Three.js Source Note (vii) Math/euler.js

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The following code is a comment for the math/quaternion.js file in the three.js source file.

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file:src/math/euler.js/** * @author mrdoob/http://mrdoob.com/* @author Westlangley/http://github.com/westlangley * @author the constructor of the Bhouston/http://exocortex.com *//*///euler object. The object that is used to create a Euler angle. The function functions of the Euler object are implemented using the function prototype object defined by///.//////Usage: var Euler = new Euler (5,3,2, ' xyz ') creates a rotation around an axis 5 degrees, rotates a degree around the y-axis, rotates 2 degrees around an axis, and rotates in the order of ' XYZ '. There is a rotation order to determine how many degrees each x, Y, Z axis rotates.///note: Parameter x, The y,z represents the rotation angle of the 3 axes, and the number of axes that are rotated depends on the order of the parameters (Order).///note: Parameter (x,y,z,order) is an optional parameter, if you do not specify a parameter (x,y,z,order), a coordinate is created ( 0,0,0, ' xyz ') eular (Euler angle) object.//Note: The default order of the parameter order (rotation order) is the ' XYZ ' value range is [' xyz ', ' yzx ', ' zxy ', ' XZY ', ' yxz ', ' ZYX ']//////popular speaking, Euler's angle is a common method used to describe the direction of an object in three-dimensional space. For example, an object in three-dimensional space, the number of degrees around the x-axis, the///y axis of how many degrees, the z-axis of how many degrees, to describe the object in the three-dimensional space in the direction of. "Flying Eagle, flying Eagle, in front of you, 5 o'clock direction, find the target, ready to gather goals." *////<summary>euler</summary>///<param name = "x" type= "number" > rotate x degrees around an axis </param>///< param name = "y" type= "number" > rotates y degree around an axis </param>///<param name = "Z" type= "number" > Rotates z degree around an axis </param>/ <param name = "Order" type= "String" >ordeThe default order of R (rotation order) is the ' XYZ ' value range is [' xyz ', ' yzx ', ' zxy ', ' XZY ', ' yxz ', ' ZYX ']</param>three. Euler = function (x, y, Z, order) {this._x = x | | 0;this._y = y | | 0;this._z = Z | | 0;this._order = ORDER | | Three. Euler.defaultorder;}; Three. Euler.rotationorders = [' xyz ', ' yzx ', ' zxy ', ' XZY ', ' yxz ', ' ZYX '];//(rotation order) The default order is ' XYZ ' value range is [' xyz ', ' yzx ', ' zxy ', ' XZY ', ' Yxz ', ' ZYX ']three. Euler.defaultorder = ' xyz ';//The default rotation order is ' xyz '/******************************************** below is the function function provided by the Euler object. ******* /three. Euler.prototype = {Constructor:three. Euler,//constructor _x:0, _y:0, _z:0, _order:three. euler.defaultorder,//(_x,_y,_z,_order) initializes x, Y, Z to 0, the rotation order is the default rotation order ' XYZ ', and the/*///get x method is used to obtain the Euler angle × value.///note:get x () The usage is euler.prototype.x (euler.x), which can be used on browsers other than IE browsers. *////<summary>get x</summary>///<returns Type= "Number" > return euler angle _x value </returns>get x () {return this._x;//return Euler angle _x value},/*///set x method is used to re-set the X-value of the Euler angle. and returns the Euler angle of the new value. The usage of///note:set x () is Euler.prototype.x=value (euler.x = value), this usage is available on browsers other than IE browsers. *////<summary>set x</summary>///<param name = "Value" type= " Number > The angle value </param>set x (value) {this._x = value;//sets the _x value of the Euler angle This.onchangecallback ();//Invokes a callback function.},/ The *///get y method is used to derive the Euler angle y value from. The use of///note:get y () is euler.prototype.y (EULER.Y), which can be used on browsers other than IE browsers. *////<summary >get y</summary>///<returns type= "number" > return euler angle _y value </returns>get y () {return this._y;// Returns the Euler angle _y value},/*///set y method is used to re-set the Y value of the Euler angle. and returns the Euler angle of the new value. The use of///note:set y () is euler.prototype.y=value (euler.y = value) , this usage is available on browsers other than IE browsers. *////<summary>set y</summary>///<param name = "value" type= "number" > The angle value rotated around the y axis </param>set y (value) {this._y = value;//sets the _y value of the Euler angle This.onchangecallback ();//Invokes a callback function.},/*///get Z method to obtain the Z-value of the Euler angle. The use of///note:get Z () is euler.prototype.z (EULER.Z), which can be used on browsers other than IE browsers. *////<summary>get Z </summary>///<returns type= "number" > return euler angle _z value </returns>get Z () {return This._z;//returns the Euler angle _z value},/*///set Z method is used to re-set the Z-value of the Euler angle. and returns the Euler angle of the new value. The use of///note:set Z () is Euler.prototype.z=value ( Euler.z = value), this usage is available on browsers other than IE browsers. *////<summary>set z</summary>///<param name = "Value" type= " Number > The angle value </param>set Z (value) {this._z = value;//sets the _z value of the Euler angle This.onchangecallback ();//Invokes a callback function.},/ The *///get order method is used to obtain the Euler angle order value. The use of///note:get order () is Euler.prototype.order (Euler.order), which can be used on browsers other than IE browsers . *////<summary>get order</summary>///<returns type= "number" > return euler angle _z value </returns>get Order () {return this._order;//returns the Euler angle _order value},/*///set The order method used to re-set the Euler angle's order value. and returns the Euler angle of the new value.///note:set Order The usage of () is euler.prototype.order=value (Euler.order = value), which can be used on browsers other than IE browsers.///note: Parameter (x,y,z,order) is an optional parameter, If you do not specify a parameter (x,y,z,order), a eular (Euler angle) object with coordinates (0,0,0, ' XYZ ') is created.//NOTE: The default order of the parameter order (rotation order) is the ' XYZ ' value range is [' xyz ', ' yzx ', ' zxy ' , ' XZY ', ' yxz ', ' ZYX ']*////<summary>set order</summary>///<param name = ' value 'Type= "Number" > the angle value of rotation around the z-axis </param>set order (value) {this._order = value; Sets the _order value of the Euler angle This.onchangecallback (); Call the callback function.},///todo: The Setx () method is missing here.///todo: The Sety () method is missing here.///todo: The Setz () method is missing here.///todo: The SETW () method is missing.///todo: The SetComponent () method is missing here.///todo: The Getcomponent () method is missing here. The/*///set method is used to set the X,y,z,order value of Euler (Euler's angle) from the new. and returns the Euler (Euler angle) of the newly-coordinate value. TODO: Modify the Set method, which is compatible with X,y,z,order parameter omitting support polymorphism. *////<summary>set</summary>///<param name = "x" type= "number" > Rotate x degrees around an axis </param>///<param name = "Y" type= "number" > rotates the y degree around an axis </param>///<param name = "Z" type= " Number "> rotate the z degree around an axis </param>///<param name =" Order "type=" # ">order (rotation order) The default order is ' XYZ ' value range is [' xyz ', ' Yzx ', ' zxy ', ' XZY ', ' yxz ', ' ZYX ']</param>///<returns type= ' Euler (Euler angle) ' > Return to New Euler (Euler angle) </returns> Set:function (x, y, Z, order) {this._x = X;this._y = Y;this._z = Z;this._order = Order | | this._order;this.onchangecall Back ();//Call the callback function. Return this;//returns the new Euler (Euler angle)},/*///copy method used to copy Euler (Euler angle) (X,y,z,ordeR) value. and returns the new Euler (Euler angle). *////<summary>copy</summary>///<param name = "Euler (Euler angle)" type= "quaternion" > Euler (Euler angle) </param>///<returns type= "Euler (Euler angle)" > Return new Euler (Euler angle) </returns>copy:function (Euler) { this._x = euler._x;this._y = Euler._y;this._z = Euler._z;this._order = Euler._order;this.onchangecallback ();// Call the callback function. Return this;//returns the new Euler (Euler angle)},/*///setfromrotationmatrix method using a parameter m (rotation matrix) to achieve the purpose of rotation transformation.///NOTE:M is a rotation matrix, more formulas : http://en.wikipedia.org/wiki/Transformation_matrix//////Example: This sample is rotated 30 degrees on the z axis./------------------------------------ ----------------|cos (heading) = 0.866| Sin (heading) = 0.5 | 0 | | -----------------------|----------------------------|matrix =|-sin (heading) = -0.5 |cos (heading) = 0.866 | 0 | |     -----------------------|----------------------|-----||     0 | 0 | 1 |\----------------------------------------------------/angle = ACOs ((m00 + M11 + m22-1)/2) angle = ACOs ((0.866 + 0.866 + 1-1)/2) angle = ACOs(0.866) angle = Degreesx = (M21-M12) = 0-0 =0y = (M02-M20) = 0-0 =0z = (m10-m01) = -0.5-0.5 = -1*////<s Ummary>setfromrotationmatrix</summary>///<param name = "M" type= "Matrix3" >3x3 Matrix (rotation matrix) </param> <param name = "Order" type= "String" >order (rotation order) The default order is ' XYZ ' value range is [' xyz ', ' yzx ', ' zxy ', ' XZY ', ' yxz ', ' ZYX ']</p Aram>///<returns type= "Euler (Euler angle)" > Return to the new Euler (Euler angle) </returns>setfromrotationmatrix:function (M, Order) {var clamp = three. Math.clamp;//clamp is used to set the value range of values//assumes the upper 3x3 of M is a pure rotation matrix (i.e, unscaled)//Ensure that the parameter m is a 3x3 rotation matrix. VA R te = M.elements;var M11 = te[0], M12 = te[4], M13 = te[8];var M21 = te[1], M22 = te[5], M23 = te[9];var M31 = te[2], M32 = te[6], M33 = te[,];order = Order | | This._order;if (Order = = = ' XYZ ') {this._y = Math.asin (Clamp (M13,-1, 1)), if (Math.Abs (M13) < 0.99999) {this. _x = math.atan2 (-M23, M33); this._z = math.atan2 (-M12, M11);} else {this._x = Math.atan2 (M32, M22); this._z = 0;}} else if (order = = = ' Yxz ') {this._x = Math.asin (-Clamp (M23,-1, 1)), if (Math.Abs (M23) < 0.99999) {this._y = Math.atan2 (M13, M33); this._z = Math.atan2 (M21, M22);} else {this._y = math.atan2 (-M31, M11); this._z = 0;}} else if (order = = = ' Zxy ') {this._x = Math.asin (Clamp (M32,-1, 1)), if (Math.Abs (M32) < 0.99999) {this._y = Ma Th.atan2 (-M31, M33); this._z = math.atan2 (-M12, M22);} else {this._y = 0;this._z = Math.atan2 (M21, M11);}} else if (order = = = ' ZYX ') {this._y = Math.asin (-Clamp (M31,-1, 1)), if (Math.Abs (M31) < 0.99999) {this._x = Math.atan2 (M32, M33); this._z = Math.atan2 (M21, M11);} else {this._x = 0;this._z = math.atan2 (-M12, M22);}} else if (order = = = ' Yzx ') {this._z = Math.asin (Clamp (M21,-1, 1)), if (Math.Abs (M21) < 0.99999) {this._x = Ma Th.atan2 (-M23, M22); this._y = math.atan2 (-M31, M11);} else {this._x = 0;this._y = Math.atan2 (M13, M33);}} else if (order == = ' XZY ') {this._z = Math.asin (-Clamp (M12,-1, 1)), if (Math.Abs (M12) < 0.99999) {this._x = Math.atan2 (M32, M22); this._y = Math.atan2 (M13, M11);} else {this._x = math.atan2 (-M23, M33); this._y = 0;}} else {Console.warn (' three. Euler:. Setfromrotationmatrix () Given unsupported order: ' + order '//failed to set Euler angle object by following several rotation sequences}this._order = order;// Reset the Rotation order this.onchangecallback ();//Call the callback function. Return this;//returns a new Euler (Euler angle)},/*///setfromquaternion method to set Euler (Euler angle) by a four-dollar number ).///NOTE: The parameter (q) must be a unit vector by calling. Normalize () to get the unit vector.//Note: Parameter update is an optional parameter. If you do not set the default to True.*////<summary> Setfromquaternion</summary>///<param name = "Q" type= "quaternion" > four $ </param>///<param name = " Order "type=" String "> Rotation order </param>///<param name =" Update "type=" bool ">update indicates whether to invoke the callback function bool type tag Value </ Param>///<returns type= "Euler (Euler angle)" > Return to the new Euler (Euler angle) </returns>setfromquaternion:function (q, Order, Update) {var clamp = three. Math.clamp;//clamp used to set the value range of the value//q is assumednormalized//Ensure that q is a unit vector//The following URL is a detailed introduction to converting four to Euler angles. There are a lot of math algorithms in it.//http://www.mathworks.com/matlabcentral/ fileexchange/20696-function-to-convert-between-dcm-euler-angles-quaternions-and-euler-vectors/content/ Spincalc.mvar sqx = q.x * Q.x;var sqy = q.y * Q.y;var SQZ = q.z * Q.z;var sqw = Q.W * Q.w;order = Order | | This._order;if (Order = = = ' XYZ ') {this._x = math.atan2 (2 * (q.x * q.w-q.y * q.z), (sqw-sqx-sqy + sqz)); _y = Math.asin (Clamp (2 * (q.x * q.z + q.y * q.w),-1, 1)); this._z = Math.atan2 (2 * (Q.Z * q.w-q.x * q.y), (s QW + Sqx-sqy-sqz));}  else if (order = = = ' Yxz ') {this._x = Math.asin (Clamp (2 * (q.x * q.w-q.y * q.z),-1, 1)); this._y = Math.atan2 ( 2 * (q.x * q.z + q.y * q.w), (sqw-sqx-sqy + sqz)), this._z = Math.atan2 (2 * (q.x * q.y + q.z * q.w), (sqw-s QX + Sqy-sqz));} else if (order = = = ' Zxy ') {this._x = Math.asin (Clamp (2 * (q.x * Q.W + q.y * q.z),-1, 1)); this._y = Math.atan2 ( 2 * (Q.Y * q.w-q.z * q.x), (sqw-sqx-sqy + sqz)); This._z = math.atan2 (2 * (Q.Z * q.w-q.x * q.y), (SQW-SQX + Sqy-sqz));} else if (order = = = ' ZYX ') {this._x = math.atan2 (2 * (q.x * Q.W + q.z * q.y), (sqw-sqx-sqy + sqz)); this._y = Ma Th.asin (Clamp (2 * (Q.Y * q.w-q.x * q.z),-1, 1)); this._z = Math.atan2 (2 * (q.x * q.y + q.z * q.w), (sqw + sq) X-SQY-SQZ));} else if (order = = = ' Yzx ') {this._x = math.atan2 (2 * (q.x * q.w-q.z * q.y), (SQW-SQX + sqy-sqz)); this._y = Ma Th.atan2 (2 * (Q.Y * q.w-q.x * q.z), (SQW + sqx-sqy-sqz)); this._z = Math.asin (Clamp (2 * (q.x * q.y + q.z * Q.W),-1, 1);} else if (order = = = ' XZY ') {this._x = math.atan2 (2 * (q.x * Q.W + q.y * q.z), (SQW-SQX + sqy-sqz)); this._y = Ma Th.atan2 (2 * (q.x * q.z + q.y * q.w), (SQW + sqx-sqy-sqz)); this._z = Math.asin (Clamp (2 * (Q.Z * q.w-q.x * Q.Y),-1, 1);} else {Console.warn (' three. Euler:. Setfromquaternion () Given unsupported order: ' + order '//by pressingSet Euler angle object in the above several rotation order failure error}this._order = order;//Reset the rotation order if (update!== false) This.onchangecallback ();// The update parameter is used to determine whether the callback function is called. Return this;//Returns a new Euler (Euler angle)},/*///reorder method to set the rotation order of Euler (Euler's angle) by a four-tuple.//NOTE: The parameter (q) must be a unit vector, The unit vector is obtained by calling. Normalize ().///The Warning:reorder method discards the rotation order information for Euler (Euler angle). *////<summary>reorder</summary>/// <param name = "Order" type= "String" > Rotation order </param>///<returns type= "Euler (Euler angle)" > Return new Euler (Euler angle) </ The Returns>reorder:function () {///Warning:reorder method discards the rotation order information for Euler (Euler angle).//Warning:this discards revolution Informat Ion-bhoustonvar q = new three. Quaternion (); return function (Neworder) {Q.setfromeuler (this); This.setfromquaternion (q, Neworder);// Call the Setfromquaternion () method to return the Euler (Euler angle) of the new rotation order;} (), the/*equals method///equals method equals the comparison operator = = =, compares the current Euler (Euler angle) with the (X,y,z,order) value in the parameter Euler and returns the bool type value .*////<summary> Equals</summary>///<param name = "V" type= "Euler (Euler Angle)" >euler (Euler angle) (X,y,z,order) </param>///< Returns type= "BOOL" > returns TRUE or false</returns>equals:function (Euler) {return (euler._x = = = this._x) && (euler._y = = = this._y) && (E Uler._z = = = This._z) && (Euler._order = = = This._order);},/*fromarray method///fromarray method will store Euler (Euler angle) (x, Y, Z, Order) value array to the current Euler (Euler angle) object///NOTE: The parameter order is an optional parameter. If you do not set the default rotation order by using the .*////<summary>fromarray</summary> <param name = "Array" type= "array" >euler (Euler angle) (x,y,z,order) value array array[x,y,z,order]</param>///< Returns type= "Euler (Euler angle)" > Return new Euler (Euler angle) </returns>fromarray:function (array) {this._x = array[0];this._y = a rray[1];this._z = array[2];if (array[3]!== undefined) This._order = array[3];this.onchangecallback ();//Call callback function. R Eturn this;//returns the new Euler (Euler angle)},/*toarray method///toarray method assigns the properties of the current Euler (Euler angle) object to the array array[5,3,2, ' XYZ ']. Returns an Array object. *//// <summary>toarray</summary>///<returns type= "Array" >euler (Euler angle) (_x,_y,_z,_order) value array array[x,y,z, Order]</returns>toarray:function () {return [this._x, this._y, This._z, tHis._order];//returns an array containing X,y,z,order values, the},/*onchange method///onchange method passes the callback function expression as a callback parameter to the Onchangecallback () method. * <summary>onchange</summary>///<param name = "Callback" type= "function" > callback function </param>/// <returns type= "Euler (Euler Angle)" >euler (Euler angle) </returns>onchange:function (callback) {This.onchangecallback = Callback;return This;},/*onchangecallback Method///onchangecallback method clones an Euler (Euler angle) object.///note:onchangecallback () The method here is an empty function attribute, the Onchangecallback () method is called in most of the above methods, which is a convenient method. *////<summary>onchangecallback</summary >onchangecallback:function () {},/*clone method///clone method clones an Euler (Euler angle) object. *////<summary>clone</summary >///<returns type= "Euler (Euler angle)" > Return Euler (Euler angle) object </returns>clone:function () {return new three. Euler (this._x, this._y, This._z, This._order);};

Commercial Territory (http://blog.csdn.net/omni360/)

This article follows "Attribution-non-commercial use-consistent" authoring public agreement

Reprint Please keep this sentence: Business Domain-this blog focuses on Agile development and mobile and IoT device research: Data visualization, Golang, HTML5, WEBGL, three. JS, Otherwise, from this blog article refused to reprint or reprint, thank you for your cooperation.

The following code is a comment for the math/quaternion.js file in the three.js source file.

More updates in: https://github.com/omni360/three.js.sourcecode/blob/master/Three.js

Three.js Source Note (vii) Math/euler.js