egret-docs-master/Engine3D/MathUtils/Vector3D/README.md

3D基本变换

3D向量（Vector3D）

该类有x/y/z/w四个成员变量，可用作记录3D坐标/3D向量/四元数。w可用作xyz的缩放分量，或该对象为四元数时候存放第四个数据。

• add():加法运算，用当前数据的x/y/z分别加上输入数据的x/y/z，结果存入target中
  • x/y/z三个分量各自相加

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var vector1:egret3d.Vector3D = new egret3d.Vector3D(1, 0, 0, 0);
var vector2:egret3d.Vector3D = new egret3d.Vector3D(0, 0, 1, 0);

var result:egret3d.Vector3D = new egret3d.Vector3D();
//加法运算后的结果存储在result中。
vector1.add(vector2, result);

//result: (1, 0, 1, 0);

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• incrementBy():加法运算，将当前数据的x/y/z分别加上输入数据的x/y/z

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var vector1:egret3d.Vector3D = new egret3d.Vector3D(1, 0, 0, 0);
var vector2:egret3d.Vector3D = new egret3d.Vector3D(0, 0, 1, 0);


//vector1加上vector2数据
vector1.incrementBy(vector2);

//vector1: (1, 0, 1, 0);

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• subtract():减法运算，用当前数据的x/y/z分别减去输入数据的x/y/z，结果存入target中

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var vector1:egret3d.Vector3D = new egret3d.Vector3D(1, 0, 0, 0);
var vector2:egret3d.Vector3D = new egret3d.Vector3D(0, 0, 1, 0);

var result:egret3d.Vector3D = new egret3d.Vector3D();
//加法运算后的结果存储在result中。
vector1.subtract(vector2, result);

//result: (1, 0, -1, 0);

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• decrementBy():减法运算，将当前数据的x/y/z分别减去输入数据的x/y/z

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var vector1:egret3d.Vector3D = new egret3d.Vector3D(1, 0, 0, 0);
var vector2:egret3d.Vector3D = new egret3d.Vector3D(0, 0, 1, 0);


//vector1减去vector2数据
vector1.decrementBy(vector2);

//vector1: (1, 0, -1, 0);

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• crossProduct():叉乘, a·b=|a|·|b|·cos(a,b),(a,b)表示a,b的夹角;
  • 通过叉乘计算可以获得一个垂直于ab所在平面的方向，在a和b为单位向量的情况下，所得结果也为单位向量。

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var vector1:egret3d.Vector3D = new egret3d.Vector3D(1, 0, 0, 0);
var vector2:egret3d.Vector3D = new egret3d.Vector3D(0, 1, 0, 0);
var result:egret3d.Vector3D = new egret3d.Vector3D();

//vector1加上vector2数据
vector1.crossProduct(result);

//result: (0, -1, 0, 1);

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• dotProduct():点乘,ab=axbx + ayby + azbz;
  • 点积也叫做内积，计算的结果反应出2个向量之间的夹角关系。
  • a和b为单位向量时候，结果为夹角的余弦值。

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var vector1:egret3d.Vector3D = new egret3d.Vector3D(1, 0, 0, 0);
var vector2:egret3d.Vector3D = new egret3d.Vector3D(0, 1, 0, 0);
	
//vector1加上vector2数据
var result:number = vector1.dotProduct(result);

//result: 0; (vector1和vector2夹角的余弦值为0)

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• negate():取反;
  • 取反操作为x/y/z三轴数据各自乘以-1

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var vector1:egret3d.Vector3D = new egret3d.Vector3D(1, 0, 0, 0);
//取反操作
vector1.negate();

//vector1: (-1, 0, 0, 0);

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• normalize():标准化
  • 在不改变向量方向的条件下，改变向量长度为指定的值

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var vector1:egret3d.Vector3D = new egret3d.Vector3D(1, 2, 3, 0);
//标准化
vector1.normalize(1);

//w	0	Number
//x	0.2672612419124244	Number
//y	0.5345224838248488	Number
//z	0.8017837257372732	Number

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• slerp():四元数平滑插值
  • 输入一个0-1之间的参数，在四元数a和四元数b的之间平滑插值获得新的向量
  • 可用于骨骼旋转计算的两个关键帧之间插值运算

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var vector1:egret3d.Vector3D = new egret3d.Vector3D(1, 0, 0, 1);
var vector2:egret3d.Vector3D = new egret3d.Vector3D(0, 1, 0, 1);
//插值
vector1.slerp(vector1, vector2, 0.2);

//w	1	Number
//x	0.9510565400123596	Number
//y	0.30901700258255005	Number
//z	0	Number

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• lerp():普通线性插值
  • 在向量a和向量b的之间线性插值获得新的向量，x/y/z三轴各自线性插值

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var vector1:egret3d.Vector3D = new egret3d.Vector3D(1, 0, 0, 1);
var vector2:egret3d.Vector3D = new egret3d.Vector3D(0, 1, 0, 1);
//插值
vector1.slerp(vector1, vector2, 0.2);

//w	1	Number
//x	0.8	Number
//y	0.2	Number
//z	0	Number

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• multiply():乘法运算;
  • 将向量a的xyz分量分别乘以向量b的xyz分量，结果存入target中

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var vector1:egret3d.Vector3D = new egret3d.Vector3D(2, 3, 4, 1);
var vector2:egret3d.Vector3D = new egret3d.Vector3D(4, 6, 8, 1);
var result:egret3d.Vector3D = new egret3d.Vector3D();
//乘法运算
vector1.multiply(vector2, result);

//result: (8, 18, 32, 1)

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• divided():除法运算，将向量a的x/y/z分量分别除以向量b的x/y/z分量，结果存入target中

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var vector1:egret3d.Vector3D = new egret3d.Vector3D(2, 3, 4, 1);
var vector2:egret3d.Vector3D = new egret3d.Vector3D(4, 6, 8, 1);
var result:egret3d.Vector3D = new egret3d.Vector3D();
//乘法运算
vector1.divided(vector2, result);

//result: (0.5, 0.5, 0.5, 1)

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