / s; quat.w = (matrix[2] - matrix[8]) * s; quat.z = (matrix[6] + matrix[9]) * s; quat.x = (matrix[4] +

matrix[1]) * s; break; s = sqrtf(matrix[10] - (matrix[0] + matrix[5]) + 1.0f); if (s > QUATERNION_TRACE_ZERO_TOLERANCE) { quat.z = s * 0.5f; s = 0.5f / s; quat.w = (matrix[4] -

} s } matrix[1]) * s; quat.x = (matrix[8] + matrix[2]) * s; quat.y = (matrix[9] +

matrix[6]) * s; break; } s = sqrtf(matrix[0] - (matrix[5] + matrix[10]) + 1.0f); if (s > QUATERNION_TRACE_ZERO_TOLERANCE) { quat.x = s * 0.5f; s = 0.5f / s; quat.w = (matrix[9] - matrix[6]) * s; quat.y = (matrix[1] + matrix[4]) * s; quat.z = (matrix[2] +

matrix[8]) * s; break; break; case I: = sqrtf(matrix[10] - (matrix[0] + matrix[5]) + 1.0f); if (s > QUATERNION_TRACE_ZERO_TOLERANCE) { quat.z = s * 0.5f; s = 0.5f / s; quat.w = (matrix[4] - matrix[1]) * s; quat.x = (matrix[8] + matrix[2]) * s; quat.y = (matrix[9] +

matrix[6]) * s; break; s = sqrtf(matrix[0] - (matrix[5] + matrix[10]) + 1.0f); if (s > QUATERNION_TRACE_ZERO_TOLERANCE) { quat.x = s * 0.5f; s = 0.5f / s; quat.w = (matrix[9] -

} s } matrix[6]) * s; quat.y = (matrix[1] + matrix[4]) * s; quat.z = (matrix[2] +

matrix[8]) * s; break; } s = sqrtf(matrix[5] - (matrix[10] + matrix[0]) + 1.0f); if (s > QUATERNION_TRACE_ZERO_TOLERANCE) { quat.y = s * 0.5f; s = 0.5f / s; quat.w = (matrix[2] - matrix[8]) * s; quat.z = (matrix[6] + matrix[9]) * s; quat.x = (matrix[4] +

matrix[1]) * s; break; } break; default: break; } } return quat;}好的，如果你想真正知道这里 …… 此处隐藏：2077字，全部文档内容请下载后查看。喜欢就下载吧 ……