Add fourier visualizer

1 files changed, 301 insertions, 0 deletions

diff --git a/ft-visualizer/js/script.js b/ft-visualizer/js/script.js
new file mode 100644
index 0000000..5c6c4a2
--- /dev/null
+++ b/ft-visualizer/js/script.js
@@ -0,0 +1,301 @@
+const RENDER_TYPE = {
+  LATEX: 1,
+  FUNC: 2,
+};
+const THRESHOLD = 1e-10;
+const LATEX_SIGFIGS = 8;
+const FONT = "Courier New";
+const FONT_HEIGHT_PX = 16;
+const DX = 3;
+
+const canvas = document.getElementById("canvas");
+const ctx = canvas.getContext("2d");
+let state = {};
+const initializeState = () => {
+  const xLabels = [
+    "Jan",
+    "Feb",
+    "Mar",
+    "Apr",
+    "May",
+    "Jun",
+    "Jul",
+    "Aug",
+    "Sept",
+    "Oct",
+    "Nov",
+    "Dec",
+    "Jan",
+  ];
+  const yLabels = ["Great", "Good", "Meh", "Bad", "Horrible"];
+  return {
+    width: canvas.parentElement.clientWidth,
+    height: canvas.parentElement.clientHeight,
+    xLabels,
+    yLabels,
+    gridBox: { width: 0.9, height: 0.9 },
+    heights: Array(xLabels.length * DX - 1).fill(0),
+  };
+};
+
+const dft = (
+  heights,
+  render = RENDER_TYPE.LATEX,
+  threshold = THRESHOLD,
+  sigfigs = LATEX_SIGFIGS
+) => {
+  const n = heights.length;
+  return Array(n)
+    .fill()
+    .map((x, w) => {
+      const rate = -2 * Math.PI * w;
+      const s = heights.reduce(
+        (a, x, i) => ({
+          re: a.re + x * Math.cos((rate * i) / n),
+          im: a.im + x * Math.sin((rate * i) / n),
+        }),
+        { re: 0, im: 0 }
+      );
+
+      Object.entries(s).forEach(
+        ([key, value]) =>
+          (s[key] = ((Math.abs(value) < threshold ? 0 : 1) * value) / n)
+      );
+
+      const amp = Math.sqrt(s.re * s.re + s.im * s.im);
+      const phase = Math.atan2(s.im, s.re);
+
+      switch (render) {
+        case RENDER_TYPE.LATEX:
+          return `${amp.toPrecision(sigfigs)}\\cos\\left(${w}x\\frac{2}{${
+            n / DX
+          }}\\pi+${phase.toPrecision(sigfigs)}\\right)`;
+        case RENDER_TYPE.FUNC:
+          return (t) => amp * Math.cos(w * t + phase);
+      }
+    });
+};
+
+const resizeCanvas = ({ width, height }) => {
+  canvas.width = width;
+  canvas.style.width = width;
+  canvas.height = height;
+  canvas.style.height = height;
+};
+
+const loop = () => {
+  const stateChanges = Object.keys(state.diff);
+  if (stateChanges.length > 0) {
+    state = { ...state, ...state.diff };
+    if (
+      state.diff.width ||
+      state.diff.height ||
+      state.diff.xLabels ||
+      state.diff.yLabels ||
+      state.diff.gridBox
+    ) {
+      resizeCanvas(state.diff);
+      state.gridBoxWidth = state.gridBox.width * state.width;
+      state.gridBoxHeight = state.gridBox.height * state.height;
+
+      state.maxYLabelWidth = state.yLabels.reduce(
+        (a, label) => Math.max(ctx.measureText(label).width, a),
+        -Infinity
+      );
+
+      state.topLeftGridPos = {
+        x: (state.width - state.gridBoxWidth) / 2 + state.maxYLabelWidth,
+        y: (state.height - state.gridBoxHeight) / 2,
+      };
+
+      state.bottomRightGridPos = {
+        x: state.topLeftGridPos.x + state.gridBoxWidth,
+        y: state.topLeftGridPos.y + state.gridBoxHeight,
+      };
+    }
+    if (Object.keys(state.diff).length) draw(state);
+    if (state.diff.heights) drawDesmos();
+    state.diff = {};
+  }
+
+  requestAnimationFrame(loop);
+};
+
+const drawLine = (pos1, pos2) => {
+  ctx.beginPath();
+  ctx.moveTo(pos1.x, pos1.y);
+  ctx.lineTo(pos2.x, pos2.y);
+  ctx.stroke();
+};
+
+const drawDividers = (
+  xDividers,
+  yDividers,
+  topLeftGridPos,
+  bottomRightGridPos,
+  yLabelPadding
+) => {
+  xDividers.forEach(({ label, position }) => {
+    ctx.fillText(
+      label,
+      position.x - ctx.measureText(label).width / 2,
+      position.y
+    );
+    drawLine(
+      { ...position, y: topLeftGridPos.y },
+      { ...position, y: bottomRightGridPos.y }
+    );
+  });
+  yDividers.forEach(({ label, position }) => {
+    ctx.fillText(
+      label,
+      topLeftGridPos.x - yLabelPadding - ctx.measureText(label).width,
+      position.y
+    );
+    drawLine(
+      { ...position, x: topLeftGridPos.x },
+      { ...position, x: bottomRightGridPos.x }
+    );
+  });
+};
+
+const draw = ({
+  heights,
+  gridBoxWidth,
+  gridBoxHeight,
+  topLeftGridPos,
+  bottomRightGridPos,
+  maxYLabelWidth,
+  xLabels,
+  yLabels,
+  width,
+  height,
+}) => {
+  ctx.clearRect(0, 0, width, height);
+
+  ctx.font = `${FONT_HEIGHT_PX}px ${FONT}`;
+
+  const xDividers = xLabels.map((label, i) => ({
+    label,
+    position: {
+      x: topLeftGridPos.x + (gridBoxWidth / (xLabels.length - 1)) * i,
+      y: bottomRightGridPos.y + FONT_HEIGHT_PX,
+    },
+  }));
+
+  const yDividers = yLabels.map((label, i) => ({
+    label,
+    position: {
+      x: 0,
+      y: topLeftGridPos.y + (gridBoxHeight / (yLabels.length - 1)) * i,
+    },
+  }));
+
+  drawDividers(xDividers, yDividers, topLeftGridPos, bottomRightGridPos, 12);
+  let dx = (bottomRightGridPos.x - topLeftGridPos.x) / (heights.length - 1);
+  const prevStrokeStyle = ctx.strokeStyle;
+  ctx.strokeStyle = "red";
+  for (let i = 0; i < heights.length; ++i) {
+    const x = dx * i + topLeftGridPos.x;
+    drawLine(
+      { x, y: (gridBoxHeight / 2) * (1 - heights[i]) + topLeftGridPos.y },
+      {
+        x: x + dx,
+        y: (gridBoxHeight / 2) * (1 - heights[i + 1]) + topLeftGridPos.y,
+      }
+    );
+  }
+  ctx.strokeStyle = prevStrokeStyle;
+};
+
+const calculator = Desmos.GraphingCalculator(
+  document.getElementById("calculator"),
+  {
+    expressionsCollapsed: true,
+    autosize: true,
+  }
+);
+calculator.setMathBounds({
+  left: -0.8,
+  right: 12,
+  bottom: -3,
+  top: 3,
+});
+
+const drawDesmos = () => {
+  const equations = dft(state.heights);
+
+  calculator.setExpression({
+    id: `graph-total`,
+    latex: equations.map((_x, i) => `y_{${i}}`).join(" + "),
+  });
+  equations.forEach((x, i) =>
+    calculator.setExpression({
+      id: `graph${i}`,
+      latex: `y_{${i}}=${x}`,
+      hidden: true,
+    })
+  );
+};
+
+let isDown = false;
+canvas.addEventListener(
+  "mousedown",
+  (e) => {
+    e.preventDefault();
+    isDown = true;
+  },
+  true
+);
+
+canvas.addEventListener(
+  "mouseup",
+  (e) => {
+    e.preventDefault();
+    isDown = false;
+  },
+  true
+);
+
+canvas.addEventListener(
+  "mousemove",
+  (e) => {
+    e.preventDefault();
+    if (isDown) {
+      const rect = canvas.getBoundingClientRect();
+      const [x, y] = [e.clientX - rect.left, e.clientY - rect.top];
+
+      const {
+        topLeftGridPos,
+        bottomRightGridPos,
+        gridBoxWidth,
+        gridBoxHeight,
+        heights,
+      } = state;
+      const delta = Math.ceil(gridBoxWidth / heights.length);
+      const bin = Math.min(
+        Math.round(Math.max(x - topLeftGridPos.x, 0) / delta),
+        heights.length - 1
+      );
+      heights[bin] = Math.min(
+        Math.max(1 - (2 * (y - topLeftGridPos.y)) / gridBoxHeight, -1),
+        1
+      );
+      state.diff.heights = heights;
+    }
+  },
+  true
+);
+
+window.addEventListener("resize", () => {
+  state.diff = {
+    ...state.diff,
+    width: canvas.parentElement.clientWidth,
+    height: canvas.parentElement.clientHeight,
+  };
+});
+
+(() => {
+  state.diff = initializeState();
+  window.requestAnimationFrame(loop);
+})();