@egjs/view360/src/YawPitchControl/input/lib/webvr-polyfill/math-util.ts

360 integrated viewing solution from inside-out view to outside-in view. It provides user-friendly service by rotating 360 degrees through various user interaction such as motion sensor and touch.

/* eslint-disable */
/*
 * Copyright 2016 Google Inc. All Rights Reserved.
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

import { window as win } from "../../../../utils/browser";

const MathUtil = win.MathUtil || {};

MathUtil.degToRad = Math.PI / 180;
MathUtil.radToDeg = 180 / Math.PI;

// Some minimal math functionality borrowed from THREE.Math and stripped down
// for the purposes of this library.


MathUtil.Vector2 = function( x, y ) {
  this.x = x || 0;
  this.y = y || 0;
};

MathUtil.Vector2.prototype = {
  constructor: MathUtil.Vector2,

  set: function( x, y ) {
    this.x = x;
    this.y = y;

    return this;
  },

  copy: function( v ) {
    this.x = v.x;
    this.y = v.y;

    return this;
  },

  subVectors: function( a, b ) {
    this.x = a.x - b.x;
    this.y = a.y - b.y;

    return this;
  }
};

MathUtil.Vector3 = function( x, y, z ) {
  this.x = x || 0;
  this.y = y || 0;
  this.z = z || 0;
};

MathUtil.Vector3.prototype = {
  constructor: MathUtil.Vector3,

  set: function( x, y, z ) {
    this.x = x;
    this.y = y;
    this.z = z;

    return this;
  },

  copy: function( v ) {
    this.x = v.x;
    this.y = v.y;
    this.z = v.z;

    return this;
  },

  length: function() {
    return Math.sqrt( this.x * this.x + this.y * this.y + this.z * this.z );
  },

  normalize: function() {
    const scalar = this.length();

    if ( scalar !== 0 ) {
      const invScalar = 1 / scalar;

      this.multiplyScalar(invScalar);
    } else {
      this.x = 0;
      this.y = 0;
      this.z = 0;
    }

    return this;
  },

  multiplyScalar: function( scalar ) {
    this.x *= scalar;
    this.y *= scalar;
    this.z *= scalar;
  },

  applyQuaternion: function( q ) {
    const x = this.x;
    const y = this.y;
    const z = this.z;

    const qx = q.x;
    const qy = q.y;
    const qz = q.z;
    const qw = q.w;

    // calculate quat * vector
    const ix =  qw * x + qy * z - qz * y;
    const iy =  qw * y + qz * x - qx * z;
    const iz =  qw * z + qx * y - qy * x;
    const iw = - qx * x - qy * y - qz * z;

    // calculate result * inverse quat
    this.x = ix * qw + iw * - qx + iy * - qz - iz * - qy;
    this.y = iy * qw + iw * - qy + iz * - qx - ix * - qz;
    this.z = iz * qw + iw * - qz + ix * - qy - iy * - qx;

    return this;
  },

  dot: function( v ) {
    return this.x * v.x + this.y * v.y + this.z * v.z;
  },

  crossVectors: function( a, b ) {
    const ax = a.x;
    const ay = a.y;
    const az = a.z;
    const bx = b.x;
    const by = b.y;
    const bz = b.z;

    this.x = ay * bz - az * by;
    this.y = az * bx - ax * bz;
    this.z = ax * by - ay * bx;

    return this;
  }
};

MathUtil.Quaternion = function( x, y, z, w ) {
  this.x = x || 0;
  this.y = y || 0;
  this.z = z || 0;
  this.w = ( w !== undefined ) ? w : 1;
};

MathUtil.Quaternion.prototype = {
  constructor: MathUtil.Quaternion,

  set: function( x, y, z, w ) {
    this.x = x;
    this.y = y;
    this.z = z;
    this.w = w;

    return this;
  },

  copy: function( quaternion ) {
    this.x = quaternion.x;
    this.y = quaternion.y;
    this.z = quaternion.z;
    this.w = quaternion.w;

    return this;
  },

  setFromEulerXYZ: function( x, y, z ) {
    const c1 = Math.cos( x / 2 );
    const c2 = Math.cos( y / 2 );
    const c3 = Math.cos( z / 2 );
    const s1 = Math.sin( x / 2 );
    const s2 = Math.sin( y / 2 );
    const s3 = Math.sin( z / 2 );

    this.x = s1 * c2 * c3 + c1 * s2 * s3;
    this.y = c1 * s2 * c3 - s1 * c2 * s3;
    this.z = c1 * c2 * s3 + s1 * s2 * c3;
    this.w = c1 * c2 * c3 - s1 * s2 * s3;

    return this;
  },

  setFromEulerYXZ: function( x, y, z ) {
    const c1 = Math.cos( x / 2 );
    const c2 = Math.cos( y / 2 );
    const c3 = Math.cos( z / 2 );
    const s1 = Math.sin( x / 2 );
    const s2 = Math.sin( y / 2 );
    const s3 = Math.sin( z / 2 );

    this.x = s1 * c2 * c3 + c1 * s2 * s3;
    this.y = c1 * s2 * c3 - s1 * c2 * s3;
    this.z = c1 * c2 * s3 - s1 * s2 * c3;
    this.w = c1 * c2 * c3 + s1 * s2 * s3;

    return this;
  },

  setFromAxisAngle: function( axis, angle ) {
    // http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/index.htm
    // assumes axis is normalized

    const halfAngle = angle / 2;
    const s = Math.sin( halfAngle );

    this.x = axis.x * s;
    this.y = axis.y * s;
    this.z = axis.z * s;
    this.w = Math.cos( halfAngle );

    return this;
  },

  multiply: function( q ) {
    return this.multiplyQuaternions( this, q );
  },

  multiplyQuaternions: function( a, b ) {
    // from http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/code/index.htm

    const qax = a.x;
    const qay = a.y;
    const qaz = a.z;
    const qaw = a.w;
    const qbx = b.x;
    const qby = b.y;
    const qbz = b.z;
    const qbw = b.w;

    this.x = qax * qbw + qaw * qbx + qay * qbz - qaz * qby;
    this.y = qay * qbw + qaw * qby + qaz * qbx - qax * qbz;
    this.z = qaz * qbw + qaw * qbz + qax * qby - qay * qbx;
    this.w = qaw * qbw - qax * qbx - qay * qby - qaz * qbz;

    return this;
  },

  inverse: function() {
    this.x *= -1;
    this.y *= -1;
    this.z *= -1;

    this.normalize();

    return this;
  },

  normalize: function() {
    let l = Math.sqrt( this.x * this.x + this.y * this.y + this.z * this.z + this.w * this.w );

    if ( l === 0 ) {
      this.x = 0;
      this.y = 0;
      this.z = 0;
      this.w = 1;
    } else {
      l = 1 / l;

      this.x = this.x * l;
      this.y = this.y * l;
      this.z = this.z * l;
      this.w = this.w * l;
    }

    return this;
  },

  slerp: function( qb, t ) {
    if ( t === 0 ) return this;
    if ( t === 1 ) return this.copy( qb );

    const x = this.x;
    const y = this.y;
    const z = this.z;
    const w = this.w;

    // http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/

    let cosHalfTheta = w * qb.w + x * qb.x + y * qb.y + z * qb.z;

    if ( cosHalfTheta < 0 ) {
      this.w = - qb.w;
      this.x = - qb.x;
      this.y = - qb.y;
      this.z = - qb.z;

      cosHalfTheta = - cosHalfTheta;
    } else {
      this.copy( qb );
    }

    if ( cosHalfTheta >= 1.0 ) {
      this.w = w;
      this.x = x;
      this.y = y;
      this.z = z;

      return this;
    }

    const halfTheta = Math.acos( cosHalfTheta );
    const sinHalfTheta = Math.sqrt( 1.0 - cosHalfTheta * cosHalfTheta );

    if ( Math.abs( sinHalfTheta ) < 0.001 ) {
      this.w = 0.5 * ( w + this.w );
      this.x = 0.5 * ( x + this.x );
      this.y = 0.5 * ( y + this.y );
      this.z = 0.5 * ( z + this.z );

      return this;
    }

    const ratioA = Math.sin( ( 1 - t ) * halfTheta ) / sinHalfTheta;
    const ratioB = Math.sin( t * halfTheta ) / sinHalfTheta;

    this.w = ( w * ratioA + this.w * ratioB );
    this.x = ( x * ratioA + this.x * ratioB );
    this.y = ( y * ratioA + this.y * ratioB );
    this.z = ( z * ratioA + this.z * ratioB );

    return this;
  },

  setFromUnitVectors: function() {
    // http://lolengine.net/blog/2014/02/24/quaternion-from-two-vectors-final
    // assumes direction vectors vFrom and vTo are normalized

    let v1;
    let r;
    const EPS = 0.000001;

    return function( vFrom, vTo ) {
      if ( v1 === undefined ) v1 = new MathUtil.Vector3();

      r = vFrom.dot( vTo ) + 1;

      if ( r < EPS ) {
        r = 0;

        if ( Math.abs( vFrom.x ) > Math.abs( vFrom.z ) ) {
          v1.set( - vFrom.y, vFrom.x, 0 );
        } else {
          v1.set( 0, - vFrom.z, vFrom.y );
        }
      } else {
        v1.crossVectors( vFrom, vTo );
      }

      this.x = v1.x;
      this.y = v1.y;
      this.z = v1.z;
      this.w = r;

      this.normalize();

      return this;
    };
  }()
};

export default MathUtil;