//@ts-check
/**
* A class representing a 2D vector.
*
* @property {Number} x The x component of the vector.
* @property {Number} y The y component of the vector.
*/
class Vector2 {
/**
* The constructor of the class Vector2.
*
* @param {(Number|Vector2)} x The initial x coordinate value or, if the single argument, a Vector2 object.
* @param {Number} y The initial y coordinate value.
*/
constructor(x, y) {
if (arguments.length == 0) {
this.x = 0;
this.y = 0;
} else if (arguments.length == 1) {
this.x = x.x;
this.y = x.y;
} else {
this.x = x;
this.y = y;
}
}
/**
* Clones this vector and returns the clone.
*
* @returns {Vector2} The clone of this vector.
*/
clone() {
return new Vector2(this.x, this.y);
}
/**
* Returns a string representation of this vector.
*
* @returns {String} A string representation of this vector.
*/
toString() {
return '(' + this.x + ',' + this.y + ')';
}
/**
* Add the x and y coordinate values of a vector to the x and y coordinate values of this vector.
*
* @param {Vector2} vec Another vector.
* @returns {Vector2} Returns itself.
*/
add(vec) {
this.x += vec.x;
this.y += vec.y;
return this;
}
/**
* Subtract the x and y coordinate values of a vector from the x and y coordinate values of this vector.
*
* @param {Vector2} vec Another vector.
* @returns {Vector2} Returns itself.
*/
subtract(vec) {
this.x -= vec.x;
this.y -= vec.y;
return this;
}
/**
* Divide the x and y coordinate values of this vector by a scalar.
*
* @param {Number} scalar The scalar.
* @returns {Vector2} Returns itself.
*/
divide(scalar) {
this.x /= scalar;
this.y /= scalar;
return this;
}
/**
* Multiply the x and y coordinate values of this vector by the values of another vector.
*
* @param {Vector2} v A vector.
* @returns {Vector2} Returns itself.
*/
multiply(v) {
this.x *= v.x;
this.y *= v.y;
return this;
}
/**
* Multiply the x and y coordinate values of this vector by a scalar.
*
* @param {Number} scalar The scalar.
* @returns {Vector2} Returns itself.
*/
multiplyScalar(scalar) {
this.x *= scalar;
this.y *= scalar;
return this;
}
/**
* Inverts this vector. Same as multiply(-1.0).
*
* @returns {Vector2} Returns itself.
*/
invert() {
this.x = -this.x;
this.y = -this.y;
return this;
}
/**
* Returns the angle of this vector in relation to the coordinate system.
*
* @returns {Number} The angle in radians.
*/
angle() {
return Math.atan2(this.y, this.x);
}
/**
* Returns the euclidean distance between this vector and another vector.
*
* @param {Vector2} vec A vector.
* @returns {Number} The euclidean distance between the two vectors.
*/
distance(vec) {
return Math.sqrt((vec.x - this.x) * (vec.x - this.x) + (vec.y - this.y) * (vec.y - this.y));
}
/**
* Returns the squared euclidean distance between this vector and another vector. When only the relative distances of a set of vectors are needed, this is is less expensive than using distance(vec).
*
* @param {Vector2} vec Another vector.
* @returns {Number} The squared euclidean distance of the two vectors.
*/
distanceSq(vec) {
return (vec.x - this.x) * (vec.x - this.x) + (vec.y - this.y) * (vec.y - this.y);
}
/**
* Checks whether or not this vector is in a clockwise or counter-clockwise rotational direction compared to another vector in relation to the coordinate system.
*
* @param {Vector2} vec Another vector.
* @returns {Number} Returns -1, 0 or 1 if the vector supplied as an argument is clockwise, neutral or counter-clockwise respectively to this vector in relation to the coordinate system.
*/
clockwise(vec) {
let a = this.y * vec.x;
let b = this.x * vec.y;
if (a > b) {
return -1;
}
else if (a === b) {
return 0;
}
return 1;
}
/**
* Checks whether or not this vector is in a clockwise or counter-clockwise rotational direction compared to another vector in relation to an arbitrary third vector.
*
* @param {Vector2} center The central vector.
* @param {Vector2} vec Another vector.
* @returns {Number} Returns -1, 0 or 1 if the vector supplied as an argument is clockwise, neutral or counter-clockwise respectively to this vector in relation to an arbitrary third vector.
*/
relativeClockwise(center, vec) {
let a = (this.y - center.y) * (vec.x - center.x);
let b = (this.x - center.x) * (vec.y - center.y);
if (a > b) {
return -1;
}
else if (a === b) {
return 0;
}
return 1;
}
/**
* Rotates this vector by a given number of radians around the origin of the coordinate system.
*
* @param {Number} angle The angle in radians to rotate the vector.
* @returns {Vector2} Returns itself.
*/
rotate(angle) {
let tmp = new Vector2(0, 0);
let cosAngle = Math.cos(angle);
let sinAngle = Math.sin(angle);
tmp.x = this.x * cosAngle - this.y * sinAngle;
tmp.y = this.x * sinAngle + this.y * cosAngle;
this.x = tmp.x;
this.y = tmp.y;
return this;
}
/**
* Rotates this vector around another vector.
*
* @param {Number} angle The angle in radians to rotate the vector.
* @param {Vector2} vec The vector which is used as the rotational center.
* @returns {Vector2} Returns itself.
*/
rotateAround(angle, vec) {
let s = Math.sin(angle);
let c = Math.cos(angle);
this.x -= vec.x;
this.y -= vec.y;
let x = this.x * c - this.y * s;
let y = this.x * s + this.y * c;
this.x = x + vec.x;
this.y = y + vec.y;
return this;
}
/**
* Rotate a vector around a given center to the same angle as another vector (so that the two vectors and the center are in a line, with both vectors on one side of the center), keeps the distance from this vector to the center.
*
* @param {Vector2} vec The vector to rotate this vector to.
* @param {Vector2} center The rotational center.
* @param {Number} [offsetAngle=0.0] An additional amount of radians to rotate the vector.
* @returns {Vector2} Returns itself.
*/
rotateTo(vec, center, offsetAngle = 0.0) {
// Problem if this is first position
this.x += 0.001;
this.y -= 0.001;
let a = Vector2.subtract(this, center);
let b = Vector2.subtract(vec, center);
let angle = Vector2.angle(b, a);
this.rotateAround(angle + offsetAngle, center);
return this;
}
/**
* Rotates the vector away from a specified vector around a center.
*
* @param {Vector2} vec The vector this one is rotated away from.
* @param {Vector2} center The rotational center.
* @param {Number} angle The angle by which to rotate.
*/
rotateAwayFrom(vec, center, angle) {
this.rotateAround(angle, center);
let distSqA = this.distanceSq(vec);
this.rotateAround(-2.0 * angle, center);
let distSqB = this.distanceSq(vec);
// If it was rotated towards the other vertex, rotate in other direction by same amount.
if (distSqB < distSqA) {
this.rotateAround(2.0 * angle, center);
}
}
/**
* Returns the angle in radians used to rotate this vector away from a given vector.
*
* @param {Vector2} vec The vector this one is rotated away from.
* @param {Vector2} center The rotational center.
* @param {Number} angle The angle by which to rotate.
* @returns {Number} The angle in radians.
*/
getRotateAwayFromAngle(vec, center, angle) {
let tmp = this.clone();
tmp.rotateAround(angle, center);
let distSqA = tmp.distanceSq(vec);
tmp.rotateAround(-2.0 * angle, center);
let distSqB = tmp.distanceSq(vec);
if (distSqB < distSqA) {
return angle;
} else {
return -angle;
}
}
/**
* Returns the angle in radians used to rotate this vector towards a given vector.
*
* @param {Vector2} vec The vector this one is rotated towards to.
* @param {Vector2} center The rotational center.
* @param {Number} angle The angle by which to rotate.
* @returns {Number} The angle in radians.
*/
getRotateTowardsAngle(vec, center, angle) {
let tmp = this.clone();
tmp.rotateAround(angle, center);
let distSqA = tmp.distanceSq(vec);
tmp.rotateAround(-2.0 * angle, center);
let distSqB = tmp.distanceSq(vec);
if (distSqB > distSqA) {
return angle;
} else {
return -angle;
}
}
/**
* Gets the angles between this vector and another vector around a common center of rotation.
*
* @param {Vector2} vec Another vector.
* @param {Vector2} center The center of rotation.
* @returns {Number} The angle between this vector and another vector around a center of rotation in radians.
*/
getRotateToAngle(vec, center) {
let a = Vector2.subtract(this, center);
let b = Vector2.subtract(vec, center);
let angle = Vector2.angle(b, a);
return Number.isNaN(angle) ? 0.0 : angle;
}
/**
* Checks whether a vector lies within a polygon spanned by a set of vectors.
*
* @param {Vector2[]} polygon An array of vectors spanning the polygon.
* @returns {Boolean} A boolean indicating whether or not this vector is within a polygon.
*/
isInPolygon(polygon) {
let inside = false;
// Its not always a given, that the polygon is convex (-> sugars)
for (let i = 0, j = polygon.length - 1; i < polygon.length; j = i++) {
if (((polygon[i].y > this.y) != (polygon[j].y > this.y)) &&
(this.x < (polygon[j].x - polygon[i].x) * (this.y - polygon[i].y) /
(polygon[j].y - polygon[i].y) + polygon[i].x)) {
inside = !inside;
}
}
return inside;
}
/**
* Returns the length of this vector.
*
* @returns {Number} The length of this vector.
*/
length() {
return Math.sqrt((this.x * this.x) + (this.y * this.y));
}
/**
* Returns the square of the length of this vector.
*
* @returns {Number} The square of the length of this vector.
*/
lengthSq() {
return (this.x * this.x) + (this.y * this.y);
}
/**
* Normalizes this vector.
*
* @returns {Vector2} Returns itself.
*/
normalize() {
this.divide(this.length());
return this;
}
/**
* Returns a normalized copy of this vector.
*
* @returns {Vector2} A normalized copy of this vector.
*/
normalized() {
return Vector2.divideScalar(this, this.length());
}
/**
* Calculates which side of a line spanned by two vectors this vector is.
*
* @param {Vector2} vecA A vector.
* @param {Vector2} vecB A vector.
* @returns {Number} A number indicating the side of this vector, given a line spanned by two other vectors.
*/
whichSide(vecA, vecB) {
return (this.x - vecA.x) * (vecB.y - vecA.y) - (this.y - vecA.y) * (vecB.x - vecA.x);
}
/**
* Checks whether or not this vector is on the same side of a line spanned by two vectors as another vector.
*
* @param {Vector2} vecA A vector spanning the line.
* @param {Vector2} vecB A vector spanning the line.
* @param {Vector2} vecC A vector to check whether or not it is on the same side as this vector.
* @returns {Boolean} Returns a boolean indicating whether or not this vector is on the same side as another vector.
*/
sameSideAs(vecA, vecB, vecC) {
let d = this.whichSide(vecA, vecB);
let dRef = vecC.whichSide(vecA, vecB);
return d < 0 && dRef < 0 || d == 0 && dRef == 0 || d > 0 && dRef > 0;
}
/**
* Adds two vectors and returns the result as a new vector.
*
* @static
* @param {Vector2} vecA A summand.
* @param {Vector2} vecB A summand.
* @returns {Vector2} Returns the sum of two vectors.
*/
static add(vecA, vecB) {
return new Vector2(vecA.x + vecB.x, vecA.y + vecB.y);
}
/**
* Subtracts one vector from another and returns the result as a new vector.
*
* @static
* @param {Vector2} vecA The minuend.
* @param {Vector2} vecB The subtrahend.
* @returns {Vector2} Returns the difference of two vectors.
*/
static subtract(vecA, vecB) {
return new Vector2(vecA.x - vecB.x, vecA.y - vecB.y);
}
/**
* Multiplies two vectors (value by value) and returns the result.
*
* @static
* @param {Vector2} vecA A vector.
* @param {Vector2} vecB A vector.
* @returns {Vector2} Returns the product of two vectors.
*/
static multiply(vecA, vecB) {
return new Vector2(vecA.x * vecB.x, vecA.y * vecB.y);
}
/**
* Multiplies two vectors (value by value) and returns the result.
*
* @static
* @param {Vector2} vec A vector.
* @param {Number} scalar A scalar.
* @returns {Vector2} Returns the product of two vectors.
*/
static multiplyScalar(vec, scalar) {
return new Vector2(vec.x, vec.y).multiplyScalar(scalar);
}
/**
* Returns the midpoint of a line spanned by two vectors.
*
* @static
* @param {Vector2} vecA A vector spanning the line.
* @param {Vector2} vecB A vector spanning the line.
* @returns {Vector2} The midpoint of the line spanned by two vectors.
*/
static midpoint(vecA, vecB) {
return new Vector2((vecA.x + vecB.x) / 2, (vecA.y + vecB.y) / 2);
}
/**
* Returns the normals of a line spanned by two vectors.
*
* @static
* @param {Vector2} vecA A vector spanning the line.
* @param {Vector2} vecB A vector spanning the line.
* @returns {Vector2[]} An array containing the two normals, each represented by a vector.
*/
static normals(vecA, vecB) {
let delta = Vector2.subtract(vecB, vecA);
return [
new Vector2(-delta.y, delta.x),
new Vector2(delta.y, -delta.x)
];
}
/**
* Returns the unit (normalized normal) vectors of a line spanned by two vectors.
*
* @static
* @param {Vector2} vecA A vector spanning the line.
* @param {Vector2} vecB A vector spanning the line.
* @returns {Vector2[]} An array containing the two unit vectors.
*/
static units(vecA, vecB) {
let delta = Vector2.subtract(vecB, vecA);
return [
(new Vector2(-delta.y, delta.x)).normalize(),
(new Vector2(delta.y, -delta.x)).normalize()
];
}
/**
* Divides a vector by another vector and returns the result as new vector.
*
* @static
* @param {Vector2} vecA The dividend.
* @param {Vector2} vecB The divisor.
* @returns {Vector2} The fraction of the two vectors.
*/
static divide(vecA, vecB) {
return new Vector2(vecA.x / vecB.x, vecA.y / vecB.y);
}
/**
* Divides a vector by a scalar and returns the result as new vector.
*
* @static
* @param {Vector2} vecA The dividend.
* @param {Number} s The scalar.
* @returns {Vector2} The fraction of the two vectors.
*/
static divideScalar(vecA, s) {
return new Vector2(vecA.x / s, vecA.y / s);
}
/**
* Returns the dot product of two vectors.
*
* @static
* @param {Vector2} vecA A vector.
* @param {Vector2} vecB A vector.
* @returns {Number} The dot product of two vectors.
*/
static dot(vecA, vecB) {
return vecA.x * vecB.x + vecA.y * vecB.y;
}
/**
* Returns the angle between two vectors.
*
* @static
* @param {Vector2} vecA A vector.
* @param {Vector2} vecB A vector.
* @returns {Number} The angle between two vectors in radians.
*/
static angle(vecA, vecB) {
let dot = Vector2.dot(vecA, vecB);
return Math.acos(dot / (vecA.length() * vecB.length()));
}
/**
* Returns the angle between two vectors based on a third vector in between.
*
* @static
* @param {Vector2} vecA A vector.
* @param {Vector2} vecB A (central) vector.
* @param {Vector2} vecC A vector.
* @returns {Number} The angle in radians.
*/
static threePointangle(vecA, vecB, vecC) {
let ab = Vector2.subtract(vecB, vecA);
let bc = Vector2.subtract(vecC, vecB);
let abLength = vecA.distance(vecB);
let bcLength = vecB.distance(vecC);
return Math.acos(Vector2.dot(ab, bc) / (abLength * bcLength));
}
/**
* Returns the scalar projection of a vector on another vector.
*
* @static
* @param {Vector2} vecA The vector to be projected.
* @param {Vector2} vecB The vector to be projection upon.
* @returns {Number} The scalar component.
*/
static scalarProjection(vecA, vecB) {
let unit = vecB.normalized();
return Vector2.dot(vecA, unit);
}
/**
* Returns the average vector (normalized) of the input vectors.
*
* @static
* @param {Array} vecs An array containing vectors.
* @returns {Vector2} The resulting vector (normalized).
*/
static averageDirection(vecs) {
let avg = new Vector2(0.0, 0.0);
for (var i = 0; i < vecs.length; i++) {
let vec = vecs[i];
avg.add(vec);
}
return avg.normalize();
}
}
module.exports = Vector2;