5 files changed, 262 insertions, 0 deletions
diff --git a/apps/web/src/math/Coord.ts b/apps/web/src/math/Coord.ts
new file mode 100644
index 0000000..db7ee6d
--- /dev/null
+++ b/apps/web/src/math/Coord.ts
@@ -0,0 +1,23 @@
+/** A coord on a grid whose origin is in the top left. */
+export default class Coord {
+  private readonly _x: number;
+  private readonly _y: number;
+
+  constructor(x: number, y: number) {
+    this._x = x;
+    this._y = y;
+  }
+
+  get x(): number {
+    return this._x;
+  }
+
+  get y(): number {
+    return this._y;
+  }
+
+  /** Get the squared distance of this point from the origin. */
+  squaredDistanceFromOrigin(): number {
+    return this._x * this._x + this._y * this._y;
+  }
+}
diff --git a/apps/web/src/math/Ratio.test.ts b/apps/web/src/math/Ratio.test.ts
new file mode 100644
index 0000000..da6fef2
--- /dev/null
+++ b/apps/web/src/math/Ratio.test.ts
@@ -0,0 +1,27 @@
+import { describe, expect, test } from "vitest";
+import Ratio from "./Ratio";
+
+describe(Ratio, () => {
+  describe(Ratio.prototype.add, () => {
+    test("returns fractions in simplest form", () => {
+      const a = Ratio.fromInteger(0);
+      const b = new Ratio(1, 4);
+
+      const c = a.add(b);
+      expect(c.numerator).toBe(1);
+      expect(c.denominator).toBe(4);
+
+      const d = c.add(b);
+      expect(d.numerator).toBe(1);
+      expect(d.denominator).toBe(2);
+
+      const e = d.add(b);
+      expect(e.numerator).toBe(3);
+      expect(e.denominator).toBe(4);
+
+      const f = e.add(b);
+      expect(f.numerator).toBe(1);
+      expect(f.denominator).toBe(1);
+    });
+  });
+});
diff --git a/apps/web/src/math/Ratio.ts b/apps/web/src/math/Ratio.ts
new file mode 100644
index 0000000..e2a1fbf
--- /dev/null
+++ b/apps/web/src/math/Ratio.ts
@@ -0,0 +1,105 @@
+import { gcd } from ".";
+
+/** Serializable representation of a ratio. */
+export type RatioData = [numerator: number, denominator: number];
+
+/** Representation of a ratio for performing fractional artithmetic. */
+export default class Ratio {
+  readonly #numerator: number;
+  readonly #denominator: number;
+
+  get numerator(): number {
+    return this.#numerator;
+  }
+
+  get denominator(): number {
+    return this.#denominator;
+  }
+
+  constructor(numerator: number, denominator: number) {
+    if (!Number.isInteger(numerator) || !Number.isInteger(denominator)) {
+      throw new TypeError(
+        `Ratio must have integer parts: ${numerator} / ${denominator}`,
+      );
+    }
+
+    if (denominator === 0) {
+      throw new RangeError("Ratio demnominator cannot be zero");
+    }
+
+    const divisor = gcd(numerator, denominator);
+
+    this.#numerator = numerator / divisor;
+    this.#denominator = denominator / divisor;
+  }
+
+  multiplyRatio(other: Ratio): Ratio {
+    return new Ratio(
+      this.numerator * other.numerator,
+      this.denominator * other.denominator,
+    );
+  }
+
+  divideRatio(other: Ratio): Ratio {
+    return new Ratio(
+      this.numerator * other.denominator,
+      this.denominator * other.numerator,
+    );
+  }
+
+  add(other: Ratio): Ratio {
+    return new Ratio(
+      this.numerator * other.denominator + other.numerator * this.denominator,
+      this.denominator * other.denominator,
+    );
+  }
+
+  subtract(other: Ratio): Ratio {
+    return new Ratio(
+      this.numerator * other.denominator - other.numerator * this.denominator,
+      this.denominator * other.denominator,
+    );
+  }
+
+  compare(other: Ratio): number {
+    const left = this.numerator * other.denominator;
+    const right = other.numerator * this.denominator;
+    return left < right ? -1 : left > right ? 1 : 0;
+  }
+
+  equals(other: Ratio): boolean {
+    return this.compare(other) === 0;
+  }
+
+  toNumber(): number {
+    return this.numerator / this.denominator;
+  }
+
+  toString(): string {
+    return `${this.numerator}/${this.denominator}`;
+  }
+
+  [Symbol.for("nodejs.util.inspect.custom")](): string {
+    return `Ratio { ${this.numerator}/${this.denominator} }`;
+  }
+
+  static fromInteger(n: number): Ratio {
+    return new Ratio(n, 1);
+  }
+
+  toData(): RatioData {
+    return [this.numerator, this.denominator];
+  }
+
+  static fromData(ratio: RatioData): Ratio {
+    return new Ratio(ratio[0], ratio[1]);
+  }
+
+  static min(...ratios: Ratio[]): Ratio {
+    return ratios.reduce((a, b) => (a.compare(b) <= 0 ? a : b));
+  }
+
+  static max(...ratios: Ratio[]): Ratio {
+    return ratios.reduce((a, b) => (a.compare(b) >= 0 ? a : b));
+  }
+}
diff --git a/apps/web/src/math/Rect.ts b/apps/web/src/math/Rect.ts
new file mode 100644
index 0000000..f52a2f7
--- /dev/null
+++ b/apps/web/src/math/Rect.ts
@@ -0,0 +1,104 @@
+import Coord from "./Coord";
+
+/** A rectangle on a grid whose origin is in the top left. */
+export default class Rect {
+  private readonly _topLeft: Coord;
+  private readonly _width: number;
+  private readonly _height: number;
+
+  constructor(
+    topLeftX: number,
+    topLeftY: number,
+    width: number,
+    height: number,
+  ) {
+    this._topLeft = new Coord(topLeftX, topLeftY);
+    this._width = width;
+    this._height = height;
+  }
+
+  /** Width of this rectangle. */
+  get width(): number {
+    return this._width;
+  }
+
+  /** Height of this rectangle. */
+  get height(): number {
+    return this._height;
+  }
+
+  /** Coord of the top-left point of this rectangle. */
+  get topLeft(): Coord {
+    return this._topLeft;
+  }
+
+  /** Coord of the bottom-right point of this rectangle. */
+  get bottomRight(): Coord {
+    return new Coord(
+      this._topLeft.x + this._width,
+      this._topLeft.y + this._height,
+    );
+  }
+
+  get center(): Coord {
+    return new Coord(
+      this.topLeft.x + (this.bottomRight.x - this.topLeft.x) / 2,
+      this.topLeft.y + (this.bottomRight.y - this.topLeft.y) / 2,
+    );
+  }
+
+  /** Determine if this rectangle contains the point at `coord`. */
+  containsCoord(coord: Coord): boolean {
+    return (
+      this.topLeft.x <= coord.x &&
+      coord.x <= this.bottomRight.x &&
+      this.topLeft.y <= coord.y &&
+      coord.y <= this.bottomRight.y
+    );
+  }
+
+  verticallyContainsCoord(coord: Coord): boolean {
+    return this.topLeft.y <= coord.y && coord.y <= this.bottomRight.y;
+  }
+
+  horizontallyContainsCoord(coord: Coord): boolean {
+    return this.topLeft.x <= coord.x && coord.x <= this.bottomRight.x;
+  }
+
+  extend(other: Rect): Rect {
+    const topLeftX = Math.min(
+      this.topLeft.x,
+      this.bottomRight.x,
+      other.topLeft.x,
+      other.bottomRight.x,
+    );
+
+    const topLeftY = Math.min(
+      this.topLeft.y,
+      this.bottomRight.y,
+      other.topLeft.y,
+      other.bottomRight.y,
+    );
+
+    const bottomRightX = Math.max(
+      this.topLeft.x,
+      this.bottomRight.x,
+      other.topLeft.x,
+      other.bottomRight.x,
+    );
+
+    const bottomRightY = Math.max(
+      this.topLeft.y,
+      this.bottomRight.y,
+      other.topLeft.y,
+      other.bottomRight.y,
+    );
+
+    return new Rect(
+      topLeftX,
+      topLeftY,
+      bottomRightX - topLeftX,
+      bottomRightY - topLeftY,
+    );
+  }
+}
diff --git a/apps/web/src/math/index.ts b/apps/web/src/math/index.ts
new file mode 100644
index 0000000..70dbb67
--- /dev/null
+++ b/apps/web/src/math/index.ts
@@ -0,0 +1,3 @@
+export function gcd(a: number, b: number): number {
+  return b === 0 ? Math.abs(a) : gcd(b, a % b);
+}