87 lines
2.1 KiB
Markdown
87 lines
2.1 KiB
Markdown
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# Quaternion
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四元数结构体，用于表示 3D 旋转，避免欧拉角的万向锁问题。
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## 头文件
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```cpp
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#include <XCEngine/Math/Quaternion.h>
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```
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## 命名空间
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`XCEngine::Math`
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## 结构体定义
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```cpp
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struct Quaternion {
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float x = 0.0f;
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float y = 0.0f;
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float z = 0.0f;
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float w = 1.0f; // w 是标量分量
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};
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```
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四元数格式: `(x, y, z, w)` = `(vec, w)`
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## 静态工厂方法
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| 方法 | 返回值 | 描述 |
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|------|--------|------|
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| `Identity()` | `Quaternion` | 返回 (0, 0, 0, 1)，恒等旋转 |
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| `FromAxisAngle(axis, radians)` | `Quaternion` | 从轴角创建 |
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| `FromEulerAngles(pitch, yaw, roll)` | `Quaternion` | 从欧拉角创建（弧度） |
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| `FromEulerAngles(euler)` | `Quaternion` | 从 Vector3 欧拉角创建 |
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| `FromRotationMatrix(matrix)` | `Quaternion` | 从旋转矩阵创建 |
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| `Slerp(a, b, t)` | `Quaternion` | 球面线性插值 |
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| `LookRotation(forward, up)` | `Quaternion` | 看向方向 |
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## 实例方法
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| 方法 | 返回值 | 描述 |
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|------|--------|------|
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| `ToEulerAngles()` | `Vector3` | 转换为欧拉角（弧度） |
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| `ToMatrix4x4()` | `Matrix4` | 转换为 4x4 旋转矩阵 |
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| `Inverse()` | `Quaternion` | 共轭/逆四元数 |
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| `Dot(other)` | `float` | 点积 |
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| `Magnitude()` | `float` | 模长 |
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| `Normalized()` | `Quaternion` | 归一化 |
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| `Normalize(q)` | `Quaternion` | 归一化（静态） |
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## 运算符
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| 运算符 | 描述 |
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|--------|------|
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| `operator*(Quaternion, Quaternion)` | 组合旋转 |
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## 与 Vector3 的乘法
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```cpp
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Vector3 operator*(const Quaternion& q, const Vector3& v);
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```
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用四元数旋转向量。
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## 使用示例
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```cpp
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// 创建旋转
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Quaternion rot = Quaternion::FromEulerAngles(0.0f, 90.0f * DEG_TO_RAD, 0.0f);
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// 组合旋转
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Quaternion combined = rot1 * rot2;
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// 球面插值
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Quaternion lerped = Quaternion::Slerp(rot1, rot2, 0.5f);
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// 旋转向量
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Vector3 rotated = rot * Vector3::Forward();
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// 转换
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Vector3 euler = rot.ToEulerAngles();
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Matrix4 mat = rot.ToMatrix4x4();
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// 看向目标
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Quaternion lookAt = Quaternion::LookRotation(target - position);
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```
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