threejs-math

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Original

English

🇨🇳

Translation

Chinese

When to use this skill

何时使用此 skill

ALWAYS use this skill when the user mentions:

Vector/matrix math order,
```
applyQuaternion
```
,
```
lookAt
```
, world vs local transforms
Bounding volumes
```
Box3
```
/
```
Sphere
```
, containment/intersection tests
```
Ray
```
vs
```
Plane
```
vs
```
Frustum
```
tests (without full picking pipeline)

IMPORTANT: math vs objects vs animation

Need	Skill
Raw math types	threejs-math
`Raycaster` + layers picking	threejs-objects
QuaternionKeyframeTrack playback	threejs-animation

Trigger phrases include:

"Vector3", "Matrix4", "Quaternion", "Box3", "Ray", "Frustum"
"向量", "矩阵", "四元数", "包围盒"

当用户提到以下内容时，始终使用此 skill：

向量/矩阵运算顺序、
```
applyQuaternion
```
、
```
lookAt
```
、世界变换与局部变换
包围体
```
Box3
```
/
```
Sphere
```
，包含/相交测试
```
Ray
```
、
```
Plane
```
与
```
Frustum
```
测试（不涉及完整的拾取流程）

重要：数学、对象与动画的区分

需求	Skill
原始数学类型	threejs-math
`Raycaster` + layers 拾取	threejs-objects
QuaternionKeyframeTrack 播放	threejs-animation

触发短语包括：

"Vector3"、"Matrix4"、"Quaternion"、"Box3"、"Ray"、"Frustum"
"向量"、"矩阵"、"四元数"、"包围盒"

How to use this skill

如何使用此 skill

Conventions: multiply vectors by matrices on the left as three.js examples show; call
```
updateMatrixWorld
```
before world-space queries (threejs-objects).
Bounding:
```
Box3().setFromObject(object)
```
for rough bounds; refine per need.
Collision-ish checks:
```
ray.intersectBox
```
,
```
sphere.containsPoint
```
, etc., per docs.
Addon structures:
```
Octree
```
/
```
OBB
```
for games—cite addon pages, avoid copying full API tables here.
Color:
```
Color
```
conversions relate to materials/textures—cross-link.
Random sampling:
```
MeshSurfaceSampler
```
for distributing points on meshes.

See examples/workflow-ray-aabb.md.

约定：按照 three.js 示例所示，将矩阵放在左侧与向量相乘；执行世界空间查询前调用
```
updateMatrixWorld
```
（threejs-objects）。
包围体：使用
```
Box3().setFromObject(object)
```
获取粗略边界；根据需求进一步细化。
类碰撞检查：按照文档使用
```
ray.intersectBox
```
、
```
sphere.containsPoint
```
等方法。
附加数据结构：游戏开发可使用
```
Octree
```
/
```
OBB
```
——引用附加组件页面，避免在此复制完整的 API 表。
颜色：
```
Color
```
转换与材质/纹理相关——建立交叉引用。
随机采样：使用
```
MeshSurfaceSampler
```
在网格表面上分布点。

请参阅 examples/workflow-ray-aabb.md。

Doc map (official)

文档地图（官方）

Docs section	Representative links
Math	https://threejs.org/docs/Vector3.html
Math	https://threejs.org/docs/Matrix4.html
Math	https://threejs.org/docs/Quaternion.html
Math	https://threejs.org/docs/Ray.html

文档章节	代表性链接
数学	https://threejs.org/docs/Vector3.html
数学	https://threejs.org/docs/Matrix4.html
数学	https://threejs.org/docs/Quaternion.html
数学	https://threejs.org/docs/Ray.html

Scope

适用范围

In scope: Core Math types; addon math entries as pointers.
Out of scope: Keyframe track evaluation beyond type references (animation skill).

**范围内：**核心 Math 类型；附加数学条目仅作为指引。
**范围外：**除类型引用之外的关键帧轨道求值（animation skill）。

Common pitfalls and best practices

常见陷阱与最佳实践

Euler gimbal lock—prefer quaternions for arbitrary rotations.
Reusing temporary vectors reduces GC thrash in hot loops.
Frustum culling helpers vary—verify against your three version.

Euler 万向节死锁——任意旋转优先使用四元数。
在热循环中复用临时向量可减少 GC 压力。
Frustum 剔除辅助工具可能有所不同——请根据你的 three 版本进行验证。

Documentation and version

文档与版本

Core math types are listed under Math; addon utilities (

Octree

OBB

, …) appear under Addons → Math in three.js docs. Global also lists constants (e.g. wrapping, blending) sometimes needed alongside materials.

核心数学类型列于 Math；附加工具（

Octree

、

OBB

等）位于 three.js 文档的 Addons → Math 下。Global 中也列出了有时需与材质一起使用的常量（例如

wrapping

、

blending

）。

Agent response checklist

Agent 响应检查清单

When answering under this skill, prefer responses that:

Link the concrete type (
```
Vector3
```
,
```
Matrix4
```
,
```
Quaternion
```
, …) from the docs.
Send
```
AnimationMixer
```
/ track math to threejs-animation when time-sampled.
Send
```
Raycaster
```
picking flows to threejs-objects when interaction is the goal.
Mention numeric stability (epsilon) where comparisons matter.
Point to Addons → Math for game-oriented structures when users need spatial acceleration.

使用此 skill 回答问题时，优先采用以下方式：

从文档中链接具体类型（
```
Vector3
```
、
```
Matrix4
```
、
```
Quaternion
```
等）。
当涉及按时间采样时，将
```
AnimationMixer
```
/轨道数学问题转至 threejs-animation。
当目标是实现交互时，将
```
Raycaster
```
拾取流程转至 threejs-objects。
当比较运算很重要时，提及数值稳定性（epsilon）。
当用户需要空间加速时，指向 Addons → Math，以获取面向游戏的数据结构。

References

参考资料

Keywords

关键词

English: vector, matrix, quaternion, euler, box3, sphere, ray, frustum, three.js

中文： 向量、矩阵、四元数、欧拉角、包围盒、射线、three.js

English: vector, matrix, quaternion, euler, box3, sphere, ray, frustum, three.js

中文： 向量、矩阵、四元数、欧拉角、包围盒、射线、three.js