Box3Vector3 / GameVector3 三维向量

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Box3Vector3（三维向量）是Box3中一个非常常见的类，通常指定一个位置，或者尺寸、方向等

构造函数¶

Box3Vector3 (x: number, y: number, z: number): Box3Vector3
GameVector3 (x: number, y: number, z: number): GameVector3
新建一个三维向量

new Box3Vector3(0, 0, 0)
new Box3Vector3(64, 64, 64)
new Box3Vector3(127.5, 64, 127.5)
new Box3Vector3(11, 45, 14)
new Box3Vector3(19, 19, 810)

new GameVector3(0, 0, 0)
new GameVector3(64, 64, 64)
new GameVector3(127.5, 64, 127.5)
new GameVector3(11, 45, 14)
new GameVector3(19, 19, 810)

常用¶

set copy clone
scale
add sub mul div
addEq subEq mulEq divEq
equals
distance
min max

属性¶

方法¶

set (x: number, y: number, z: number): Box3Vector3

set (x: number, y: number, z: number): GameVector3

设置三维向量的值

示例

旧版编辑器Arena 编辑器

new Box3Vector3(0, 0, 0).set(5, 5, 0) //<~ { x: 5, y: 5, z: 0 }
new Box3Vector3(1, 2, 3).set(4, 5, 6) //<~ { x: 4, y: 5, z: 6 }
new Box3Vector3().set(5, 5, 5) //<~ { x: 5, y: 5, z: 5 }

new GameVector3(0, 0, 0).set(5, 5, 0) //<~ { x: 5, y: 5, z: 0 }
new GameVector3(1, 2, 3).set(4, 5, 6) //<~ { x: 4, y: 5, z: 6 }
new GameVector3().set(5, 5, 5) //<~ { x: 5, y: 5, z: 5 }

copy (v: Box3Vector3): Box3Vector3

copy (v: GameVector3): GameVector3

把v的值复制到这个三维向量中

示例

旧版编辑器Arena 编辑器

new Box3Vector3(0, 0, 0).copy(new Box3Vector3(5, 0, 0)) //<~ { x: 5, y: 0, z: 0 }
new Box3Vector3().copy(new Box3Vector3(1, 0, 0)) //<~ { x: 1, y: 0, z: 0 }

new GameVector3(0, 0, 0).copy(new GameVector3(5, 0, 0)) //<~ { x: 5, y: 0, z: 0 }
new GameVector3().copy(new GameVector3(1, 0, 0)) //<~ { x: 1, y: 0, z: 0 }

clone (): Box3Vector3

clone (): GameVector3

复制该向量

示例

旧版编辑器Arena 编辑器

new Box3Vector3(5, 5, 5).clone() //<~ { x: 5, y: 5, z: 5 }

new GameVector3(5, 5, 5).clone() //<~ { x: 5, y: 5, z: 5 }

add (v: Box3Vector3): Box3Vector3

add (v: GameVector3): GameVector3

将这个三维向量加上v，返回结果

此方法不会改变原来的向量

示例

旧版编辑器Arena 编辑器

new Box3Vector3(1, 1, 1).add(new Box3Vector3(5, 5, 5)) //<~ { x: 6, y: 6, z: 6 }

new GameVector3(1, 1, 1).add(new GameVector3(5, 5, 5)) //<~ { x: 6, y: 6, z: 6 }

sub (v: Box3Vector3): Box3Vector3

sub (v: GameVector3): GameVector3

将这个三维向量减去v，返回结果

此方法不会改变原来的向量

示例

旧版编辑器Arena 编辑器

new Box3Vector3(6, 6, 6).sub(new Box3Vector3(1, 1, 1)) //<~ { x: 5, y: 5, z: 5 }

new GameVector3(6, 6, 6).sub(new GameVector3(1, 1, 1)) //<~ { x: 5, y: 5, z: 5 }

mul (v: Box3Vector3): Box3Vector3

mul (v: GameVector3): GameVector3

将这个向量与v点乘，返回结果
也可理解为，将这个向量的x、y、z分别乘v.x、v.y、v.z

此方法不会改变原来的向量

示例

旧版编辑器Arena 编辑器

new Box3Vector3(5, 5, 5).mul(new Box3Vector3(5, 5, 5)) //<~ { x: 25, y: 25, z: 25 }

new GameVector3(5, 5, 5).mul(new GameVector3(5, 5, 5)) //<~ { x: 25, y: 25, z: 25 }

div (v: Box3Vector3): Box3Vector3

div (v: GameVector3): GameVector3

将这个三维向量除以v，返回结果
也可理解为，将这个向量的x、y、z分别除以v.x、v.y、v.z

此方法不会改变原来的向量

示例

旧版编辑器Arena 编辑器

new Box3Vector3(25, 25, 25).mul(new Box3Vector3(5, 5, 5)) //<~ { x: 5, y: 5, z: 5 }

new GameVector3(25, 25, 25).mul(new GameVector3(5, 5, 5)) //<~ { x: 5, y: 5, z: 5 }

new Box3Vector3(6, 6, 6).add(new Box3Vector3(1, 1, 1))

new GameVector3(6, 6, 6).add(new GameVector3(1, 1, 1))

new Box3Vector3(6, 6, 6).add(1, 1, 1)

new GameVector3(6, 6, 6).add(1, 1, 1)

addEq (v: Box3Vector3): Box3Vector3

addEq (v: GameVector3): GameVector3

将这个三维向量加上v，返回结果

此方法会改变原来的向量

subEq (v: Box3Vector3): Box3Vector3

subEq (v: GameVector3): GameVector3

将这个三维向量减去v，返回结果

此方法会改变原来的向量

mulEq (v: Box3Vector3): Box3Vector3

mulEq (v: GameVector3): GameVector3

将这个向量与v点乘，返回结果
也可理解为，将这个向量的x、y、z分别乘v.x、v.y、v.z

此方法会改变原来的向量

divEq (v: Box3Vector3): Box3Vector3

divEq (v: GameVector3): GameVector3

将这个三维向量除以v，返回结果
也可理解为，将这个向量的x、y、z分别除以v.x、v.y、v.z

此方法会改变原来的向量

dot (v: Box3Vector3): number

dot (v: GameVector3): number

向量点积
也可理解为，将这个向量与v相乘，返回结果的三个方向的值的和

示例

旧版编辑器Arena 编辑器

new Box3Vector3(1, 1, 1).dot(new Box3Vector3(5, 5, 5)) //<~ 15

new GameVector3(1, 1, 1).dot(new GameVector3(5, 5, 5)) //<~ 15

cross (v: Box3Vector3): Box3Vector3

cross (v: GameVector3): GameVector3

将这个向量与v叉乘，返回结果
也可以理解为，返回与这个向量和v所在的平面垂直的向量

提示

无法理解？把下面的示例画个图就好了

示例

旧版编辑器Arena 编辑器

new Box3Vector3(1, 1, 1).cross(new Box3Vector3(5, 5, 5)) //<~ { x: 0, y: 0, z: 0 }
new Box3Vector3(1, 1, 1).cross(new Box3Vector3(1, 1, 1)) //<~ { x: 0, y: 0, z: 0 }
new Box3Vector3(1, 1, 1).cross(new Box3Vector3(1, -1, 1)) //<~ { x:2, y:0, z:-2 }
new Box3Vector3(1, 1, -1).cross(new Box3Vector3(1, -1, 1)) //<~ { x:0, y:-2, z:-2 }

new GameVector3(1, 1, 1).cross(new GameVector3(5, 5, 5)) //<~ { x: 0, y: 0, z: 0 }
new GameVector3(1, 1, 1).cross(new GameVector3(1, 1, 1)) //<~ { x: 0, y: 0, z: 0 }
new GameVector3(1, 1, 1).cross(new GameVector3(1, -1, 1)) //<~ { x:2, y:0, z:-2 }
new GameVector3(1, 1, -1).cross(new GameVector3(1, -1, 1)) //<~ { x:0, y:-2, z:-2 }

scale (n: number): Box3Vector3

scale (n: number): GameVector3

将这个向量与n数乘，返回结果
也可理解为，将这个向量缩放至原来的n倍

此方法不会改变原来的向量

示例

旧版编辑器Arena 编辑器

new Box3Vector3(1, 1, 1).scale(5) //<~ {x: 5, y: 5, z: 5 }

new GameVector3(1, 1, 1).scale(5) //<~ {x: 5, y: 5, z: 5 }

lerp (v: Box3Vector3, n: number): Box3Vector3

lerp (v: GameVector3, n: number): GameVector3

插值函数
可以理解为，以该向量的坐标为起点，v的坐标为终点的一段线段，取线段的第n部分的点的位置

示例

旧版编辑器Arena 编辑器

new Box3Vector3(0, 0, 0).lerp(new Box3Vector3(1, 1, 1), 0.5) // <~ { x: 0.5, y: 0.5, z: 0.5 }
new Box3Vector3(0, 0, 0).lerp(new Box3Vector3(1, 1, 1), 0.25) // <~ { x: 0.25, y: 0.25, z: 0.25 }
new Box3Vector3(0, 0, 0).lerp(new Box3Vector3(0.5, 0.5, 0.5), 0.5) // <~ { x: 0.25, y: 0.25, z: 0.25 }

new GameVector3(0, 0, 0).lerp(new GameVector3(1, 1, 1), 0.5) // <~ { x: 0.5, y: 0.5, z: 0.5 }
new GameVector3(0, 0, 0).lerp(new GameVector3(1, 1, 1), 0.25) // <~ { x: 0.25, y: 0.25, z: 0.25 }
new GameVector3(0, 0, 0).lerp(new GameVector3(0.5, 0.5, 0.5), 0.5) // <~ { x: 0.25, y: 0.25, z: 0.25 }

mag (): number

求这个向量的大小（也称模）

示例

旧版编辑器Arena 编辑器

new Box3Vector3(1, 0, 0).mag() //<~ 1
new Box3Vector3(3, 4, 5).mag() //<~ 7.0710678118654755
new Box3Vector3(11, 45, 14).mag() //<~ 48.394214530251446

new GameVector3(1, 0, 0).mag() //<~ 1
new GameVector3(3, 4, 5).mag() //<~ 7.0710678118654755
new GameVector3(11, 45, 14).mag() //<~ 48.394214530251446

sqrMag (): number

求这个向量的大小（也称模）的平方
比你用mag再用pow函数快

示例

旧版编辑器Arena 编辑器

new Box3Vector3(1, 0, 0).sqrMag() //<~ 1
new Box3Vector3(3, 4, 5).sqrMag() //<~ 50
new Box3Vector3(11, 45, 14).sqrMag() //<~ 2342

new GameVector3(1, 0, 0).sqrMag() //<~ 1
new GameVector3(3, 4, 5).sqrMag() //<~ 50
new GameVector3(11, 45, 14).sqrMag() //<~ 2342

towards (v: Box3Vector3): Box3Vector3

towards (v: GameVector3): GameVector3

返回这个向量面向v的值

示例

旧版编辑器Arena 编辑器

new Box3Vector3(6, 6, 6).sub(new Box3Vector3(1, 1, 1)) //<~ { x: 5, y: 5, z: 5 }
new Box3Vector3(-6, 6, 6).sub(new Box3Vector3(1, 1, 1)) //<~ { x: -7, y: 5, z: 5 }

new GameVector3(6, 6, 6).sub(new GameVector3(1, 1, 1)) //<~ { x: 5, y: 5, z: 5 }
new GameVector3(-6, 6, 6).sub(new GameVector3(1, 1, 1)) //<~ { x: -7, y: 5, z: 5 }

distance (v: Box3Vector3): number

distance (v: GameVector3): number

返回这个向量到v的距离

示例

旧版编辑器Arena 编辑器

new Box3Vector3(6, 0, 0).distance(new Box3Vector3(1, 0, 0)) //<~ 5
new Box3Vector3(6, 6, 6).distance(new Box3Vector3(1, 1, 1)) //<~ 8.660254037844387

new GameVector3(6, 0, 0).distance(new GameVector3(1, 0, 0)) //<~ 5
new GameVector3(6, 6, 6).distance(new GameVector3(1, 1, 1)) //<~ 8.660254037844387

normalize (): Box3Vector3

normalize (): GameVector3

归一化函数

示例

旧版编辑器Arena 编辑器

new Box3Vector3(6, 0, 0).normalize() //<~ { x: 1, y: 0, z: 0 }
new Box3Vector3(11, 45, 14).normalize() //<~ { x:0.17032272243312657, y:0.6967747735900632, z:0.6967747735900632 }

new GameVector3(6, 0, 0).normalize() //<~ { x: 1, y: 0, z: 0 }
new GameVector3(11, 45, 14).normalize() //<~ { x:0.17032272243312657, y:0.6967747735900632, z:0.6967747735900632 }

angle (v: Box3Vector3): number

angle (v: GameVector3): number

求这个向量与v的弧度

是弧度，不是角度！

弧度

另一种表示角度的方法，单位为\(rad\)，\(\pi rad\)相当于\(180°\)，\(2\pi rad\)相当于\(360°\)
其定义为：弧长等于圆半径的弧所对应的圆心角为\(1rad\)。

示例

旧版编辑器Arena 编辑器

new Box3Vector3(6, 0, 0).angle(new Box3Vector3(-6, 0, 0)) //<~ 3.141592653589793
new Box3Vector3(1, 1, 0).angle(new Box3Vector3(1, 0, 0)) //<~ 0.7853981633974484 //约为0.25 * Math.PI

new GameVector3(6, 0, 0).angle(new GameVector3(-6, 0, 0)) //<~ 3.141592653589793
new GameVector3(1, 1, 0).angle(new GameVector3(1, 0, 0)) //<~ 0.7853981633974484 //约为0.25 * Math.PI

max (v: Box3Vector3): Box3Vector3

max (v: GameVector3): GameVector3

分别对v和该向量的每个方向的坐标值取较大值

示例

旧版编辑器Arena 编辑器

new Box3Vector3(1, 2, 1).max(new Box3Vector3(2, 1, 2)) //<~ { x:2, y:2, z:2 }

new GameVector3(1, 2, 1).max(new GameVector3(2, 1, 2)) //<~ { x:2, y:2, z:2 }

min (v: Box3Vector3): Box3Vector3

min (v: GameVector3): GameVector3

分别对v和该向量的每个方向的坐标值取较小值

示例

旧版编辑器Arena 编辑器

new Box3Vector3(1, 2, 1).min(new Box3Vector3(2, 1, 2)) //<~ { x:1, y:1, z:1 }

new GameVector3(1, 2, 1).min(new GameVector3(2, 1, 2)) //<~ { x:1, y:1, z:1 }

exactEquals (v: Box3Vector3): boolean

exactEquals (v: GameVector3): boolean

判断两个向量是否完全相等

示例

旧版编辑器Arena 编辑器

new Box3Vector3(1, 2, 3).exactEquals(new Box3Vector3(1, 2, 3)) //<~ true
new Box3Vector3(1, 2, 3).exactEquals(new Box3Vector3(4, 5, 6)) //<~ false
new Box3Vector3(1, 2, 3).exactEquals(new Box3Vector3(1.000001, 2, 3)) //<~ false
new Box3Vector3(1, 2, 3).exactEquals(new Box3Vector3(1.000000000000001, 2, 3)) //<~ false

new GameVector3(1, 2, 3).exactEquals(new GameVector3(1, 2, 3)) //<~ true
new GameVector3(1, 2, 3).exactEquals(new GameVector3(4, 5, 6)) //<~ false
new GameVector3(1, 2, 3).exactEquals(new GameVector3(1.000001, 2, 3)) //<~ false
new GameVector3(1, 2, 3).exactEquals(new GameVector3(1.000000000000001, 2, 3)) //<~ false

equals (v: Box3Vector3): boolean

equals (v: GameVector3): boolean

此处与官方API不符

该文档没有tolerance: number参数

此处与社区API不符

该文档没有tolerance: number参数

经 2024/7/18 测试：该文档内容无问题

Arena 编辑器

new GameVector3(1, 2, 3).equals(new GameVector3(1.1, 2, 3), 1) // <~ false

判断两个向量是否大致相等
容差为0.000001

示例

旧版编辑器Arena 编辑器

new Box3Vector3(1, 2, 3).equals(new Box3Vector3(1, 2, 3)) //<~ true
new Box3Vector3(1, 2, 3).equals(new Box3Vector3(4, 5, 6)) //<~ false
new Box3Vector3(1, 2, 3).equals(new Box3Vector3(1.000001, 2, 3)) //<~ true
new Box3Vector3(1, 2, 3).equals(new Box3Vector3(1.000000000000001, 2, 3)) //<~ true

new GameVector3(1, 2, 3).equals(new GameVector3(1, 2, 3)) //<~ true
new GameVector3(1, 2, 3).equals(new GameVector3(4, 5, 6)) //<~ false
new GameVector3(1, 2, 3).equals(new GameVector3(1.000001, 2, 3)) //<~ true
new GameVector3(1, 2, 3).equals(new GameVector3(1.000000000000001, 2, 3)) //<~ true

toString (): string

将这个三维向量转换成字符串

示例

旧版编辑器Arena 编辑器

JSON.stringify(new Box3Vector3(114514, 1919810, 31415926535).toString()) //<~ "{ x:114514, y:1919810, z:31415926535 }"

JSON.stringify(new GameVector3(114514, 1919810, 31415926535).toString()) //<~ "{ x:114514, y:1919810, z:31415926535 }"

fromPolar (mag: number, phi: number, theta: number): Box3Vector3

fromPolar (mag: number, phi: number, theta: number): GameVector3

使用大小和方向创建向量

内容缺失

由于编者的能力有限，无法编写该内容
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参数	类型	说明
mag		向量大小
phi		\(\phi\)，磁通量，单位是韦伯Wb
theta		\(\theta\)

示例

旧版编辑器Arena 编辑器

Box3Vector3.fromPolar(114514, 1919810, 31415926535) //<~ { x:-89551.55210093308, y:71368.36064229338, z:729.9394121558898 }
Box3Vector3.fromPolar(1, 0, 0) //<~ { x:0, y:1, z:0 }
Box3Vector3.fromPolar(1, 0, Math.PI) //<~ { x:0, y:-1, z:1.2246467991473532e-16 }
Box3Vector3.fromPolar(1, 0, Math.PI / 2) //<~ { x:0, y:6.123233995736766e-17, z:1 }
Box3Vector3.fromPolar(1, Math.PI / 2, 0) //<~ { x:0, y:1, z:0 }
Box3Vector3.fromPolar(2, Math.PI, 0) //<~ { x:0, y:2, z:0 }
Box3Vector3.fromPolar(2, -Math.PI, 0) //<~ { x:0, y:2, z:0 }
Box3Vector3.fromPolar(1, 0, -Math.PI) //<~ { x:0, y:-1, z:-1.2246467991473532e-16 }
Box3Vector3.fromPolar(2, Math.PI / 4, Math.PI / 4) //<~ { x:0.9999999999999998, y:1.4142135623730951, z:1 }
Box3Vector3.fromPolar(2, Math.PI / 8 * 7, Math.PI / 8) //<~ { x:0.2928932188134526, y:1.8477590650225735, z:-0.7071067811865476 }
Box3Vector3.fromPolar(2, Math.PI / -4, Math.PI / 4) //<~ { x:-0.9999999999999998, y:1.4142135623730951, z:1 }
Box3Vector3.fromPolar(2, Math.PI / -4, Math.PI / -4) //<~ { x:0.9999999999999998, y:1.4142135623730951, z:-1 }
Box3Vector3.fromPolar(2, Math.PI / 4, Math.PI / -4) //<~ { x:-0.9999999999999998, y:1.4142135623730951, z:-1 }
Box3Vector3.fromPolar(100, -Math.PI, Math.PI) //<~ { x:-1.4997597826618577e-30, y:-100, z:-1.2246467991473532e-14 }
Box3Vector3.fromPolar(100, -Math.PI, Math.PI / 2) //<~ { x:-1.2246467991473532e-14, y:6.123233995736766e-15, z:-100 }

GameVector3.fromPolar(114514, 1919810, 31415926535) //<~ { x:-89551.55210093308, y:71368.36064229338, z:729.9394121558898 }
GameVector3.fromPolar(1, 0, 0) //<~ { x:0, y:1, z:0 }
GameVector3.fromPolar(1, 0, Math.PI) //<~ { x:0, y:-1, z:1.2246467991473532e-16 }
GameVector3.fromPolar(1, 0, Math.PI / 2) //<~ { x:0, y:6.123233995736766e-17, z:1 }
GameVector3.fromPolar(1, Math.PI / 2, 0) //<~ { x:0, y:1, z:0 }
GameVector3.fromPolar(2, Math.PI, 0) //<~ { x:0, y:2, z:0 }
GameVector3.fromPolar(2, -Math.PI, 0) //<~ { x:0, y:2, z:0 }
GameVector3.fromPolar(1, 0, -Math.PI) //<~ { x:0, y:-1, z:-1.2246467991473532e-16 }
GameVector3.fromPolar(2, Math.PI / 4, Math.PI / 4) //<~ { x:0.9999999999999998, y:1.4142135623730951, z:1 }
GameVector3.fromPolar(2, Math.PI / 8 * 7, Math.PI / 8) //<~ { x:0.2928932188134526, y:1.8477590650225735, z:-0.7071067811865476 }
GameVector3.fromPolar(2, Math.PI / -4, Math.PI / 4) //<~ { x:-0.9999999999999998, y:1.4142135623730951, z:1 }
GameVector3.fromPolar(2, Math.PI / -4, Math.PI / -4) //<~ { x:0.9999999999999998, y:1.4142135623730951, z:-1 }
GameVector3.fromPolar(2, Math.PI / 4, Math.PI / -4) //<~ { x:-0.9999999999999998, y:1.4142135623730951, z:-1 }
GameVector3.fromPolar(100, -Math.PI, Math.PI) //<~ { x:-1.4997597826618577e-30, y:-100, z:-1.2246467991473532e-14 }
GameVector3.fromPolar(100, -Math.PI, Math.PI / 2) //<~ { x:-1.2246467991473532e-14, y:6.123233995736766e-15, z:-100 }

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