80 lines
2.5 KiB
Markdown
80 lines
2.5 KiB
Markdown
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# Matrix4 / Matrix4x4
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4x4 矩阵结构体，用于表示完整的 3D 变换（平移、旋转、缩放）、视图和投影变换。
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**头文件：** `#include <XCEngine/Math/Matrix4.h>`
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**命名空间：** `XCEngine::Math`
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## 类型别名
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```cpp
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using Matrix4 = Matrix4x4;
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```
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## 存储方式
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行优先存储 (row-major)：
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```
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m[0][0] m[0][1] m[0][2] m[0][3]
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m[1][0] m[1][1] m[1][2] m[1][3]
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m[2][0] m[2][1] m[2][2] m[2][3]
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m[3][0] m[3][1] m[3][2] m[3][3]
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```
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## 静态工厂方法
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### 基础变换
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| 方法 | 返回值 | 描述 |
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|------|--------|------|
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| [Identity()](identity.md) | `Matrix4` | 单位矩阵 |
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| [Zero()](zero.md) | `Matrix4` | 零矩阵 |
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| [Translation(v)](translation.md) | `Matrix4` | 平移矩阵 |
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| [Scale(v)](scale.md) | `Matrix4` | 缩放矩阵 |
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| [Rotation(q)](rotation.md) | `Matrix4` | 旋转矩阵（四元数） |
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| [TRS(translation, rotation, scale)](trs.md) | `Matrix4` | 完整变换 |
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### 旋转
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| 方法 | 返回值 | 描述 |
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|------|--------|------|
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| [RotationX(radians)](rotationx.md) | `Matrix4` | X 轴旋转 |
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| [RotationY(radians)](rotationy.md) | `Matrix4` | Y 轴旋转 |
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| [RotationZ(radians)](rotationz.md) | `Matrix4` | Z 轴旋转 |
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### 相机变换
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| 方法 | 返回值 | 描述 |
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|------|--------|------|
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| [LookAt(eye, target, up)](lookat.md) | `Matrix4` | 视图矩阵 |
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| [Perspective(fov, aspect, near, far)](perspective.md) | `Matrix4` | 透视投影 |
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| [Orthographic(left, right, bottom, top, near, far)](orthographic.md) | `Matrix4` | 正交投影 |
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## 实例方法
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### 乘法
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| 方法 | 返回值 | 描述 |
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|------|--------|------|
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| `operator*(Matrix4, Matrix4)` | `Matrix4` | 矩阵乘法 |
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| `operator*(Matrix4, Vector4)` | `Vector4` | 矩阵-向量乘法 |
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| [MultiplyPoint(v)](multiplypoint.md) | `Vector3` | 点变换（带平移） |
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| [MultiplyVector(v)](multiplyvector.md) | `Vector3` | 方向变换（不带平移） |
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### 分解
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| 方法 | 返回值 | 描述 |
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|------|--------|------|
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| [Transpose()](transpose.md) | `Matrix4` | 转置矩阵 |
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| [Inverse()](inverse.md) | `Matrix4` | 逆矩阵 |
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| [Determinant()](determinant.md) | `float` | 行列式 |
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| [GetTranslation()](gettranslation.md) | `Vector3` | 获取平移分量 |
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| [GetRotation()](getrotation.md) | `Quaternion` | 获取旋转分量 |
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| [GetScale()](getscale.md) | `Vector3` | 获取缩放分量 |
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| [Decompose(translation, rotation, scale)](decompose.md) | `void` | 分解所有分量 |
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## 相关文档
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- [Math 模块总览](../math.md) - 返回 Math 模块总览
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