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docs/api/math/plane/frompoints.md
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docs/api/math/plane/frompoints.md
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# Plane::FromPoints
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```cpp
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static Plane FromPoints(const Vector3& a, const Vector3& b, const Vector3& c)
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```
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从三个不共线点创建平面。
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**参数:**
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- `a` - 第一个点
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- `b` - 第二个点
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- `c` - 第三个点
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**返回:** `Plane` - 由三点定义的平面
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**复杂度:** O(1)
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**示例:**
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```cpp
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Plane plane = Plane::FromPoints(p0, p1, p2);
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```
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docs/api/math/plane/getclosestpoint.md
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docs/api/math/plane/getclosestpoint.md
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# Plane::GetClosestPoint
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```cpp
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Vector3 GetClosestPoint(const Vector3& point) const
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```
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计算平面上最接近给定点的点。
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**参数:**
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- `point` - 参考点
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**返回:** `Vector3` - 平面上最接近的点
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**复杂度:** O(1)
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**示例:**
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```cpp
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Vector3 closest = plane.GetClosestPoint(point);
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```
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docs/api/math/plane/getdistancetopoint.md
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docs/api/math/plane/getdistancetopoint.md
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# Plane::GetDistanceToPoint
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```cpp
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float GetDistanceToPoint(const Vector3& point) const
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```
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计算点到平面的有符号距离。
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**参数:**
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- `point` - 要计算的点
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**返回:** `float` - 有符号距离
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**复杂度:** O(1)
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**示例:**
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```cpp
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float dist = plane.GetDistanceToPoint(point);
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```
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docs/api/math/plane/getside.md
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docs/api/math/plane/getside.md
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# Plane::GetSide
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```cpp
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bool GetSide(const Vector3& point) const
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```
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判断点在平面的哪一侧。
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**参数:**
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- `point` - 要测试的点
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**返回:** `bool` - true 表示点在法线方向一侧
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**复杂度:** O(1)
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**示例:**
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```cpp
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if (plane.GetSide(point)) { /* point is on normal side */ }
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```
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docs/api/math/plane/intersects.md
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docs/api/math/plane/intersects.md
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# Plane::Intersects
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```cpp
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bool Intersects(const Sphere& sphere) const
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```
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检测平面是否与球体相交。
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**参数:**
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- `sphere` - 要检测的球体
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**返回:** `bool` - true 表示相交
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**复杂度:** O(1)
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**示例:**
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```cpp
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if (plane.Intersects(sphere)) { /* collision */ }
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```
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docs/api/math/plane/plane.md
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docs/api/math/plane/plane.md
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# Plane
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3D 平面结构体,由法线和距离表示。
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**头文件:** `#include <XCEngine/Math/Plane.h>`
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**命名空间:** `XCEngine::Math`
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## 结构体定义
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```cpp
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struct Plane {
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Vector3 normal = Vector3::Up();
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float distance = 0.0f;
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};
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```
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## 构造函数
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- `Plane()` - 默认构造 (y=0 平面)
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- `Plane(const Vector3& normal, float distance)` - 从法线和距离构造
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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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| [FromPoints(a, b, c)](frompoints.md) | `Plane` | 从三个不共线点创建 |
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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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| [GetDistanceToPoint(point)](getdistancetopoint.md) | `float` | 点到平面的有符号距离 |
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| [GetClosestPoint(point)](getclosestpoint.md) | `Vector3` | 平面上最接近给定点的点 |
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| [GetSide(point)](getside.md) | `bool` | 点在平面的哪一侧 |
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| [Intersects(sphere)](intersects.md) | `bool` | 与球体相交 |
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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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