r2: Point

index.ts

@@ -1 +1,2 @@
+export * as r2 from './r2/_index'
 export * as s2 from './s2/_index'

r2/Point.ts

@@ -0,0 +1,70 @@
+/**
+ * Point represents a point in ℝ².
+ */
+export class Point {
+  x: number = 0.0
+  y: number = 0.0
+
+  /**
+   * Returns a new Point.
+   * @category Constructors
+   */
+  constructor(x: number = 0.0, y: number = 0.0) {
+    this.x = x
+    this.y = y
+  }
+
+  /** Returns the sum of p and op. */
+  add(op: Point): Point {
+    return new Point(this.x + op.x, this.y + op.y)
+  }
+
+  /** Returns the difference of p and op. */
+  sub(op: Point): Point {
+    return new Point(this.x - op.x, this.y - op.y)
+  }
+
+  /** Returns the scalar product of p and m. */
+  mul(m: number): Point {
+    return new Point(this.x * m, this.y * m)
+  }
+
+  /** Returns a counterclockwise orthogonal point with the same norm. */
+  ortho(): Point {
+    return new Point(-this.y, this.x)
+  }
+
+  /** Returns the dot product between p and op. */
+  dot(op: Point): number {
+    return this.x * op.x + this.y * op.y
+  }
+
+  /** Returns the cross product of p and op. */
+  cross(op: Point): number {
+    return this.x * op.y - this.y * op.x
+  }
+
+  /** Returns the vector's norm. */
+  norm(): number {
+    return Math.hypot(this.x, this.y)
+  }
+
+  /** Returns a unit point in the same direction as p. */
+  normalize(): Point {
+    if (this.x == 0.0 && this.y == 0.0) return this
+    return this.mul(1 / this.norm())
+  }
+
+  /** Truncates {x, y} floats to n digits of precision. */
+  trunc(n: number = 15): Point {
+    const p = Number(`1e${n}`)
+    const trunc = (dim: number) => Math.round(dim * p) / p
+    return new Point(trunc(this.x), trunc(this.y))
+  }
+
+  /** Generates a human readable string. */
+  toString(): string {
+    const t = this.trunc(12)
+    return `(${t.x.toFixed(12)}, ${t.y.toFixed(12)})`
+  }
+}

r2/Point_test.ts

@@ -0,0 +1,88 @@
+import test from 'node:test'
+import { equal, deepEqual } from 'node:assert/strict'
+import { Point } from './Point'
+
+export const MAX_FLOAT32 = Math.pow(2, 127) * (2 - 1 / Math.pow(2, 23))
+
+test('add', t => {
+  deepEqual(new Point(0, 0).add(new Point(0, 0)), new Point(0, 0))
+  deepEqual(new Point(0, 1).add(new Point(0, 0)), new Point(0, 1))
+  deepEqual(new Point(1, 1).add(new Point(4, 3)), new Point(5, 4))
+  deepEqual(new Point(-4, 7).add(new Point(1, 5)), new Point(-3, 12))
+})
+
+test('sub', t => {
+  deepEqual(new Point(0, 0).sub(new Point(0, 0)), new Point(0, 0))
+  deepEqual(new Point(0, 1).sub(new Point(0, 0)), new Point(0, 1))
+  deepEqual(new Point(1, 1).sub(new Point(4, 3)), new Point(-3, -2))
+  deepEqual(new Point(-4, 7).sub(new Point(1, 5)), new Point(-5, 2))
+})
+
+test('mul', t => {
+  deepEqual(new Point(0, 0).mul(0), new Point(0, 0))
+  deepEqual(new Point(0, 1).mul(1), new Point(0, 1))
+  deepEqual(new Point(1, 1).mul(5), new Point(5, 5))
+})
+
+test('ortho', t => {
+  deepEqual(new Point(0, 0).ortho(), new Point(-0, 0))
+  deepEqual(new Point(0, 1).ortho(), new Point(-1, 0))
+  deepEqual(new Point(1, 1).ortho(), new Point(-1, 1))
+  deepEqual(new Point(-4, 7).ortho(), new Point(-7, -4))
+  deepEqual(new Point(1, Math.sqrt(3)).ortho(), new Point(-Math.sqrt(3), 1))
+})
+
+test('dot', t => {
+  equal(new Point(0, 0).dot(new Point(0, 0)), 0)
+  equal(new Point(0, 1).dot(new Point(0, 0)), 0)
+  equal(new Point(1, 1).dot(new Point(4, 3)), 7)
+  equal(new Point(-4, 7).dot(new Point(1, 5)), 31)
+})
+
+test('cross', t => {
+  equal(new Point(0, 0).cross(new Point(0, 0)), 0)
+  equal(new Point(0, 1).cross(new Point(0, 0)), 0)
+  equal(new Point(1, 1).cross(new Point(-1, -1)), 0)
+  equal(new Point(1, 1).cross(new Point(4, 3)), -1)
+  equal(new Point(1, 5).cross(new Point(-2, 3)), 13)
+})
+
+test('norm', t => {
+  equal(new Point(0, 0).norm(), 0)
+  equal(new Point(0, 1).norm(), 1)
+  equal(new Point(-1, 0).norm(), 1)
+  equal(new Point(3, 4).norm(), 5)
+  equal(new Point(3, -4).norm(), 5)
+  equal(new Point(2, 2).norm(), 2 * Math.sqrt(2))
+  equal(new Point(1, Math.sqrt(3)).norm(), 2)
+  equal(new Point(29, 29 * Math.sqrt(3)).norm(), 29 * 2 + 0.00000000000001)
+  equal(new Point(1, 1e15).norm(), 1e15)
+  equal(new Point(1e14, MAX_FLOAT32 - 1).norm(), MAX_FLOAT32)
+})
+
+test('normalize', t => {
+  deepEqual(new Point().normalize(), new Point(0, 0))
+  deepEqual(new Point(0, 0).normalize(), new Point(0, 0))
+  deepEqual(new Point(0, 1).normalize(), new Point(0, 1))
+  deepEqual(new Point(-1, 0).normalize(), new Point(-1, 0))
+  deepEqual(new Point(3, 4).normalize().trunc(), new Point(0.6, 0.8))
+  deepEqual(new Point(3, -4).normalize().trunc(), new Point(0.6, -0.8))
+  deepEqual(new Point(2, 2).normalize().trunc(), new Point(Math.sqrt(2) / 2, Math.sqrt(2) / 2).trunc())
+  deepEqual(new Point(7, 7 * Math.sqrt(3)).normalize().trunc(), new Point(0.5, Math.sqrt(3) / 2).trunc())
+  deepEqual(new Point(1e21, 1e21 * Math.sqrt(3)).normalize().trunc(), new Point(0.5, Math.sqrt(3) / 2).trunc())
+  deepEqual(new Point(1, 1e16).normalize().trunc(), new Point(0, 1))
+  deepEqual(new Point(1e4, MAX_FLOAT32 - 1).normalize().trunc(), new Point(0, 1))
+})
+
+test('trunc', t => {
+  deepEqual(new Point().trunc(), new Point(0, 0))
+  deepEqual(new Point(0.0000000000000001, 0.0000000000000001).trunc(), new Point(0, 0))
+  deepEqual(new Point(0.00000000001, 0.00000000001).trunc(10), new Point(0, 0))
+})
+
+test('toString', t => {
+  equal(new Point().toString(), '(0.000000000000, 0.000000000000)')
+  equal(new Point(0.0000000000000001, 0.0000000000000001).toString(), '(0.000000000000, 0.000000000000)')
+  equal(new Point(-1, 1).toString(), '(-1.000000000000, 1.000000000000)')
+  equal(new Point(-1.123456789123456789, 1).toString(), '(-1.123456789123, 1.000000000000)')
+})

r2/_index.ts

@@ -0,0 +1,5 @@
+/**
+ * Module r2 implements types and functions for working with geometry in ℝ².
+ * @module r2
+ */
+export { Point } from './Point'