threejs中矩阵旋转原理

矩阵的概念

threejs中的矩阵

矩阵的应用

用于旋转一个几何体

创建一个立方体cube放到场景中；

绕向量(1,1,0)旋转30度

var axis = new THREE.Vector3(1,1,0);    //创建一个三维向量
var rotWorldMatrix = new THREE.Matrix4();      //创建一个4*4矩阵
rotWorldMatrix.makeRotationAxis(axis.normalize(),  30 * Math.PI / 180 );
rotWorldMatrix.multiply(cube.matrix);                // pre-multiply
cube.matrix = rotWorldMatrix;
cube.rotation.setFromRotationMatrix(cube.matrix);

旋转之前与之后对比

• 向量一定是从几何体中心指向外面？
• 能围绕一个不以圆点位起点的向量旋转？

代码详解

创建一个三维空间中的点

var axis = new THREE.Vector3(1,1,0);

打印出axios

THREE.Vector3(1,1,0).normalize()

axis.normalize()  //返回一个向量，其方向与指定向量相同，但长度为一。
如：
var axis = new THREE.Vector3(10,20,0);
console.log( axis.normalize() )；   //{x: 0.4472135954999579, y: 0.8944271909999159, z: 0}
(0.4472135954999579^2)+(0.8944271909999159^2)+(0^2) = 1

var axis1 = new THREE.Vector3(1,1,0);
console.log( axis1.normalize() )   //{x: 0.7071067811865475, y: 0.7071067811865475, z: 0}
(0.7071067811865475^2)+(0.7071067811865475^2)+(0^2) = 1

创建一个4*4的矩阵

var rotWorldMatrix = new THREE.Matrix4();
console.log( rotWorldMatrix )

将上面创建的4×4矩阵按照传入的轴旋转传入的弧度

rotWorldMatrix.makeRotationAxis( 旋转轴，旋转弧度 )

//Matrix4原型上的方法
//axis = axis.normalize()   值为 {x: 0.7071067811865475, y: 0.7071067811865475, z: 0}
//angle = 30 * Math.PI / 180     值为 pi/6
makeRotationAxis: function ( axis, angle ) {

    var c = Math.cos( angle );    //Math.cos(π/6)
    var s = Math.sin( angle );    //Math.sin(π/6)
    var t = 1 - c;
    var x = axis.x, y = axis.y, z = axis.z;
    var tx = t * x, ty = t * y;

    this.set(

        tx * x + c, tx * y - s * z, tx * z + s * y, 0,
        tx * y + s * z, ty * y + c, ty * z - s * x, 0,
        tx * z - s * y, ty * z + s * x, t * z * z + c, 0,
        0, 0, 0, 1

    );

     return this;

},

rotWorldMatrix.makeRotationAxis(axis.normalize(), 30 * Math.PI / 180 );
rotWorldMatrix初始值为{ elements:[1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1] }
执行makeRotationAxis()之后的值为：

将按照旋转轴和弧度旋转完成的矩阵和几何体的矩阵相乘

rotWorldMatrix.multiply(cube.matrix);

//框架源码
multiply: function ( m, n ) {
    if ( n !== undefined ) {      //这里的n是undefined因为只传入一个值cube.matrix
        return this.multiplyMatrices( m, n );
    }
    return this.multiplyMatrices( this, m );
},
multiplyMatrices: function ( a, b ) {

    var ae = a.elements;   //rotWorldMatrix.elements
    var be = b.elements;   //cube.matrix.elements
    var te = this.elements;  //ae和te是全等的

    var a11 = ae[ 0 ], a12 = ae[ 4 ], a13 = ae[ 8 ], a14 = ae[ 12 ];
    var a21 = ae[ 1 ], a22 = ae[ 5 ], a23 = ae[ 9 ], a24 = ae[ 13 ];
    var a31 = ae[ 2 ], a32 = ae[ 6 ], a33 = ae[ 10 ], a34 = ae[ 14 ];
    var a41 = ae[ 3 ], a42 = ae[ 7 ], a43 = ae[ 11 ], a44 = ae[ 15 ];

    var b11 = be[ 0 ], b12 = be[ 4 ], b13 = be[ 8 ], b14 = be[ 12 ];
    var b21 = be[ 1 ], b22 = be[ 5 ], b23 = be[ 9 ], b24 = be[ 13 ];
    var b31 = be[ 2 ], b32 = be[ 6 ], b33 = be[ 10 ], b34 = be[ 14 ];
    var b41 = be[ 3 ], b42 = be[ 7 ], b43 = be[ 11 ], b44 = be[ 15 ];

    te[ 0 ] = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41;
    te[ 4 ] = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42;
    te[ 8 ] = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43;
    te[ 12 ] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44;

    te[ 1 ] = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41;
    te[ 5 ] = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42;
    te[ 9 ] = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43;
    te[ 13 ] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44;

    te[ 2 ] = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41;
    te[ 6 ] = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42;
    te[ 10 ] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43;
    te[ 14 ] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44;

    te[ 3 ] = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41;
    te[ 7 ] = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42;
    te[ 11 ] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43;
    te[ 15 ] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44;

    return this;

},