AoC 2021 D13: Transparent Origami

| Problem statement | Source code | Tags: GeometryManual inspection

Part 1

I represent the points as a list of $(x, y)$ coordinates. A fold along $x = x_0$ transforms $(x, y)$ to:

(x', y') = \begin{cases} (x, y) &\text{ if } x \le x_0 \\ (2x_0 - x, y) &\text{ if } x > x_0 \end{cases}

A fold along $y = y_0$ is similar:

(x', y') = \begin{cases} (x, y) &\text{ if } y \le y_0 \\ (x, 2y_0 - y) &\text{ if } y > y_0 \end{cases}

Unfortunately again, JavaScript doesn't have composite keys for sets, so to deduplicate points after folding, I serialize each point as a string x,y and store them in a set.

function fold(
  points: [number, number][],
  axis: "x" | "y",
  line: number,
): [number, number][] {
  const newPoints = points.map(([x, y]) => {
    if (axis === "x" && x > line) {
      return [2 * line - x, y];
    } else if (axis === "y" && y > line) {
      return [x, 2 * line - y];
    } else {
      return [x, y];
    }
  });
  const uniquePoints = new Set<string>();
  for (const [x, y] of newPoints) {
    uniquePoints.add(`${x},${y}`);
  }
  return Array.from(uniquePoints).map(
    (s) => s.split(",").map(Number) as [number, number],
  );
}

Part 2

Just apply all folds in sequence, and plot the resulting points. Like every time, I take some time to admire the ASCII art.

#  # #### #    #### #  #   ## ###  #  #
#  #    # #    #    #  #    # #  # # #
####   #  #    ###  ####    # #  # ##
#  #  #   #    #    #  #    # ###  # #
#  # #    #    #    #  # #  # # #  # #
#  # #### #### #### #  #  ##  #  # #  #

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