threejs中矩阵旋转原理

摘要：如创建一个的矩阵将上面创建的矩阵按照传入的轴旋转传入的弧度旋转轴，旋转弧度原型上的方法值为值为初始值为执行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框架源码这里的是因为只传入一个值和是全等的

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);

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？

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;

},