Add Vector2 (#593)

* add Vector2.js
* Rename Data-Structures/Vector2.js to Data-Structures/Vectors/Vector2.js

Data-Structures/Vectors/Vector2.js

@@ -0,0 +1,205 @@
+/**
+ * In mathematics and physics, a vector is an element of a vector space. The Vector2-class
+ * implements 2-dimensional vectors together with various vector-operations (description adapted from
+ * https://en.wikipedia.org/wiki/Vector_(mathematics_and_physics)).
+ */
+
+/*
+Doctests
+
+// Test equalsExactly-method
+> new Vector2(1, 0).equalsExactly(new Vector2(1, 0))
+true
+> new Vector2(1.23, 4.56).equalsExactly(new Vector2(0, 0))
+false
+
+// Test equalsApproximately-method
+> new Vector2(1, 0).equalsApproximately(new Vector2(1, 0.0000001), 0.000001)
+true
+> new Vector2(1.23, 4.56).equalsApproximately(new Vector2(1.24, 4.56), 0.000001)
+false
+
+// Test add-method
+> new Vector2(1, 0).add(new Vector2(0, 1)).equalsApproximately(new Vector2(1, 1), 0.000001)
+true
+> new Vector2(-3.3, -9).add(new Vector2(-2.2, 3)).equalsApproximately(new Vector2(-5.5, -6), 0.000001)
+true
+
+// Test subtract-method
+> new Vector2(1, 0).subtract(new Vector2(0, 1)).equalsApproximately(new Vector2(1, -1), 0.000001)
+true
+> new Vector2(234.5, 1.7).subtract(new Vector2(3.3, 2.7)).equalsApproximately(new Vector2(231.2, -1), 0.000001)
+true
+
+// Test multiply-method
+> new Vector2(1, 0).multiply(5).equalsApproximately(new Vector2(5, 0), 0.000001)
+true
+> new Vector2(3.41, -7.12).multiply(-3.1).equalsApproximately(new Vector2(-10.571, 22.072), 0.000001)
+true
+
+// Test length-method
+> new Vector2(1, 0).length()
+1
+> new Vector2(-1, 1).length()
+Math.sqrt(2)
+
+// Test normalize-method
+> new Vector2(1, 0).normalize().equalsApproximately(new Vector2(1, 0), 0.000001)
+true
+> new Vector2(1, -1).normalize().equalsApproximately(new Vector2(Math.sqrt(2) / 2, -Math.sqrt(2) / 2), 0.000001)
+true
+
+// Test distance-method
+> new Vector2(0, 0).distance(new Vector2(0, -1))
+1
+> new Vector2(1, 0).distance(new Vector2(0, 1))
+Math.sqrt(2)
+
+// Test dotProduct-method
+> new Vector2(1, 0).dotProduct(new Vector2(0, 1))
+0
+> new Vector2(1, 2).dotProduct(new Vector2(3, 4))
+1 * 3 + 2 * 4
+
+// Test rotate-method
+> new Vector2(0, -1).rotate(Math.PI / 2).equalsApproximately(new Vector2(1, 0), 0.000001)
+true
+> new Vector2(1.23, -4.56).rotate(Math.PI).equalsApproximately(new Vector2(-1.23, 4.56), 0.000001)
+true
+
+// Test angleBetween-method
+> new Vector2(1, 0).angleBetween(new Vector2(0, 1))
+Math.PI / 2
+> new Vector2(1, 0).angleBetween(new Vector2(1, -1))
+-Math.PI / 4
+*/
+class Vector2 { // eslint-disable-line no-unused-vars
+  constructor (x, y) {
+    this.x = x
+    this.y = y
+  }
+
+  /**
+   * Check for exact vector equality.
+   *
+   * @param vector The vector to compare to.
+   * @returns Whether they are exactly equal or not.
+   */
+  equalsExactly (vector) {
+    return this.x === vector.x && this.y === vector.y
+  }
+
+  /**
+   * Check for approximate vector equality.
+   *
+   * @param vector The vector to compare to.
+   * @param epsilon The allowed discrepancy for the x-values and the y-values.
+   * @returns Whether they are approximately equal or not.
+   */
+  equalsApproximately (vector, epsilon) {
+    return (Math.abs(this.x - vector.x) < epsilon && Math.abs(this.y - vector.y) < epsilon)
+  }
+
+  /**
+   * Vector length.
+   *
+   * @returns The length of the vector.
+   */
+  length () {
+    return Math.sqrt(this.x * this.x + this.y * this.y)
+  }
+
+  /**
+   * Normalization sets the vector to length 1 while maintaining its direction.
+   *
+   * @returns The normalized vector.
+   */
+  normalize () {
+    const length = this.length()
+    if (length === 0) {
+      throw new Error('Cannot normalize vectors of length 0')
+    }
+    return new Vector2(this.x / length, this.y / length)
+  }
+
+  /**
+   * Vector addition
+   *
+   * @param vector The vector to be added.
+   * @returns The sum-vector.
+   */
+  add (vector) {
+    const x = this.x + vector.x
+    const y = this.y + vector.y
+    return new Vector2(x, y)
+  }
+
+  /**
+   * Vector subtraction
+   *
+   * @param vector The vector to be subtracted.
+   * @returns The difference-vector.
+   */
+  subtract (vector) {
+    const x = this.x - vector.x
+    const y = this.y - vector.y
+    return new Vector2(x, y)
+  }
+
+  /**
+   * Vector scalar multiplication
+   *
+   * @param scalar The factor by which to multiply the vector.
+   * @returns The scaled vector.
+   */
+  multiply (scalar) {
+    const x = this.x * scalar
+    const y = this.y * scalar
+    return new Vector2(x, y)
+  }
+
+  /**
+   * Distance between this vector and another vector.
+   *
+   * @param vector The vector to which to calculate the distance.
+   * @returns The distance.
+   */
+  distance (vector) {
+    const difference = vector.subtract(this)
+    return difference.length()
+  }
+
+  /**
+   * Vector dot product
+   *
+   * @param vector The vector used for the multiplication.
+   * @returns The resulting dot product.
+   */
+  dotProduct (vector) {
+    return this.x * vector.x + this.y * vector.y
+  }
+
+  /**
+   * Vector rotation (see https://en.wikipedia.org/wiki/Rotation_matrix)
+   *
+   * @param angleInRadians The angle in radians by which to rotate the vector.
+   * @returns The rotated vector.
+   */
+  rotate (angleInRadians) {
+    const ca = Math.cos(angleInRadians)
+    const sa = Math.sin(angleInRadians)
+    const x = ca * this.x - sa * this.y
+    const y = sa * this.x + ca * this.y
+    return new Vector2(x, y)
+  }
+
+  /**
+   * Measure angle between two vectors
+   *
+   * @param vector The 2nd vector for the measurement.
+   * @returns The angle in radians.
+   */
+  angleBetween (vector) {
+    return Math.atan2(vector.y, vector.x) - Math.atan2(this.y, this.x)
+  }
+}