687 lines
12 KiB
JavaScript
687 lines
12 KiB
JavaScript
import * as MathUtils from './MathUtils.js';
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class Quaternion {
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constructor( x = 0, y = 0, z = 0, w = 1 ) {
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this.isQuaternion = true;
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this._x = x;
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this._y = y;
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this._z = z;
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this._w = w;
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}
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static slerpFlat( dst, dstOffset, src0, srcOffset0, src1, srcOffset1, t ) {
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// fuzz-free, array-based Quaternion SLERP operation
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let x0 = src0[ srcOffset0 + 0 ],
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y0 = src0[ srcOffset0 + 1 ],
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z0 = src0[ srcOffset0 + 2 ],
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w0 = src0[ srcOffset0 + 3 ];
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const x1 = src1[ srcOffset1 + 0 ],
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y1 = src1[ srcOffset1 + 1 ],
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z1 = src1[ srcOffset1 + 2 ],
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w1 = src1[ srcOffset1 + 3 ];
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if ( t === 0 ) {
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dst[ dstOffset + 0 ] = x0;
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dst[ dstOffset + 1 ] = y0;
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dst[ dstOffset + 2 ] = z0;
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dst[ dstOffset + 3 ] = w0;
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return;
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}
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if ( t === 1 ) {
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dst[ dstOffset + 0 ] = x1;
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dst[ dstOffset + 1 ] = y1;
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dst[ dstOffset + 2 ] = z1;
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dst[ dstOffset + 3 ] = w1;
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return;
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}
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if ( w0 !== w1 || x0 !== x1 || y0 !== y1 || z0 !== z1 ) {
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let s = 1 - t;
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const cos = x0 * x1 + y0 * y1 + z0 * z1 + w0 * w1,
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dir = ( cos >= 0 ? 1 : - 1 ),
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sqrSin = 1 - cos * cos;
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// Skip the Slerp for tiny steps to avoid numeric problems:
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if ( sqrSin > Number.EPSILON ) {
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const sin = Math.sqrt( sqrSin ),
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len = Math.atan2( sin, cos * dir );
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s = Math.sin( s * len ) / sin;
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t = Math.sin( t * len ) / sin;
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}
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const tDir = t * dir;
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x0 = x0 * s + x1 * tDir;
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y0 = y0 * s + y1 * tDir;
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z0 = z0 * s + z1 * tDir;
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w0 = w0 * s + w1 * tDir;
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// Normalize in case we just did a lerp:
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if ( s === 1 - t ) {
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const f = 1 / Math.sqrt( x0 * x0 + y0 * y0 + z0 * z0 + w0 * w0 );
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x0 *= f;
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y0 *= f;
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z0 *= f;
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w0 *= f;
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}
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}
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dst[ dstOffset ] = x0;
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dst[ dstOffset + 1 ] = y0;
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dst[ dstOffset + 2 ] = z0;
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dst[ dstOffset + 3 ] = w0;
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}
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static multiplyQuaternionsFlat( dst, dstOffset, src0, srcOffset0, src1, srcOffset1 ) {
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const x0 = src0[ srcOffset0 ];
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const y0 = src0[ srcOffset0 + 1 ];
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const z0 = src0[ srcOffset0 + 2 ];
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const w0 = src0[ srcOffset0 + 3 ];
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const x1 = src1[ srcOffset1 ];
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const y1 = src1[ srcOffset1 + 1 ];
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const z1 = src1[ srcOffset1 + 2 ];
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const w1 = src1[ srcOffset1 + 3 ];
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dst[ dstOffset ] = x0 * w1 + w0 * x1 + y0 * z1 - z0 * y1;
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dst[ dstOffset + 1 ] = y0 * w1 + w0 * y1 + z0 * x1 - x0 * z1;
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dst[ dstOffset + 2 ] = z0 * w1 + w0 * z1 + x0 * y1 - y0 * x1;
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dst[ dstOffset + 3 ] = w0 * w1 - x0 * x1 - y0 * y1 - z0 * z1;
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return dst;
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}
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get x() {
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return this._x;
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}
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set x( value ) {
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this._x = value;
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this._onChangeCallback();
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}
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get y() {
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return this._y;
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}
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set y( value ) {
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this._y = value;
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this._onChangeCallback();
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}
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get z() {
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return this._z;
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}
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set z( value ) {
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this._z = value;
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this._onChangeCallback();
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}
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get w() {
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return this._w;
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}
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set w( value ) {
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this._w = value;
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this._onChangeCallback();
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}
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set( x, y, z, w ) {
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this._x = x;
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this._y = y;
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this._z = z;
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this._w = w;
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this._onChangeCallback();
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return this;
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}
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clone() {
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return new this.constructor( this._x, this._y, this._z, this._w );
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}
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copy( quaternion ) {
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this._x = quaternion.x;
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this._y = quaternion.y;
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this._z = quaternion.z;
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this._w = quaternion.w;
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this._onChangeCallback();
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return this;
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}
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setFromEuler( euler, update = true ) {
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const x = euler._x, y = euler._y, z = euler._z, order = euler._order;
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// http://www.mathworks.com/matlabcentral/fileexchange/
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// 20696-function-to-convert-between-dcm-euler-angles-quaternions-and-euler-vectors/
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// content/SpinCalc.m
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const cos = Math.cos;
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const sin = Math.sin;
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const c1 = cos( x / 2 );
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const c2 = cos( y / 2 );
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const c3 = cos( z / 2 );
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const s1 = sin( x / 2 );
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const s2 = sin( y / 2 );
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const s3 = sin( z / 2 );
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switch ( order ) {
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case 'XYZ':
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this._x = s1 * c2 * c3 + c1 * s2 * s3;
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this._y = c1 * s2 * c3 - s1 * c2 * s3;
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this._z = c1 * c2 * s3 + s1 * s2 * c3;
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this._w = c1 * c2 * c3 - s1 * s2 * s3;
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break;
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case 'YXZ':
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this._x = s1 * c2 * c3 + c1 * s2 * s3;
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this._y = c1 * s2 * c3 - s1 * c2 * s3;
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this._z = c1 * c2 * s3 - s1 * s2 * c3;
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this._w = c1 * c2 * c3 + s1 * s2 * s3;
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break;
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case 'ZXY':
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this._x = s1 * c2 * c3 - c1 * s2 * s3;
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this._y = c1 * s2 * c3 + s1 * c2 * s3;
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this._z = c1 * c2 * s3 + s1 * s2 * c3;
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this._w = c1 * c2 * c3 - s1 * s2 * s3;
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break;
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case 'ZYX':
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this._x = s1 * c2 * c3 - c1 * s2 * s3;
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this._y = c1 * s2 * c3 + s1 * c2 * s3;
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this._z = c1 * c2 * s3 - s1 * s2 * c3;
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this._w = c1 * c2 * c3 + s1 * s2 * s3;
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break;
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case 'YZX':
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this._x = s1 * c2 * c3 + c1 * s2 * s3;
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this._y = c1 * s2 * c3 + s1 * c2 * s3;
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this._z = c1 * c2 * s3 - s1 * s2 * c3;
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this._w = c1 * c2 * c3 - s1 * s2 * s3;
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break;
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case 'XZY':
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this._x = s1 * c2 * c3 - c1 * s2 * s3;
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this._y = c1 * s2 * c3 - s1 * c2 * s3;
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this._z = c1 * c2 * s3 + s1 * s2 * c3;
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this._w = c1 * c2 * c3 + s1 * s2 * s3;
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break;
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default:
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console.warn( 'THREE.Quaternion: .setFromEuler() encountered an unknown order: ' + order );
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}
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if ( update === true ) this._onChangeCallback();
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return this;
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}
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setFromAxisAngle( axis, angle ) {
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// http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/index.htm
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// assumes axis is normalized
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const halfAngle = angle / 2, s = Math.sin( halfAngle );
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this._x = axis.x * s;
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this._y = axis.y * s;
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this._z = axis.z * s;
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this._w = Math.cos( halfAngle );
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this._onChangeCallback();
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return this;
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}
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setFromRotationMatrix( m ) {
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// http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
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// assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled)
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const te = m.elements,
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m11 = te[ 0 ], m12 = te[ 4 ], m13 = te[ 8 ],
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m21 = te[ 1 ], m22 = te[ 5 ], m23 = te[ 9 ],
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m31 = te[ 2 ], m32 = te[ 6 ], m33 = te[ 10 ],
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trace = m11 + m22 + m33;
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if ( trace > 0 ) {
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const s = 0.5 / Math.sqrt( trace + 1.0 );
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this._w = 0.25 / s;
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this._x = ( m32 - m23 ) * s;
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this._y = ( m13 - m31 ) * s;
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this._z = ( m21 - m12 ) * s;
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} else if ( m11 > m22 && m11 > m33 ) {
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const s = 2.0 * Math.sqrt( 1.0 + m11 - m22 - m33 );
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this._w = ( m32 - m23 ) / s;
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this._x = 0.25 * s;
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this._y = ( m12 + m21 ) / s;
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this._z = ( m13 + m31 ) / s;
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} else if ( m22 > m33 ) {
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const s = 2.0 * Math.sqrt( 1.0 + m22 - m11 - m33 );
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this._w = ( m13 - m31 ) / s;
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this._x = ( m12 + m21 ) / s;
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this._y = 0.25 * s;
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this._z = ( m23 + m32 ) / s;
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} else {
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const s = 2.0 * Math.sqrt( 1.0 + m33 - m11 - m22 );
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this._w = ( m21 - m12 ) / s;
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this._x = ( m13 + m31 ) / s;
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this._y = ( m23 + m32 ) / s;
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this._z = 0.25 * s;
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}
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this._onChangeCallback();
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return this;
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}
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setFromUnitVectors( vFrom, vTo ) {
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// assumes direction vectors vFrom and vTo are normalized
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let r = vFrom.dot( vTo ) + 1;
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if ( r < Number.EPSILON ) {
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// vFrom and vTo point in opposite directions
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r = 0;
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if ( Math.abs( vFrom.x ) > Math.abs( vFrom.z ) ) {
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this._x = - vFrom.y;
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this._y = vFrom.x;
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this._z = 0;
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this._w = r;
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} else {
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this._x = 0;
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this._y = - vFrom.z;
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this._z = vFrom.y;
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this._w = r;
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}
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} else {
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// crossVectors( vFrom, vTo ); // inlined to avoid cyclic dependency on Vector3
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this._x = vFrom.y * vTo.z - vFrom.z * vTo.y;
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this._y = vFrom.z * vTo.x - vFrom.x * vTo.z;
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this._z = vFrom.x * vTo.y - vFrom.y * vTo.x;
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this._w = r;
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}
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return this.normalize();
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}
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angleTo( q ) {
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return 2 * Math.acos( Math.abs( MathUtils.clamp( this.dot( q ), - 1, 1 ) ) );
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}
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rotateTowards( q, step ) {
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const angle = this.angleTo( q );
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if ( angle === 0 ) return this;
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const t = Math.min( 1, step / angle );
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this.slerp( q, t );
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return this;
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}
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identity() {
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return this.set( 0, 0, 0, 1 );
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}
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invert() {
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// quaternion is assumed to have unit length
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return this.conjugate();
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}
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conjugate() {
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this._x *= - 1;
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this._y *= - 1;
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this._z *= - 1;
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this._onChangeCallback();
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return this;
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}
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dot( v ) {
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return this._x * v._x + this._y * v._y + this._z * v._z + this._w * v._w;
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}
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lengthSq() {
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return this._x * this._x + this._y * this._y + this._z * this._z + this._w * this._w;
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}
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length() {
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return Math.sqrt( this._x * this._x + this._y * this._y + this._z * this._z + this._w * this._w );
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}
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normalize() {
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let l = this.length();
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if ( l === 0 ) {
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this._x = 0;
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this._y = 0;
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this._z = 0;
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this._w = 1;
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} else {
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l = 1 / l;
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this._x = this._x * l;
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this._y = this._y * l;
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this._z = this._z * l;
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this._w = this._w * l;
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}
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this._onChangeCallback();
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return this;
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}
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multiply( q ) {
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return this.multiplyQuaternions( this, q );
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}
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premultiply( q ) {
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return this.multiplyQuaternions( q, this );
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}
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multiplyQuaternions( a, b ) {
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// from http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/code/index.htm
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const qax = a._x, qay = a._y, qaz = a._z, qaw = a._w;
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const qbx = b._x, qby = b._y, qbz = b._z, qbw = b._w;
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this._x = qax * qbw + qaw * qbx + qay * qbz - qaz * qby;
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this._y = qay * qbw + qaw * qby + qaz * qbx - qax * qbz;
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this._z = qaz * qbw + qaw * qbz + qax * qby - qay * qbx;
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this._w = qaw * qbw - qax * qbx - qay * qby - qaz * qbz;
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this._onChangeCallback();
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return this;
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}
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slerp( qb, t ) {
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if ( t === 0 ) return this;
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if ( t === 1 ) return this.copy( qb );
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const x = this._x, y = this._y, z = this._z, w = this._w;
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// http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/
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let cosHalfTheta = w * qb._w + x * qb._x + y * qb._y + z * qb._z;
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if ( cosHalfTheta < 0 ) {
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this._w = - qb._w;
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this._x = - qb._x;
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this._y = - qb._y;
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this._z = - qb._z;
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cosHalfTheta = - cosHalfTheta;
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} else {
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this.copy( qb );
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}
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if ( cosHalfTheta >= 1.0 ) {
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this._w = w;
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this._x = x;
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this._y = y;
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this._z = z;
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return this;
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}
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const sqrSinHalfTheta = 1.0 - cosHalfTheta * cosHalfTheta;
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if ( sqrSinHalfTheta <= Number.EPSILON ) {
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const s = 1 - t;
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this._w = s * w + t * this._w;
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this._x = s * x + t * this._x;
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this._y = s * y + t * this._y;
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this._z = s * z + t * this._z;
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this.normalize(); // normalize calls _onChangeCallback()
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return this;
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}
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const sinHalfTheta = Math.sqrt( sqrSinHalfTheta );
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const halfTheta = Math.atan2( sinHalfTheta, cosHalfTheta );
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const ratioA = Math.sin( ( 1 - t ) * halfTheta ) / sinHalfTheta,
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ratioB = Math.sin( t * halfTheta ) / sinHalfTheta;
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this._w = ( w * ratioA + this._w * ratioB );
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this._x = ( x * ratioA + this._x * ratioB );
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this._y = ( y * ratioA + this._y * ratioB );
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this._z = ( z * ratioA + this._z * ratioB );
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this._onChangeCallback();
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return this;
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}
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slerpQuaternions( qa, qb, t ) {
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return this.copy( qa ).slerp( qb, t );
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}
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random() {
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// sets this quaternion to a uniform random unit quaternnion
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// Ken Shoemake
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// Uniform random rotations
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// D. Kirk, editor, Graphics Gems III, pages 124-132. Academic Press, New York, 1992.
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const theta1 = 2 * Math.PI * Math.random();
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const theta2 = 2 * Math.PI * Math.random();
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const x0 = Math.random();
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const r1 = Math.sqrt( 1 - x0 );
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const r2 = Math.sqrt( x0 );
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|
|
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return this.set(
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r1 * Math.sin( theta1 ),
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r1 * Math.cos( theta1 ),
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r2 * Math.sin( theta2 ),
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|
r2 * Math.cos( theta2 ),
|
|
);
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}
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equals( quaternion ) {
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|
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return ( quaternion._x === this._x ) && ( quaternion._y === this._y ) && ( quaternion._z === this._z ) && ( quaternion._w === this._w );
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}
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fromArray( array, offset = 0 ) {
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|
|
|
this._x = array[ offset ];
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|
this._y = array[ offset + 1 ];
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|
this._z = array[ offset + 2 ];
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|
this._w = array[ offset + 3 ];
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|
|
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this._onChangeCallback();
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|
|
|
return this;
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|
|
|
}
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|
|
|
toArray( array = [], offset = 0 ) {
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|
|
|
array[ offset ] = this._x;
|
|
array[ offset + 1 ] = this._y;
|
|
array[ offset + 2 ] = this._z;
|
|
array[ offset + 3 ] = this._w;
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|
|
|
return array;
|
|
|
|
}
|
|
|
|
fromBufferAttribute( attribute, index ) {
|
|
|
|
this._x = attribute.getX( index );
|
|
this._y = attribute.getY( index );
|
|
this._z = attribute.getZ( index );
|
|
this._w = attribute.getW( index );
|
|
|
|
this._onChangeCallback();
|
|
|
|
return this;
|
|
|
|
}
|
|
|
|
toJSON() {
|
|
|
|
return this.toArray();
|
|
|
|
}
|
|
|
|
_onChange( callback ) {
|
|
|
|
this._onChangeCallback = callback;
|
|
|
|
return this;
|
|
|
|
}
|
|
|
|
_onChangeCallback() {}
|
|
|
|
*[ Symbol.iterator ]() {
|
|
|
|
yield this._x;
|
|
yield this._y;
|
|
yield this._z;
|
|
yield this._w;
|
|
|
|
}
|
|
|
|
}
|
|
|
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export { Quaternion };
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