3D基本变换
四元数（egret3d.Quaternion）
var quat1:egret3d.Quaternion = new egret3d.Quaternion(2, 3, 4, 1);
var quat2:egret3d.Quaternion = new egret3d.Quaternion(4, 6, 8, 1);
//乘法运算
quat1.multiply(quat1, quat2);
//quat1
//w -57 Number
//x 6 Number
//y 9 Number
//z 12 Number
- normalize():单位化一个四元数;
- 将四元数的四个分量缩放至长度为指定的标准，默认为1
var quat1:egret3d.Quaternion = new egret3d.Quaternion(2, 3, 4, 1);
//单位化
quat1.normalize();
//quat1
//w 0.18257418583505536 Number
//x 0.3651483716701107 Number
//y 0.5477225575051661 Number
//z 0.7302967433402214 Number
- transformVector():四元数转换一个3D坐标点
- 按照四元数所描述的规则，对3D点坐标进行旋转，得到旋转后的位置信息
var quat1:egret3d.Quaternion = new egret3d.Quaternion(2, 3, 4, 1);
var point:egret3d.Vector3D = new egret3d.Vector3D(10, 10, 10, 1);
//乘法运算
quat1.normalize();
quat1.transformVector(point, point);
//point
//w 1 Number
//x 1.9999999999999991 Number
//y 9.999999999999996 Number
//z 13.999999999999996 Number
- fromAxisAngle(): 创建一个以指定轴旋转一定角度的四元数;
- 重新设置该四元数的xyzw数据，使其表达的意思为以axis轴为中心旋转angle角
var quat:egret3d.Quaternion = new egret3d.Quaternion();
var axis:egret3d.Vector3D = new egret3d.Vector3D(10, 10, 10, 1);
var angle:number = 45 / 180 * Math.PI;
axis.normalize();
//赋值四元数
quat.fromAxisAngle(axis, angle);
//quat
//w 0.9999765121745486 Number
//x 0.003957065378313664 Number
//y 0.003957065378313664 Number
//z 0.003957065378313664 Number
- toAxisAngle():以指定axis为旋转轴，获得对应旋转角度;
var quat:egret3d.Quaternion = new egret3d.Quaternion(2, -1, 1, 1);
var axis:egret3d.Vector3D = new egret3d.Vector3D(10, 10, 10, 1);
axis.normalize();
quat.normalize();
//根据传入的旋转轴，获得旋转角度
var angle:number = quat.toAxisAngle(axis);
//angle: 135.58469140280704
- slerp():两个四元数之间球形插值，插值之间提供旋转恒定角变化率
- 在四元数a和四元数b之间，输入0-1之间的参数t，获得圆滑变化插值数据
- 可用于骨骼动画关节旋转的插值
var quat1:egret3d.Quaternion = new egret3d.Quaternion(2, -1, 1, 1);
var quat2:egret3d.Quaternion = new egret3d.Quaternion(-1, 4, 10, 1);
quat1.normalize();
quat2.normalize();
var result:egret3d.Quaternion = new egret3d.Quaternion();
//做插值计算
result.slerp(quat1, quat2);
var quat1:egret3d.Quaternion = new egret3d.Quaternion(2, -1, 1, 1);
var quat2:egret3d.Quaternion = new egret3d.Quaternion(-1, 4, 10, 1);
quat1.normalize();
quat2.normalize();
var result:egret3d.Quaternion = new egret3d.Quaternion();
//做插值计算
result.lerp(quat1, quat2);
- fromEulerAngles():根据传入的x/y/z三轴的旋转(欧拉角)，生成四元数数据
var quat:egret3d.Quaternion = new egret3d.Quaternion();
var angleX:number = 10;
var angleY:number = 140;
var angleZ:number = -20;
//欧拉角转换成四元数对象
quat.fromEulerAngles(angleX, angleY, angleZ);
- toEulerAngles():转换四元数对象到欧拉角
var quat:egret3d.Quaternion = new egret3d.Quaternion(2, -1, 1, 1);
var angleVector3D:egret3d.Vector3D = new egret3d.Vector3D();
quat.normalize();
//四元数对象转换成欧拉角
quat.toEulerAngles(angleVector3D);
//angleVector3D
//w 0 Number
//x 146.3099324740202 Number
//y -58.99728086612599 Number
//z -33.69006752597977 Number
- toMatrix3D():转换这个四元数旋转信息至一个4X4的矩阵中。
var quat:egret3d.Quaternion = new egret3d.Quaternion(2, -1, 1, 1);
var matrix:egret3d.Matrix4_4 = new egret3d.Matrix4_4();
quat.normalize();
//四元数对象转换成3D矩阵
quat.toMatrix3D(matrix);
//matrix
//[0] 0.4285714328289032 Number
//[1] -0.2857142984867096 Number
//[2] 0.8571428656578064 Number
//[3] 0 Number
//[4] -0.8571428656578064 Number
//[5] -0.4285714328289032 Number
//[6] 0.2857142984867096 Number
//[7] 0 Number
//[8] 0.2857142984867096 Number
//[9] -0.8571428656578064 Number
//[10] -0.4285714328289032 Number
//[11] 0 Number
//[12] 0 Number
//[13] 0 Number
//[14] 0 Number
//[15] 1 Number
- fromToRotation():计算由一个向量变换到另一个向量的四元数
- 获得向量a至向量b的变换的旋转信息，用四元数的形式表达
var quat:egret3d.Quaternion = new egret3d.Quaternion();
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();
//求出旋转四元数
quat.fromToRotation(direction1, direction2);
//quat
//w 0.5836404565967115 Number
//x -0.34131419516801636 Number
//y 0.7167597945339911 Number
//z -0.1706570848183054 Number
quat.transformVector(direction1, direction1);
//使用四元数旋转单位化之后的向量1，所得的结果和向量2对比：
// direction1
// w 1 Number
// x 0.8908708047027715 Number
// y 0.4454354229276571 Number
// z 0.08908706666455851 Number
// direction2
// w 1 Number
// x 0.8908708063747479 Number
// y 0.44543540318737395 Number
// z 0.0890870806374748 Number
guofei
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