egret-docs-master/Engine3D/MathUtils/Matrix4_4
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README.md

3D基本变换

3D矩阵Matrix4_4

* Matrix4_4 类表示一个转换矩阵,该矩阵描述了三维 (3D) 显示对象的缩放/旋转/位移
* 该矩阵可以追加转换功能,包括缩放/旋转/位移
* Matrix4_4 类可用于视锥投影,这会将 3D 坐标空间中的点映射到二维 (2D) 视图,常用有透视投影和正交投影
* 单一矩阵可以将多个转换组合在一起,并一次性对 3D 显示对象应用这些转换
* 例如,可以将一个矩阵应用于 3D 坐标,以便依次执行旋转和平移

  • lookAt:从3D坐标点A观察坐标点B设定观察视角的正上方获得满足这个条件的矩阵
    • 可以用于控制相机或者显示对象的方向,使面向目标
    • egret3d.Camera3D和egret3d.Object3D已经封装过该函数你只需要调用camera3D.lookAt()或者object3D.lookAt()

var matrix: egret3d.Matrix4_4 = new egret3d.Matrix4_4();
var eyePosition: egret3d.Vector3D = new egret3d.Vector3D(0, 0, 0);
var atPosition: egret3d.Vector3D = new egret3d.Vector3D(100, 20, 40);
matrix.lookAt(eyePosition, atPosition, egret3d.Vector3D.Y_AXIS);

//matrix
//[0]	0.3713906705379486	Number
//[1]	-0.16951587796211243	Number
//[2]	0.9128709435462952	Number
//[3]	0	Number
//[4]	0	Number
//[5]	0.9831920862197876	Number
//[6]	0.18257418274879455	Number
//[7]	0	Number
//[8]	-0.9284766912460327	Number
//[9]	-0.06780634820461273	Number
//[10]	0.3651483654975891	Number
//[11]	0	Number
//[12]	0	Number
//[13]	0	Number
//[14]	0	Number
//[15]	1	Number

  • multiply:矩阵相乘
    • 矩阵A和矩阵B相乘的得到矩阵C
    • 一个3D对象先使用矩阵A进行转换然后用矩阵B进行转换其结果与直接用C矩阵转换是等价的操作
    • 注意前乘和后乘的区别,矩阵相乘不满足交换律

var matrix1: egret3d.Matrix4_4 = new egret3d.Matrix4_4();
var matrix2: egret3d.Matrix4_4 = new egret3d.Matrix4_4();
matrix1.multiply(matrix2);

  • perspective:生成一个透视投影矩阵
    • 通过设定视锥体的空间数据,包括远近裁剪面距离/观察范围夹角/屏幕横纵比,获得矩阵
    • egret3d.Camera3D封装有该矩阵的方法调用通过设定CameraType即可自动构造透视投影矩阵
    • 3D场景渲染中会使用到该功能

var projectMatrix: egret3d.Matrix4_4 = new egret3d.Matrix4_4();
var fovY:number = 60;
var aspectRatio:number = 3/4;
var near:number = 1;
var far:number = 10000;
//构造透视投影矩阵
projectMatrix.perspective(fovY, aspectRatio, near, far);

  • ortho:生成一个正交投影矩阵
    • 通过设定视锥体的空间数据,包括远近裁剪面距离/屏幕宽度和高度
    • egret3d.Camera3D封装有该矩阵的方法调用通过设定CameraType即可自动构造正交投影矩阵
    • GUI和HUD的渲染会使用到该功能

var projectMatrix: egret3d.Matrix4_4 = new egret3d.Matrix4_4();
var width:number = 1024;
var height:number = 768;
var near:number = 1;
var far:number = 10000;
//构造正交投影矩阵
projectMatrix.ortho(fovY, aspectRatio, near, far);

  • fromToRotation:获得一个矩阵使他能够将A向量变换成B向量

var matrix:egret3d.Matrix4_4 = new egret3d.Matrix4_4();
var direction1:egret3d.Vector3D = new egret3d.Vector3D(-1,0,2,1);
var direction2:egret3d.Vector3D = new egret3d.Vector3D(10,5,1,1);
direction1.normalize();
direction2.normalize();
//求出模型矩阵
matrix.fromToRotation(direction1, direction2);

  • append:矩阵前乘
    • 与multiply相同

var matrix1: egret3d.Matrix4_4 = new egret3d.Matrix4_4();
var matrix2: egret3d.Matrix4_4 = new egret3d.Matrix4_4();
matrix1.append(matrix2);

  • appendRotation:获得一个矩阵,该矩阵描述着绕设定的旋转轴旋转一定的角度

var matrix: egret3d.Matrix4_4 = new egret3d.Matrix4_4();
var axis: egret3d.Vector3D = new egret3d.Vector3D(1, -1, 10, 1);
axis.normalize();
//围绕axis指定的方向旋转45度角
matrix.appendRotation(45, axis);

  • appendScale:追加三轴缩放值
    • 将当前的矩阵追加xyz三个方向缩放值

var matrix: egret3d.Matrix4_4 = new egret3d.Matrix4_4();
var scaleX:number = 0.5;
var scaleY:number = 1.5;
var scaleZ:number = 2.5;
//X Y Z 方向分别缩放 0.5 1.5 2.5
matrix.appendScale(scaleX, scaleY, scaleZ);

//matrix
//[0]	0.5	Number
//[1]	0	Number
//[2]	0	Number
//[3]	0	Number
//[4]	0	Number
//[5]	1.5	Number
//[6]	0	Number
//[7]	0	Number
//[8]	0	Number
//[9]	0	Number
//[10]	2.5	Number
//[11]	0	Number
//[12]	0	Number
//[13]	0	Number
//[14]	0	Number
//[15]	1	Number

  • appendTranslation:追加平移数据
    • 将当前的矩阵追加xyz三个方向平移数据

var matrix: egret3d.Matrix4_4 = new egret3d.Matrix4_4();
var offsetX:number = 0.5;
var offsetY:number = 1.5;
var offsetZ:number = 2.5;
//X Y Z 方向分别平移 0.5 1.5 2.5
matrix.appendTranslation(offsetX, offsetY, offsetZ);

//matrix
//[0]	1	Number
//[1]	0	Number
//[2]	0	Number
//[3]	0	Number
//[4]	0	Number
//[5]	1	Number
//[6]	0	Number
//[7]	0	Number
//[8]	0	Number
//[9]	0	Number
//[10]	1	Number
//[11]	0	Number
//[12]	0.5	Number
//[13]	1.5	Number
//[14]	2.5	Number
//[15]	1	Number

  • decompose:分解一个矩阵,获得缩放/平移/旋转数据
    • 分解得出的结果为egret3D.Vector3D的数组中长度为3.其中第一个记录平移数据,第二个记录旋转数据,第三个记录缩放数据
    • 需要指定旋转数据格式请参照egret3d.Orientation3D中枚举出的3个值

var matrix: egret3d.Matrix4_4 = new egret3d.Matrix4_4();

var offsetX:number = 0.2;
var offsetY:number = 0.4;
var offsetZ:number = 0.6;
//X Y Z 方向分别平移 0.2 0.4 0.6
matrix.appendTranslation(offsetX, offsetY, offsetZ);

var scaleX:number = 0.5;
var scaleY:number = 1.5;
var scaleZ:number = 2.5;
//X Y Z 方向分别缩放 0.5 1.5 2.5
matrix.appendScale(scaleX, scaleY, scaleZ);

var axis: egret3d.Vector3D = new egret3d.Vector3D(1, -1, 10, 1);
axis.normalize();
//围绕axis指定的方向旋转45度角
matrix.appendRotation(45, axis);

//拆分矩阵
var result:egret3d.Vector3D[] = matrix.decompose(egret3d.Orientation3D.QUATERNION);
var pos:egret3d.Vector3D = result[0];
var rot:egret3d.Vector3D = result[1];
var scale:egret3d.Vector3D = result[2];

//<-0.41275760531425476, 0.34762030839920044, 1.5260378122329712>
//<0.03789130620377082, -0.037891307211827124, 0.37891307413438385, 0.9238795211721623>
//<0.5000000018751693, 1.5000000284558414, 2.49999994435313>

  • deltaTransformVector:按照该矩阵所包含的旋转信息,变换另外一个向量
    • 向量没有平移信息

var matrix: egret3d.Matrix4_4 = new egret3d.Matrix4_4();

var offsetX:number = 0.2;
var offsetY:number = 0.4;
var offsetZ:number = 0.6;
//X Y Z 方向分别平移 0.2 0.4 0.6
matrix.appendTranslation(offsetX, offsetY, offsetZ);

var scaleX:number = 0.5;
var scaleY:number = 1.5;
var scaleZ:number = 2.5;
//X Y Z 方向分别缩放 0.5 1.5 2.5
matrix.appendScale(scaleX, scaleY, scaleZ);

var axis: egret3d.Vector3D = new egret3d.Vector3D(1, -1, 10, 1);
axis.normalize();
//围绕axis指定的方向旋转45度角
matrix.appendRotation(45, axis);

//给定原向量
var direction:egret3d.Vector3D = new egret3d.Vector3D(10, 10, -5, 1);
direction.normalize();

matrix.deltaTransformVector(direction, direction);

//w	0	Number
//x	-0.43193634599447245	Number
//y	1.024675299723943	Number
//z	-0.75433882077535	Number

  • transformVector:使用当前矩阵变换另外一个位置点
    • 初始位置被变换之后,得到的结果为按照当前矩阵所给定的数据获得的新位置
    • 坐标数据不包含缩放/旋转信息

var matrix: egret3d.Matrix4_4 = new egret3d.Matrix4_4();

var offsetX:number = 0.2;
var offsetY:number = 0.4;
var offsetZ:number = 0.6;
//X Y Z 方向分别平移 0.2 0.4 0.6
matrix.appendTranslation(offsetX, offsetY, offsetZ);

var scaleX:number = 0.5;
var scaleY:number = 1.5;
var scaleZ:number = 2.5;
//X Y Z 方向分别缩放 0.5 1.5 2.5
matrix.appendScale(scaleX, scaleY, scaleZ);

var axis: egret3d.Vector3D = new egret3d.Vector3D(1, -1, 10, 1);
axis.normalize();
//围绕axis指定的方向旋转45度角
matrix.appendRotation(45, axis);

//给定原向量
var direction:egret3d.Vector3D = new egret3d.Vector3D(10, 10, -5, 1);
direction.normalize();

matrix.transformVector(direction, direction);

//w	1	Number
//x	-0.8446939513087273	Number
//y	1.3722956081231434	Number
//z	0.7716989914576212	Number

  • invert:获取当前矩阵的逆矩阵
    • 理想状态下,矩阵和逆矩阵的乘积为单位矩阵
    • 不是所有的矩阵都有逆矩阵

var matrix: egret3d.Matrix4_4 = new egret3d.Matrix4_4();

var offsetX:number = 0.2;
var offsetY:number = 0.4;
var offsetZ:number = 0.6;
//X Y Z 方向分别平移 0.2 0.4 0.6
matrix.appendTranslation(offsetX, offsetY, offsetZ);

var scaleX:number = 0.5;
var scaleY:number = 1.5;
var scaleZ:number = 2.5;
//X Y Z 方向分别缩放 0.5 1.5 2.5
matrix.appendScale(scaleX, scaleY, scaleZ);

var axis: egret3d.Vector3D = new egret3d.Vector3D(1, -1, 10, 1);
axis.normalize();
//围绕axis指定的方向旋转45度角
matrix.appendRotation(45, axis);

//给定原向量
var direction:egret3d.Vector3D = new egret3d.Vector3D(10, 10, -5, 1);
direction.normalize();

var enable:boolean = matrix.invert();

//enable : true

//[0]	1.4199564456939697	Number
//[1]	-0.46867436170578003	Number
//[2]	-0.016519593074917793	Number
//[3]	0	Number
//[4]	1.394537091255188	Number
//[5]	0.47331884503364563	Number
//[6]	-0.03949161246418953	Number
//[7]	0	Number
//[8]	0.19745805859565735	Number
//[9]	0.027532655745744705	Number
//[10]	0.39770281314849853	Number
//[11]	0	Number
//[12]	-0.20000006258487701	Number
//[13]	-0.4000000059604645	Number
//[14]	-0.6000000238418579	Number
//[15]	1	Number

  • makeTransform:输入缩放/旋转/位移信息,生成一个矩阵
    • 旋转数据为四元数格式

var matrix: egret3d.Matrix4_4 = new egret3d.Matrix4_4();

var pos:egret3d.Vector3D = new egret3d.Vector3D(0.2, 0.4, 0.6, 1);
var scale:egret3d.Vector3D = new egret3d.Vector3D(0.5, 1.5, 2.5, 1);
var rot:egret3d.Quaternion = new egret3d.Quaternion(-1, 2, 10, 1);
rot.normalize();
//组装
matrix.makeTransform(pos, scale, rot);

//[0]	-0.4811320900917053	Number56939697	Number
//[1]	0.07547169923782348	Number6170578003	Number
//[2]	-0.11320754885673523	Number93074917793	Number
//[3]	0	Number
//[4]	-0.3396226465702057	Number1255188	Number
//[5]	-1.3584905862808227	Number503364563	Number
//[6]	0.5377358198165893	Number1246418953	Number
//[7]	0	Number
//[8]	-0.37735849618911743	Number859565735	Number
//[9]	0.9905660152435303	Number5745744705	Number
//[10]	2.264151096343994	Number314849853	Number
//[11]	0	Number
//[12]	0.20000000298023224	Number6258487701	Number
//[13]	0.4000000059604645	Number059604645	Number
//[14]	0.6000000238418579	Number238418579	Number
//[15]	1	Number

  • recompose:输入缩放/旋转/位移信息,重组矩阵
    • 旋转数据为欧拉角格式
    • 该函数先将欧拉角转化成四元数然后调用makeTransform方法实现

var matrix: egret3d.Matrix4_4 = new egret3d.Matrix4_4();

var pos:egret3d.Vector3D = new egret3d.Vector3D(0.2, 0.4, 0.6, 1);
var scale:egret3d.Vector3D = new egret3d.Vector3D(0.5, 1.5, 2.5, 1);
var rot:egret3d.Vector3D = new egret3d.Vector3D(-1, 2, 10, 1);
rot.normalize();
//组装
matrix.recompose([pos, rot, scale]);

  • transpose:转置一个矩阵,使矩阵按照右上和左下角互换规则交换所有数据


  • lerp:矩阵插值操作
    • 从矩阵A到矩阵B通过输入0-1之间的一个时间作为插值系数进行平滑插值

var matrixA: egret3d.Matrix4_4 = new egret3d.Matrix4_4();
var matrixB: egret3d.Matrix4_4 = new egret3d.Matrix4_4();

var result: egret3d.Matrix4_4 = new egret3d.Matrix4_4();
var t:number = 0.2;
result.lerp(matrixA, matrixB, t);