227 lines
5.6 KiB
Markdown
227 lines
5.6 KiB
Markdown
3D基本变换
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===============
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## 四元数（egret3d.Quaternion） ##
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* multiply():两个四元数相乘
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* 两个四元数乘法运算之后的结果，为叠加后的旋转
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----------
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var quat1:egret3d.Quaternion = new egret3d.Quaternion(2, 3, 4, 1);
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var quat2:egret3d.Quaternion = new egret3d.Quaternion(4, 6, 8, 1);
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//乘法运算
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quat1.multiply(quat1, quat2);
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//quat1
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//w -57 Number
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//x 6 Number
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//y 9 Number
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//z 12 Number
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---------
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* normalize():单位化一个四元数;
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* 将四元数的四个分量缩放至长度为指定的标准，默认为1
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----------
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var quat1:egret3d.Quaternion = new egret3d.Quaternion(2, 3, 4, 1);
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//单位化
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quat1.normalize();
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//quat1
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//w 0.18257418583505536 Number
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//x 0.3651483716701107 Number
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//y 0.5477225575051661 Number
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//z 0.7302967433402214 Number
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---------
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* transformVector():四元数转换一个3D坐标点
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* 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
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----------
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var quat1:egret3d.Quaternion = new egret3d.Quaternion(2, 3, 4, 1);
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var point:egret3d.Vector3D = new egret3d.Vector3D(10, 10, 10, 1);
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//乘法运算
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quat1.normalize();
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quat1.transformVector(point, point);
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//point
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//w 1 Number
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//x 1.9999999999999991 Number
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//y 9.999999999999996 Number
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//z 13.999999999999996 Number
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---------
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* fromAxisAngle(): 创建一个以指定轴旋转一定角度的四元数;
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* 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
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----------
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var quat:egret3d.Quaternion = new egret3d.Quaternion();
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var axis:egret3d.Vector3D = new egret3d.Vector3D(10, 10, 10, 1);
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var angle:number = 45 / 180 * Math.PI;
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axis.normalize();
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//赋值四元数
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quat.fromAxisAngle(axis, angle);
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//quat
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//w 0.9999765121745486 Number
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//x 0.003957065378313664 Number
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//y 0.003957065378313664 Number
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//z 0.003957065378313664 Number
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---------
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* toAxisAngle():以指定axis为旋转轴，获得对应旋转角度;
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----------
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var quat:egret3d.Quaternion = new egret3d.Quaternion(2, -1, 1, 1);
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var axis:egret3d.Vector3D = new egret3d.Vector3D(10, 10, 10, 1);
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axis.normalize();
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quat.normalize();
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//根据传入的旋转轴，获得旋转角度
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var angle:number = quat.toAxisAngle(axis);
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//angle: 135.58469140280704
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---------
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* 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
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* 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
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* 可用于骨骼动画关节旋转的插值
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----------
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var quat1:egret3d.Quaternion = new egret3d.Quaternion(2, -1, 1, 1);
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var quat2:egret3d.Quaternion = new egret3d.Quaternion(-1, 4, 10, 1);
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quat1.normalize();
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quat2.normalize();
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var result:egret3d.Quaternion = new egret3d.Quaternion();
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//做插值计算
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result.slerp(quat1, quat2);
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---------
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* lerp():两个四元数之间线形插值
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----------
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var quat1:egret3d.Quaternion = new egret3d.Quaternion(2, -1, 1, 1);
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var quat2:egret3d.Quaternion = new egret3d.Quaternion(-1, 4, 10, 1);
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quat1.normalize();
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quat2.normalize();
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var result:egret3d.Quaternion = new egret3d.Quaternion();
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//做插值计算
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result.lerp(quat1, quat2);
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---------
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* fromEulerAngles():根据传入的x/y/z三轴的旋转(欧拉角)，生成四元数数据
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----------
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var quat:egret3d.Quaternion = new egret3d.Quaternion();
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var angleX:number = 10;
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var angleY:number = 140;
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var angleZ:number = -20;
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//欧拉角转换成四元数对象
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quat.fromEulerAngles(angleX, angleY, angleZ);
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---------
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* toEulerAngles():转换四元数对象到欧拉角
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----------
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var quat:egret3d.Quaternion = new egret3d.Quaternion(2, -1, 1, 1);
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var angleVector3D:egret3d.Vector3D = new egret3d.Vector3D();
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quat.normalize();
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//四元数对象转换成欧拉角
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quat.toEulerAngles(angleVector3D);
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//angleVector3D
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//w 0 Number
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//x 146.3099324740202 Number
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//y -58.99728086612599 Number
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//z -33.69006752597977 Number
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---------
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* toMatrix3D():转换这个四元数旋转信息至一个4X4的矩阵中。
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----------
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var quat:egret3d.Quaternion = new egret3d.Quaternion(2, -1, 1, 1);
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var matrix:egret3d.Matrix4_4 = new egret3d.Matrix4_4();
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quat.normalize();
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//四元数对象转换成3D矩阵
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quat.toMatrix3D(matrix);
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//matrix
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//[0] 0.4285714328289032 Number
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//[1] -0.2857142984867096 Number
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//[2] 0.8571428656578064 Number
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//[3] 0 Number
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//[4] -0.8571428656578064 Number
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//[5] -0.4285714328289032 Number
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//[6] 0.2857142984867096 Number
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//[7] 0 Number
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//[8] 0.2857142984867096 Number
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//[9] -0.8571428656578064 Number
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//[10] -0.4285714328289032 Number
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//[11] 0 Number
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//[12] 0 Number
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//[13] 0 Number
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//[14] 0 Number
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//[15] 1 Number
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---------
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* fromToRotation():计算由一个向量变换到另一个向量的四元数
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* 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
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----------
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var quat:egret3d.Quaternion = new egret3d.Quaternion();
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var direction1:egret3d.Vector3D = new egret3d.Vector3D(-1,0,2,1);
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var direction2:egret3d.Vector3D = new egret3d.Vector3D(10,5,1,1);
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direction1.normalize();
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direction2.normalize();
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//求出旋转四元数
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quat.fromToRotation(direction1, direction2);
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//quat
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//w 0.5836404565967115 Number
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//x -0.34131419516801636 Number
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//y 0.7167597945339911 Number
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//z -0.1706570848183054 Number
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quat.transformVector(direction1, direction1);
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//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：
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// direction1
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// w 1 Number
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// x 0.8908708047027715 Number
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// y 0.4454354229276571 Number
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// z 0.08908706666455851 Number
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// direction2
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// w 1 Number
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// x 0.8908708063747479 Number
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// y 0.44543540318737395 Number
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// z 0.0890870806374748 Number
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---------
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