front_end/ui/legacy/Geometry.ts - devtools/devtools-frontend - Git at Google

 /*
  * Copyright (C) 2013 Google Inc. All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without
  * modification, are permitted provided that the following conditions are
  * met:
  *
  *     * Redistributions of source code must retain the above copyright
  * notice, this list of conditions and the following disclaimer.
  *     * Redistributions in binary form must reproduce the above
  * copyright notice, this list of conditions and the following disclaimer
  * in the documentation and/or other materials provided with the
  * distribution.
  *     * Neither the name of Google Inc. nor the names of its
  * contributors may be used to endorse or promote products derived from
  * this software without specific prior written permission.
  *
  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
  * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
  * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
  * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
  * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
  * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  */

 /* eslint-disable rulesdir/no_underscored_properties */

 // TODO(crbug.com/1172300) Ignored during the jsdoc to ts migration
 // eslint-disable-next-line @typescript-eslint/naming-convention
 export const _Eps: number = 1e-5;

 export class Vector {
   x: number;
   y: number;
   z: number;

   constructor(x: number, y: number, z: number) {
     this.x = x;
     this.y = y;
     this.z = z;
   }

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

   normalize(): void {
     const length = this.length();
     if (length <= _Eps) {
       return;
     }

     this.x /= length;
     this.y /= length;
     this.z /= length;
   }
 }

 export class Point {
   x: number;
   y: number;

   constructor(x: number, y: number) {
     this.x = x;
     this.y = y;
   }

   distanceTo(p: Point): number {
     return Math.sqrt(Math.pow(p.x - this.x, 2) + Math.pow(p.y - this.y, 2));
   }

   projectOn(line: Point): Point {
     if (line.x === 0 && line.y === 0) {
       return new Point(0, 0);
     }
     return line.scale((this.x * line.x + this.y * line.y) / (Math.pow(line.x, 2) + Math.pow(line.y, 2)));
   }

   scale(scalar: number): Point {
     return new Point(this.x * scalar, this.y * scalar);
   }

   toString(): string {
     return Math.round(this.x * 100) / 100 + ', ' + Math.round(this.y * 100) / 100;
   }
 }

 export class CubicBezier {
   controlPoints: Point[];
   constructor(point1: Point, point2: Point) {
     this.controlPoints = [point1, point2];
   }

   static parse(text: string): CubicBezier|null {
     const keywordValues = CubicBezier.KeywordValues;
     const value = text.toLowerCase().replace(/\s+/g, '');
     if (keywordValues.has(value)) {
       return CubicBezier.parse((keywordValues.get(value) as string));
     }
     const bezierRegex = /^cubic-bezier\(([^,]+),([^,]+),([^,]+),([^,]+)\)$/;
     const match = value.match(bezierRegex);
     if (match) {
       const control1 = new Point(parseFloat(match[1]), parseFloat(match[2]));
       const control2 = new Point(parseFloat(match[3]), parseFloat(match[4]));
       return new CubicBezier(control1, control2);
     }
     return null;
   }

   evaluateAt(t: number): Point {
     function evaluate(v1: number, v2: number, t: number): number {
       return 3 * (1 - t) * (1 - t) * t * v1 + 3 * (1 - t) * t * t * v2 + Math.pow(t, 3);
     }

     const x = evaluate(this.controlPoints[0].x, this.controlPoints[1].x, t);
     const y = evaluate(this.controlPoints[0].y, this.controlPoints[1].y, t);
     return new Point(x, y);
   }

   asCSSText(): string {
     const raw = 'cubic-bezier(' + this.controlPoints.join(', ') + ')';
     const keywordValues = CubicBezier.KeywordValues;
     for (const [keyword, value] of keywordValues) {
       if (raw === value) {
         return keyword;
       }
     }
     return raw;
   }

   // TODO(crbug.com/1172300) Ignored during the jsdoc to ts migration
   // eslint-disable-next-line @typescript-eslint/naming-convention
   static readonly Regex = /((cubic-bezier\([^)]+\))|\b(linear(?!-)|ease-in-out|ease-in|ease-out|ease)\b)/g;
   // TODO(crbug.com/1172300) Ignored during the jsdoc to ts migration
   // eslint-disable-next-line @typescript-eslint/naming-convention
   static readonly KeywordValues = new Map([
     ['linear', 'cubic-bezier(0, 0, 1, 1)'],
     ['ease', 'cubic-bezier(0.25, 0.1, 0.25, 1)'],
     ['ease-in', 'cubic-bezier(0.42, 0, 1, 1)'],
     ['ease-in-out', 'cubic-bezier(0.42, 0, 0.58, 1)'],
     ['ease-out', 'cubic-bezier(0, 0, 0.58, 1)'],
   ]);
 }

 export class EulerAngles {
   alpha: number;
   beta: number;
   gamma: number;

   constructor(alpha: number, beta: number, gamma: number) {
     this.alpha = alpha;
     this.beta = beta;
     this.gamma = gamma;
   }

   /**
    * Derives orientation angles from a rotation matrix.
    *
    * The angles alpha, beta and gamma are in the [0, 360), [-180, 180) and
    * [-90, 90) intervals respectively, as specified in the Device Orientation
    * spec (https://w3c.github.io/deviceorientation/#deviceorientation).
    *
    * The Euler angles derived here follow a Z-X'-Y'' sequence.
    *
    * In particular we compute the decomposition of a given rotation matrix r
    * such that
    *    r = rz(alpha) * rx(beta) * ry(gamma)
    * where rz, rx and ry are rotation matrices around z, x and y axes in the
    * world coordinate reference frame respectively. The reference frame
    * consists of three orthogonal axes x, y, z where x points East, y points
    * north and z points upwards perpendicular to the ground plane. The computed
    * angles alpha, beta and gamma are in degrees and clockwise-positive when
    * viewed along the positive direction of the corresponding axis. Except for
    * the special case when the beta angle is +-90 these angles uniquely
    * define the orientation of a mobile device in 3D space. The
    * alpha-beta-gamma representation resembles the yaw-pitch-roll convention
    * used in vehicle dynamics, however it does not exactly match it. One of the
    * differences is that the 'pitch' angle beta is allowed to be within [-180,
    * 180). A mobile device with pitch angle greater than 90 could
    * correspond to a user lying down and looking upward at the screen.
    */
   static fromDeviceOrientationRotationMatrix(rotationMatrix: DOMMatrixReadOnly): EulerAngles {
     let alpha, beta, gamma;

     // A few implementation notes:
     // - This code has been ported from Chromium's
     //   //services/device/generic_sensor/orientation_util.cc at commit
     //   1be837b6f142.
     //
     // - Since |rotationMatrix| contains non-integer numbers, directly
     //   comparing them to 0 will not be accurate, so we use |_Eps| to check if
     //   some numbers are close enough to 0.
     //
     // - The C++ code in Chromium uses a std::vector<double> to represent a 3x3
     //   rotation matrix in row-major order. |rotationMatrix| is a 4x4 matrix
     //   defined in column-major order, so |rotationMatrix.m13| here
     //   corresponds to |r[8]| in the original C++ code.
     //
     // - There are rounding errors and approximations in the floating-point
     //   arithmetics below, but it does not interfere with the use cases in
     //   DevTools (i.e. angles that are mostly within the allowed intervals). A
     //   rotation around the Z axis by 360 degrees will correctly return
     //   alpha=0, but a rotation around the Z axis by 360 * 20000000000000000
     //   will return alpha=~75 degrees, for example.
     if (Math.abs(rotationMatrix.m33) < _Eps) {    // m33 == 0
       if (Math.abs(rotationMatrix.m13) < _Eps) {  // m13 == 0, cos(beta) == 0
         // Gimbal lock discontinuity: in the Z-X'-Y'' angle system used here, a
         // rotation of 90 or -90 degrees around the X axis (beta) causes a
         // Gimbal lock, which we handle by always setting gamma = 0 and
         // handling the rotation in alpha.
         alpha = Math.atan2(rotationMatrix.m12, rotationMatrix.m11);
         beta = (rotationMatrix.m23 > 0) ? (Math.PI / 2) : -(Math.PI / 2);  // beta = +-pi/2
         gamma = 0;                                                         // gamma = 0
       } else if (rotationMatrix.m13 > 0) {                                 // cos(gamma) == 0, cos(beta) > 0
         alpha = Math.atan2(-rotationMatrix.m21, rotationMatrix.m22);
         beta = Math.asin(rotationMatrix.m23);  // beta [-pi/2, pi/2]
         gamma = -(Math.PI / 2);                // gamma = -pi/2
       } else {                                 // cos(gamma) == 0, cos(beta) < 0
         alpha = Math.atan2(rotationMatrix.m21, -rotationMatrix.m22);
         beta = -Math.asin(rotationMatrix.m23);
         beta += (beta > 0 || Math.abs(beta) < _Eps) ? -Math.PI : Math.PI;  // beta [-pi,-pi/2) U (pi/2,pi)
         gamma = -(Math.PI / 2);                                            // gamma = -pi/2
       }
     } else if (rotationMatrix.m33 > 0) {  // cos(beta) > 0
       alpha = Math.atan2(-rotationMatrix.m21, rotationMatrix.m22);
       beta = Math.asin(rotationMatrix.m23);                         // beta (-pi/2, pi/2)
       gamma = Math.atan2(-rotationMatrix.m13, rotationMatrix.m33);  // gamma (-pi/2, pi/2)
     } else {                                                        // cos(beta) < 0
       alpha = Math.atan2(rotationMatrix.m21, -rotationMatrix.m22);
       beta = -Math.asin(rotationMatrix.m23);
       beta += (beta > 0 || Math.abs(beta) < _Eps) ? -Math.PI : Math.PI;  // beta [-pi,-pi/2) U (pi/2,pi)
       gamma = Math.atan2(rotationMatrix.m13, -rotationMatrix.m33);       // gamma (-pi/2, pi/2)
     }

     // alpha is in [-pi, pi], make sure it is in [0, 2*pi).
     if (alpha < -_Eps) {
       alpha += 2 * Math.PI;  // alpha [0, 2*pi)
     }

     // We do not need a lot of precision in degrees. Arbitrarily set it to 6
     // digits after the decimal point. In most use cases, this may be rounded
     // even further in SensorsView and when passing these degrees to CSS.
     alpha = Number(radiansToDegrees(alpha).toFixed(6));
     beta = Number(radiansToDegrees(beta).toFixed(6));
     gamma = Number(radiansToDegrees(gamma).toFixed(6));

     return new EulerAngles(alpha, beta, gamma);
   }
 }

 export const scalarProduct = function(u: Vector, v: Vector): number {
   return u.x * v.x + u.y * v.y + u.z * v.z;
 };

 export const crossProduct = function(u: Vector, v: Vector): Vector {
   const x = u.y * v.z - u.z * v.y;
   const y = u.z * v.x - u.x * v.z;
   const z = u.x * v.y - u.y * v.x;
   return new Vector(x, y, z);
 };

 export const subtract = function(u: Vector, v: Vector): Vector {
   const x = u.x - v.x;
   const y = u.y - v.y;
   const z = u.z - v.z;
   return new Vector(x, y, z);
 };

 export const multiplyVectorByMatrixAndNormalize = function(v: Vector, m: DOMMatrix): Vector {
   const t = v.x * m.m14 + v.y * m.m24 + v.z * m.m34 + m.m44;
   const x = (v.x * m.m11 + v.y * m.m21 + v.z * m.m31 + m.m41) / t;
   const y = (v.x * m.m12 + v.y * m.m22 + v.z * m.m32 + m.m42) / t;
   const z = (v.x * m.m13 + v.y * m.m23 + v.z * m.m33 + m.m43) / t;
   return new Vector(x, y, z);
 };

 export const calculateAngle = function(u: Vector, v: Vector): number {
   const uLength = u.length();
   const vLength = v.length();
   if (uLength <= _Eps || vLength <= _Eps) {
     return 0;
   }
   const cos = scalarProduct(u, v) / uLength / vLength;
   if (Math.abs(cos) > 1) {
     return 0;
   }
   return radiansToDegrees(Math.acos(cos));
 };

 export const degreesToRadians = function(deg: number): number {
   return deg * Math.PI / 180;
 };

 export const degreesToGradians = function(deg: number): number {
   return deg / 9 * 10;
 };

 export const degreesToTurns = function(deg: number): number {
   return deg / 360;
 };

 export const radiansToDegrees = function(rad: number): number {
   return rad * 180 / Math.PI;
 };

 export const radiansToGradians = function(rad: number): number {
   return rad * 200 / Math.PI;
 };

 export const radiansToTurns = function(rad: number): number {
   return rad / (2 * Math.PI);
 };

 export const gradiansToRadians = function(grad: number): number {
   return grad * Math.PI / 200;
 };

 export const turnsToRadians = function(turns: number): number {
   return turns * 2 * Math.PI;
 };

 export const boundsForTransformedPoints = function(matrix: DOMMatrix, points: number[], aggregateBounds?: {
   minX: number,
   maxX: number,
   minY: number,
   maxY: number,
 }): {
   minX: number,
   maxX: number,
   minY: number,
   maxY: number,
 } {
   if (!aggregateBounds) {
     aggregateBounds = {minX: Infinity, maxX: -Infinity, minY: Infinity, maxY: -Infinity};
   }
   if (points.length % 3) {
     console.warn('Invalid size of points array');
   }
   for (let p = 0; p < points.length; p += 3) {
     let vector: Vector = new Vector(points[p], points[p + 1], points[p + 2]);
     vector = multiplyVectorByMatrixAndNormalize(vector, matrix);
     aggregateBounds.minX = Math.min(aggregateBounds.minX, vector.x);
     aggregateBounds.maxX = Math.max(aggregateBounds.maxX, vector.x);
     aggregateBounds.minY = Math.min(aggregateBounds.minY, vector.y);
     aggregateBounds.maxY = Math.max(aggregateBounds.maxY, vector.y);
   }
   return aggregateBounds;
 };

 export class Size {
   width: number;
   height: number;
   constructor(width: number, height: number) {
     this.width = width;
     this.height = height;
   }

   clipTo(size?: Size|null): Size {
     if (!size) {
       return this;
     }
     return new Size(Math.min(this.width, size.width), Math.min(this.height, size.height));
   }

   scale(scale: number): Size {
     return new Size(this.width * scale, this.height * scale);
   }

   isEqual(size: Size|null): boolean {
     return size !== null && this.width === size.width && this.height === size.height;
   }

   widthToMax(size: number|Size): Size {
     return new Size(Math.max(this.width, (typeof size === 'number' ? size : size.width)), this.height);
   }

   addWidth(size: number|Size): Size {
     return new Size(this.width + (typeof size === 'number' ? size : size.width), this.height);
   }

   heightToMax(size: number|Size): Size {
     return new Size(this.width, Math.max(this.height, (typeof size === 'number' ? size : size.height)));
   }

   addHeight(size: number|Size): Size {
     return new Size(this.width, this.height + (typeof size === 'number' ? size : size.height));
   }
 }

 export class Constraints {
   minimum: Size;
   preferred: Size;
   constructor(minimum?: Size, preferred?: Size|null) {
     this.minimum = minimum || new Size(0, 0);

     this.preferred = preferred || this.minimum;

     if (this.minimum.width > this.preferred.width || this.minimum.height > this.preferred.height) {
       throw new Error('Minimum size is greater than preferred.');
     }
   }

   isEqual(constraints: Constraints|null): boolean {
     return constraints !== null && this.minimum.isEqual(constraints.minimum) &&
         this.preferred.isEqual(constraints.preferred);
   }

   widthToMax(value: number|Constraints): Constraints {
     if (typeof value === 'number') {
       return new Constraints(this.minimum.widthToMax(value), this.preferred.widthToMax(value));
     }
     return new Constraints(this.minimum.widthToMax(value.minimum), this.preferred.widthToMax(value.preferred));
   }

   addWidth(value: number|Constraints): Constraints {
     if (typeof value === 'number') {
       return new Constraints(this.minimum.addWidth(value), this.preferred.addWidth(value));
     }
     return new Constraints(this.minimum.addWidth(value.minimum), this.preferred.addWidth(value.preferred));
   }

   heightToMax(value: number|Constraints): Constraints {
     if (typeof value === 'number') {
       return new Constraints(this.minimum.heightToMax(value), this.preferred.heightToMax(value));
     }
     return new Constraints(this.minimum.heightToMax(value.minimum), this.preferred.heightToMax(value.preferred));
   }

   addHeight(value: number|Constraints): Constraints {
     if (typeof value === 'number') {
       return new Constraints(this.minimum.addHeight(value), this.preferred.addHeight(value));
     }
     return new Constraints(this.minimum.addHeight(value.minimum), this.preferred.addHeight(value.preferred));
   }
 }
	/*
	* Copyright (C) 2013 Google Inc. All rights reserved.
	*
	* Redistribution and use in source and binary forms, with or without
	* modification, are permitted provided that the following conditions are
	* met:
	*
	* * Redistributions of source code must retain the above copyright
	* notice, this list of conditions and the following disclaimer.
	* * Redistributions in binary form must reproduce the above
	* copyright notice, this list of conditions and the following disclaimer
	* in the documentation and/or other materials provided with the
	* distribution.
	* * Neither the name of Google Inc. nor the names of its
	* contributors may be used to endorse or promote products derived from
	* this software without specific prior written permission.
	*
	* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
	* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
	* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
	* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
	* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
	* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
	* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
	* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
	* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
	* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
	* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
	*/

	/* eslint-disable rulesdir/no_underscored_properties */

	// TODO(crbug.com/1172300) Ignored during the jsdoc to ts migration
	// eslint-disable-next-line @typescript-eslint/naming-convention
	export const _Eps: number = 1e-5;

	export class Vector {
	x: number;
	y: number;
	z: number;

	constructor(x: number, y: number, z: number) {
	this.x = x;
	this.y = y;
	this.z = z;
	}

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

	normalize(): void {
	const length = this.length();
	if (length <= _Eps) {
	return;
	}

	this.x /= length;
	this.y /= length;
	this.z /= length;
	}
	}

	export class Point {
	x: number;
	y: number;

	constructor(x: number, y: number) {
	this.x = x;
	this.y = y;
	}

	distanceTo(p: Point): number {
	return Math.sqrt(Math.pow(p.x - this.x, 2) + Math.pow(p.y - this.y, 2));
	}

	projectOn(line: Point): Point {
	if (line.x === 0 && line.y === 0) {
	return new Point(0, 0);
	}
	return line.scale((this.x * line.x + this.y * line.y) / (Math.pow(line.x, 2) + Math.pow(line.y, 2)));
	}

	scale(scalar: number): Point {
	return new Point(this.x * scalar, this.y * scalar);
	}

	toString(): string {
	return Math.round(this.x * 100) / 100 + ', ' + Math.round(this.y * 100) / 100;
	}
	}

	export class CubicBezier {
	controlPoints: Point[];
	constructor(point1: Point, point2: Point) {
	this.controlPoints = [point1, point2];
	}

	static parse(text: string): CubicBezier\|null {
	const keywordValues = CubicBezier.KeywordValues;
	const value = text.toLowerCase().replace(/\s+/g, '');
	if (keywordValues.has(value)) {
	return CubicBezier.parse((keywordValues.get(value) as string));
	}
	const bezierRegex = /^cubic-bezier\(([^,]+),([^,]+),([^,]+),([^,]+)\)$/;
	const match = value.match(bezierRegex);
	if (match) {
	const control1 = new Point(parseFloat(match[1]), parseFloat(match[2]));
	const control2 = new Point(parseFloat(match[3]), parseFloat(match[4]));
	return new CubicBezier(control1, control2);
	}
	return null;
	}

	evaluateAt(t: number): Point {
	function evaluate(v1: number, v2: number, t: number): number {
	return 3 * (1 - t) * (1 - t) * t * v1 + 3 * (1 - t) * t * t * v2 + Math.pow(t, 3);
	}

	const x = evaluate(this.controlPoints[0].x, this.controlPoints[1].x, t);
	const y = evaluate(this.controlPoints[0].y, this.controlPoints[1].y, t);
	return new Point(x, y);
	}

	asCSSText(): string {
	const raw = 'cubic-bezier(' + this.controlPoints.join(', ') + ')';
	const keywordValues = CubicBezier.KeywordValues;
	for (const [keyword, value] of keywordValues) {
	if (raw === value) {
	return keyword;
	}
	}
	return raw;
	}

	// TODO(crbug.com/1172300) Ignored during the jsdoc to ts migration
	// eslint-disable-next-line @typescript-eslint/naming-convention
	static readonly Regex = /((cubic-bezier\([^)]+\))\|\b(linear(?!-)\|ease-in-out\|ease-in\|ease-out\|ease)\b)/g;
	// TODO(crbug.com/1172300) Ignored during the jsdoc to ts migration
	// eslint-disable-next-line @typescript-eslint/naming-convention
	static readonly KeywordValues = new Map([
	['linear', 'cubic-bezier(0, 0, 1, 1)'],
	['ease', 'cubic-bezier(0.25, 0.1, 0.25, 1)'],
	['ease-in', 'cubic-bezier(0.42, 0, 1, 1)'],
	['ease-in-out', 'cubic-bezier(0.42, 0, 0.58, 1)'],
	['ease-out', 'cubic-bezier(0, 0, 0.58, 1)'],
	]);
	}

	export class EulerAngles {
	alpha: number;
	beta: number;
	gamma: number;

	constructor(alpha: number, beta: number, gamma: number) {
	this.alpha = alpha;
	this.beta = beta;
	this.gamma = gamma;
	}

	/**
	* Derives orientation angles from a rotation matrix.
	*
	* The angles alpha, beta and gamma are in the [0, 360), [-180, 180) and
	* [-90, 90) intervals respectively, as specified in the Device Orientation
	* spec (https://w3c.github.io/deviceorientation/#deviceorientation).
	*
	* The Euler angles derived here follow a Z-X'-Y'' sequence.
	*
	* In particular we compute the decomposition of a given rotation matrix r
	* such that
	* r = rz(alpha) * rx(beta) * ry(gamma)
	* where rz, rx and ry are rotation matrices around z, x and y axes in the
	* world coordinate reference frame respectively. The reference frame
	* consists of three orthogonal axes x, y, z where x points East, y points
	* north and z points upwards perpendicular to the ground plane. The computed
	* angles alpha, beta and gamma are in degrees and clockwise-positive when
	* viewed along the positive direction of the corresponding axis. Except for
	* the special case when the beta angle is +-90 these angles uniquely
	* define the orientation of a mobile device in 3D space. The
	* alpha-beta-gamma representation resembles the yaw-pitch-roll convention
	* used in vehicle dynamics, however it does not exactly match it. One of the
	* differences is that the 'pitch' angle beta is allowed to be within [-180,
	* 180). A mobile device with pitch angle greater than 90 could
	* correspond to a user lying down and looking upward at the screen.
	*/
	static fromDeviceOrientationRotationMatrix(rotationMatrix: DOMMatrixReadOnly): EulerAngles {
	let alpha, beta, gamma;

	// A few implementation notes:
	// - This code has been ported from Chromium's
	// //services/device/generic_sensor/orientation_util.cc at commit
	// 1be837b6f142.
	//
	// - Since \|rotationMatrix\| contains non-integer numbers, directly
	// comparing them to 0 will not be accurate, so we use \|_Eps\| to check if
	// some numbers are close enough to 0.
	//
	// - The C++ code in Chromium uses a std::vector<double> to represent a 3x3
	// rotation matrix in row-major order. \|rotationMatrix\| is a 4x4 matrix
	// defined in column-major order, so \|rotationMatrix.m13\| here
	// corresponds to \|r[8]\| in the original C++ code.
	//
	// - There are rounding errors and approximations in the floating-point
	// arithmetics below, but it does not interfere with the use cases in
	// DevTools (i.e. angles that are mostly within the allowed intervals). A
	// rotation around the Z axis by 360 degrees will correctly return
	// alpha=0, but a rotation around the Z axis by 360 * 20000000000000000
	// will return alpha=~75 degrees, for example.
	if (Math.abs(rotationMatrix.m33) < _Eps) { // m33 == 0
	if (Math.abs(rotationMatrix.m13) < _Eps) { // m13 == 0, cos(beta) == 0
	// Gimbal lock discontinuity: in the Z-X'-Y'' angle system used here, a
	// rotation of 90 or -90 degrees around the X axis (beta) causes a
	// Gimbal lock, which we handle by always setting gamma = 0 and
	// handling the rotation in alpha.
	alpha = Math.atan2(rotationMatrix.m12, rotationMatrix.m11);
	beta = (rotationMatrix.m23 > 0) ? (Math.PI / 2) : -(Math.PI / 2); // beta = +-pi/2
	gamma = 0; // gamma = 0
	} else if (rotationMatrix.m13 > 0) { // cos(gamma) == 0, cos(beta) > 0
	alpha = Math.atan2(-rotationMatrix.m21, rotationMatrix.m22);
	beta = Math.asin(rotationMatrix.m23); // beta [-pi/2, pi/2]
	gamma = -(Math.PI / 2); // gamma = -pi/2
	} else { // cos(gamma) == 0, cos(beta) < 0
	alpha = Math.atan2(rotationMatrix.m21, -rotationMatrix.m22);
	beta = -Math.asin(rotationMatrix.m23);
	beta += (beta > 0 \|\| Math.abs(beta) < _Eps) ? -Math.PI : Math.PI; // beta [-pi,-pi/2) U (pi/2,pi)
	gamma = -(Math.PI / 2); // gamma = -pi/2
	}
	} else if (rotationMatrix.m33 > 0) { // cos(beta) > 0
	alpha = Math.atan2(-rotationMatrix.m21, rotationMatrix.m22);
	beta = Math.asin(rotationMatrix.m23); // beta (-pi/2, pi/2)
	gamma = Math.atan2(-rotationMatrix.m13, rotationMatrix.m33); // gamma (-pi/2, pi/2)
	} else { // cos(beta) < 0
	alpha = Math.atan2(rotationMatrix.m21, -rotationMatrix.m22);
	beta = -Math.asin(rotationMatrix.m23);
	beta += (beta > 0 \|\| Math.abs(beta) < _Eps) ? -Math.PI : Math.PI; // beta [-pi,-pi/2) U (pi/2,pi)
	gamma = Math.atan2(rotationMatrix.m13, -rotationMatrix.m33); // gamma (-pi/2, pi/2)
	}

	// alpha is in [-pi, pi], make sure it is in [0, 2*pi).
	if (alpha < -_Eps) {
	alpha += 2 * Math.PI; // alpha [0, 2*pi)
	}

	// We do not need a lot of precision in degrees. Arbitrarily set it to 6
	// digits after the decimal point. In most use cases, this may be rounded
	// even further in SensorsView and when passing these degrees to CSS.
	alpha = Number(radiansToDegrees(alpha).toFixed(6));
	beta = Number(radiansToDegrees(beta).toFixed(6));
	gamma = Number(radiansToDegrees(gamma).toFixed(6));

	return new EulerAngles(alpha, beta, gamma);
	}
	}

	export const scalarProduct = function(u: Vector, v: Vector): number {
	return u.x * v.x + u.y * v.y + u.z * v.z;
	};

	export const crossProduct = function(u: Vector, v: Vector): Vector {
	const x = u.y * v.z - u.z * v.y;
	const y = u.z * v.x - u.x * v.z;
	const z = u.x * v.y - u.y * v.x;
	return new Vector(x, y, z);
	};

	export const subtract = function(u: Vector, v: Vector): Vector {
	const x = u.x - v.x;
	const y = u.y - v.y;
	const z = u.z - v.z;
	return new Vector(x, y, z);
	};

	export const multiplyVectorByMatrixAndNormalize = function(v: Vector, m: DOMMatrix): Vector {
	const t = v.x * m.m14 + v.y * m.m24 + v.z * m.m34 + m.m44;
	const x = (v.x * m.m11 + v.y * m.m21 + v.z * m.m31 + m.m41) / t;
	const y = (v.x * m.m12 + v.y * m.m22 + v.z * m.m32 + m.m42) / t;
	const z = (v.x * m.m13 + v.y * m.m23 + v.z * m.m33 + m.m43) / t;
	return new Vector(x, y, z);
	};

	export const calculateAngle = function(u: Vector, v: Vector): number {
	const uLength = u.length();
	const vLength = v.length();
	if (uLength <= _Eps \|\| vLength <= _Eps) {
	return 0;
	}
	const cos = scalarProduct(u, v) / uLength / vLength;
	if (Math.abs(cos) > 1) {
	return 0;
	}
	return radiansToDegrees(Math.acos(cos));
	};

	export const degreesToRadians = function(deg: number): number {
	return deg * Math.PI / 180;
	};

	export const degreesToGradians = function(deg: number): number {
	return deg / 9 * 10;
	};

	export const degreesToTurns = function(deg: number): number {
	return deg / 360;
	};

	export const radiansToDegrees = function(rad: number): number {
	return rad * 180 / Math.PI;
	};

	export const radiansToGradians = function(rad: number): number {
	return rad * 200 / Math.PI;
	};

	export const radiansToTurns = function(rad: number): number {
	return rad / (2 * Math.PI);
	};

	export const gradiansToRadians = function(grad: number): number {
	return grad * Math.PI / 200;
	};

	export const turnsToRadians = function(turns: number): number {
	return turns * 2 * Math.PI;
	};

	export const boundsForTransformedPoints = function(matrix: DOMMatrix, points: number[], aggregateBounds?: {
	minX: number,
	maxX: number,
	minY: number,
	maxY: number,
	}): {
	minX: number,
	maxX: number,
	minY: number,
	maxY: number,
	} {
	if (!aggregateBounds) {
	aggregateBounds = {minX: Infinity, maxX: -Infinity, minY: Infinity, maxY: -Infinity};
	}
	if (points.length % 3) {
	console.warn('Invalid size of points array');
	}
	for (let p = 0; p < points.length; p += 3) {
	let vector: Vector = new Vector(points[p], points[p + 1], points[p + 2]);
	vector = multiplyVectorByMatrixAndNormalize(vector, matrix);
	aggregateBounds.minX = Math.min(aggregateBounds.minX, vector.x);
	aggregateBounds.maxX = Math.max(aggregateBounds.maxX, vector.x);
	aggregateBounds.minY = Math.min(aggregateBounds.minY, vector.y);
	aggregateBounds.maxY = Math.max(aggregateBounds.maxY, vector.y);
	}
	return aggregateBounds;
	};

	export class Size {
	width: number;
	height: number;
	constructor(width: number, height: number) {
	this.width = width;
	this.height = height;
	}

	clipTo(size?: Size\|null): Size {
	if (!size) {
	return this;
	}
	return new Size(Math.min(this.width, size.width), Math.min(this.height, size.height));
	}

	scale(scale: number): Size {
	return new Size(this.width * scale, this.height * scale);
	}

	isEqual(size: Size\|null): boolean {
	return size !== null && this.width === size.width && this.height === size.height;
	}

	widthToMax(size: number\|Size): Size {
	return new Size(Math.max(this.width, (typeof size === 'number' ? size : size.width)), this.height);
	}

	addWidth(size: number\|Size): Size {
	return new Size(this.width + (typeof size === 'number' ? size : size.width), this.height);
	}

	heightToMax(size: number\|Size): Size {
	return new Size(this.width, Math.max(this.height, (typeof size === 'number' ? size : size.height)));
	}

	addHeight(size: number\|Size): Size {
	return new Size(this.width, this.height + (typeof size === 'number' ? size : size.height));
	}
	}

	export class Constraints {
	minimum: Size;
	preferred: Size;
	constructor(minimum?: Size, preferred?: Size\|null) {
	this.minimum = minimum \|\| new Size(0, 0);

	this.preferred = preferred \|\| this.minimum;

	if (this.minimum.width > this.preferred.width \|\| this.minimum.height > this.preferred.height) {
	throw new Error('Minimum size is greater than preferred.');
	}
	}

	isEqual(constraints: Constraints\|null): boolean {
	return constraints !== null && this.minimum.isEqual(constraints.minimum) &&
	this.preferred.isEqual(constraints.preferred);
	}

	widthToMax(value: number\|Constraints): Constraints {
	if (typeof value === 'number') {
	return new Constraints(this.minimum.widthToMax(value), this.preferred.widthToMax(value));
	}
	return new Constraints(this.minimum.widthToMax(value.minimum), this.preferred.widthToMax(value.preferred));
	}

	addWidth(value: number\|Constraints): Constraints {
	if (typeof value === 'number') {
	return new Constraints(this.minimum.addWidth(value), this.preferred.addWidth(value));
	}
	return new Constraints(this.minimum.addWidth(value.minimum), this.preferred.addWidth(value.preferred));
	}

	heightToMax(value: number\|Constraints): Constraints {
	if (typeof value === 'number') {
	return new Constraints(this.minimum.heightToMax(value), this.preferred.heightToMax(value));
	}
	return new Constraints(this.minimum.heightToMax(value.minimum), this.preferred.heightToMax(value.preferred));
	}

	addHeight(value: number\|Constraints): Constraints {
	if (typeof value === 'number') {
	return new Constraints(this.minimum.addHeight(value), this.preferred.addHeight(value));
	}
	return new Constraints(this.minimum.addHeight(value.minimum), this.preferred.addHeight(value.preferred));
	}
	}