packages/utils/src/shape.ts

/**
 * this file defines pure geometric shapes
 *
 * for instance, a cubic bezier curve is specified by its four control points and
 * an ellipse is defined by its center, angle, semi major axis and semi minor axis
 * (but in semi-width and semi-height so it's more relevant to Excalidraw)
 *
 * the idea with pure shapes is so that we can provide collision and other geoemtric methods not depending on
 * the specifics of roughjs or elements in Excalidraw; instead, we can focus on the pure shapes themselves
 *
 * also included in this file are methods for converting an Excalidraw element or a Drawable from roughjs
 * to pure shapes
 */
import { pointsOnBezierCurves } from "points-on-curve";

import { invariant } from "@excalidraw/common";
import {
  curve,
  lineSegment,
  pointFrom,
  pointDistance,
  pointFromArray,
  pointFromVector,
  pointRotateRads,
  polygon,
  polygonFromPoints,
  PRECISION,
  segmentsIntersectAt,
  vector,
  vectorAdd,
  vectorFromPoint,
  vectorScale,
  type GlobalPoint,
  type LocalPoint,
} from "@excalidraw/math";

import { getElementAbsoluteCoords } from "@excalidraw/element";

import type {
  ElementsMap,
  ExcalidrawBindableElement,
  ExcalidrawDiamondElement,
  ExcalidrawElement,
  ExcalidrawEllipseElement,
  ExcalidrawEmbeddableElement,
  ExcalidrawFrameLikeElement,
  ExcalidrawFreeDrawElement,
  ExcalidrawIframeElement,
  ExcalidrawImageElement,
  ExcalidrawLinearElement,
  ExcalidrawRectangleElement,
  ExcalidrawSelectionElement,
  ExcalidrawTextElement,
} from "@excalidraw/element/types";
import type { Curve, LineSegment, Polygon, Radians } from "@excalidraw/math";

import type { Drawable, Op } from "roughjs/bin/core";

// a polyline (made up term here) is a line consisting of other line segments
// this corresponds to a straight line element in the editor but it could also
// be used to model other elements
export type Polyline<Point extends GlobalPoint | LocalPoint> =
  LineSegment<Point>[];

// a polycurve is a curve consisting of ther curves, this corresponds to a complex
// curve on the canvas
export type Polycurve<Point extends GlobalPoint | LocalPoint> = Curve<Point>[];

// an ellipse is specified by its center, angle, and its major and minor axes
// but for the sake of simplicity, we've used halfWidth and halfHeight instead
// in replace of semi major and semi minor axes
export type Ellipse<Point extends GlobalPoint | LocalPoint> = {
  center: Point;
  angle: Radians;
  halfWidth: number;
  halfHeight: number;
};

export type GeometricShape<Point extends GlobalPoint | LocalPoint> =
  | {
      type: "line";
      data: LineSegment<Point>;
    }
  | {
      type: "polygon";
      data: Polygon<Point>;
    }
  | {
      type: "curve";
      data: Curve<Point>;
    }
  | {
      type: "ellipse";
      data: Ellipse<Point>;
    }
  | {
      type: "polyline";
      data: Polyline<Point>;
    }
  | {
      type: "polycurve";
      data: Polycurve<Point>;
    };

type RectangularElement =
  | ExcalidrawRectangleElement
  | ExcalidrawDiamondElement
  | ExcalidrawFrameLikeElement
  | ExcalidrawEmbeddableElement
  | ExcalidrawImageElement
  | ExcalidrawIframeElement
  | ExcalidrawTextElement
  | ExcalidrawSelectionElement;

// polygon
export const getPolygonShape = <Point extends GlobalPoint | LocalPoint>(
  element: RectangularElement,
): GeometricShape<Point> => {
  const { angle, width, height, x, y } = element;

  const cx = x + width / 2;
  const cy = y + height / 2;

  const center: Point = pointFrom(cx, cy);

  let data: Polygon<Point>;

  if (element.type === "diamond") {
    data = polygon(
      pointRotateRads(pointFrom(cx, y), center, angle),
      pointRotateRads(pointFrom(x + width, cy), center, angle),
      pointRotateRads(pointFrom(cx, y + height), center, angle),
      pointRotateRads(pointFrom(x, cy), center, angle),
    );
  } else {
    data = polygon(
      pointRotateRads(pointFrom(x, y), center, angle),
      pointRotateRads(pointFrom(x + width, y), center, angle),
      pointRotateRads(pointFrom(x + width, y + height), center, angle),
      pointRotateRads(pointFrom(x, y + height), center, angle),
    );
  }

  return {
    type: "polygon",
    data,
  };
};

// return the selection box for an element, possibly rotated as well
export const getSelectionBoxShape = <Point extends GlobalPoint | LocalPoint>(
  element: ExcalidrawElement,
  elementsMap: ElementsMap,
  padding = 10,
) => {
  let [x1, y1, x2, y2, cx, cy] = getElementAbsoluteCoords(
    element,
    elementsMap,
    true,
  );

  x1 -= padding;
  x2 += padding;
  y1 -= padding;
  y2 += padding;

  //const angleInDegrees = angleToDegrees(element.angle);
  const center = pointFrom(cx, cy);
  const topLeft = pointRotateRads(pointFrom(x1, y1), center, element.angle);
  const topRight = pointRotateRads(pointFrom(x2, y1), center, element.angle);
  const bottomLeft = pointRotateRads(pointFrom(x1, y2), center, element.angle);
  const bottomRight = pointRotateRads(pointFrom(x2, y2), center, element.angle);

  return {
    type: "polygon",
    data: [topLeft, topRight, bottomRight, bottomLeft],
  } as GeometricShape<Point>;
};

// ellipse
export const getEllipseShape = <Point extends GlobalPoint | LocalPoint>(
  element: ExcalidrawEllipseElement,
): GeometricShape<Point> => {
  const { width, height, angle, x, y } = element;

  return {
    type: "ellipse",
    data: {
      center: pointFrom(x + width / 2, y + height / 2),
      angle,
      halfWidth: width / 2,
      halfHeight: height / 2,
    },
  };
};

export const getCurvePathOps = (shape: Drawable): Op[] => {
  // NOTE (mtolmacs): Temporary fix for extremely large elements
  if (!shape) {
    return [];
  }

  for (const set of shape.sets) {
    if (set.type === "path") {
      return set.ops;
    }
  }
  return shape.sets[0].ops;
};

// linear
export const getCurveShape = <Point extends GlobalPoint | LocalPoint>(
  roughShape: Drawable,
  startingPoint: Point = pointFrom(0, 0),
  angleInRadian: Radians,
  center: Point,
): GeometricShape<Point> => {
  const transform = (p: Point): Point =>
    pointRotateRads(
      pointFrom(p[0] + startingPoint[0], p[1] + startingPoint[1]),
      center,
      angleInRadian,
    );

  const ops = getCurvePathOps(roughShape);
  const polycurve: Polycurve<Point> = [];
  let p0 = pointFrom<Point>(0, 0);

  for (const op of ops) {
    if (op.op === "move") {
      const p = pointFromArray<Point>(op.data);
      invariant(p != null, "Ops data is not a point");
      p0 = transform(p);
    }
    if (op.op === "bcurveTo") {
      const p1 = transform(pointFrom<Point>(op.data[0], op.data[1]));
      const p2 = transform(pointFrom<Point>(op.data[2], op.data[3]));
      const p3 = transform(pointFrom<Point>(op.data[4], op.data[5]));
      polycurve.push(curve<Point>(p0, p1, p2, p3));
      p0 = p3;
    }
  }

  return {
    type: "polycurve",
    data: polycurve,
  };
};

const polylineFromPoints = <Point extends GlobalPoint | LocalPoint>(
  points: Point[],
): Polyline<Point> => {
  let previousPoint: Point = points[0];
  const polyline: LineSegment<Point>[] = [];

  for (let i = 1; i < points.length; i++) {
    const nextPoint = points[i];
    polyline.push(lineSegment<Point>(previousPoint, nextPoint));
    previousPoint = nextPoint;
  }

  return polyline;
};

export const getFreedrawShape = <Point extends GlobalPoint | LocalPoint>(
  element: ExcalidrawFreeDrawElement,
  center: Point,
  isClosed: boolean = false,
): GeometricShape<Point> => {
  const transform = (p: Point) =>
    pointRotateRads(
      pointFromVector(
        vectorAdd(vectorFromPoint(p), vector(element.x, element.y)),
      ),
      center,
      element.angle,
    );

  const polyline = polylineFromPoints(
    element.points.map((p) => transform(p as Point)),
  );

  return (
    isClosed
      ? {
          type: "polygon",
          data: polygonFromPoints(polyline.flat()),
        }
      : {
          type: "polyline",
          data: polyline,
        }
  ) as GeometricShape<Point>;
};

export const getClosedCurveShape = <Point extends GlobalPoint | LocalPoint>(
  element: ExcalidrawLinearElement,
  roughShape: Drawable,
  startingPoint: Point = pointFrom<Point>(0, 0),
  angleInRadian: Radians,
  center: Point,
): GeometricShape<Point> => {
  const transform = (p: Point) =>
    pointRotateRads(
      pointFrom(p[0] + startingPoint[0], p[1] + startingPoint[1]),
      center,
      angleInRadian,
    );

  if (element.roundness === null) {
    return {
      type: "polygon",
      data: polygonFromPoints(
        element.points.map((p) => transform(p as Point)) as Point[],
      ),
    };
  }

  const ops = getCurvePathOps(roughShape);

  const points: Point[] = [];
  let odd = false;
  for (const operation of ops) {
    if (operation.op === "move") {
      odd = !odd;
      if (odd) {
        points.push(pointFrom(operation.data[0], operation.data[1]));
      }
    } else if (operation.op === "bcurveTo") {
      if (odd) {
        points.push(pointFrom(operation.data[0], operation.data[1]));
        points.push(pointFrom(operation.data[2], operation.data[3]));
        points.push(pointFrom(operation.data[4], operation.data[5]));
      }
    } else if (operation.op === "lineTo") {
      if (odd) {
        points.push(pointFrom(operation.data[0], operation.data[1]));
      }
    }
  }

  const polygonPoints = pointsOnBezierCurves(points, 10, 5).map((p) =>
    transform(p as Point),
  ) as Point[];

  return {
    type: "polygon",
    data: polygonFromPoints<Point>(polygonPoints),
  };
};

/**
 * Determine intersection of a rectangular shaped element and a
 * line segment.
 *
 * @param element The rectangular element to test against
 * @param segment The segment intersecting the element
 * @param gap Optional value to inflate the shape before testing
 * @returns An array of intersections
 */
// TODO: Replace with final rounded rectangle code
export const segmentIntersectRectangleElement = <
  Point extends LocalPoint | GlobalPoint,
>(
  element: ExcalidrawBindableElement,
  segment: LineSegment<Point>,
  gap: number = 0,
): Point[] => {
  const bounds = [
    element.x - gap,
    element.y - gap,
    element.x + element.width + gap,
    element.y + element.height + gap,
  ];
  const center = pointFrom(
    (bounds[0] + bounds[2]) / 2,
    (bounds[1] + bounds[3]) / 2,
  );

  return [
    lineSegment(
      pointRotateRads(pointFrom(bounds[0], bounds[1]), center, element.angle),
      pointRotateRads(pointFrom(bounds[2], bounds[1]), center, element.angle),
    ),
    lineSegment(
      pointRotateRads(pointFrom(bounds[2], bounds[1]), center, element.angle),
      pointRotateRads(pointFrom(bounds[2], bounds[3]), center, element.angle),
    ),
    lineSegment(
      pointRotateRads(pointFrom(bounds[2], bounds[3]), center, element.angle),
      pointRotateRads(pointFrom(bounds[0], bounds[3]), center, element.angle),
    ),
    lineSegment(
      pointRotateRads(pointFrom(bounds[0], bounds[3]), center, element.angle),
      pointRotateRads(pointFrom(bounds[0], bounds[1]), center, element.angle),
    ),
  ]
    .map((s) => segmentsIntersectAt(segment, s))
    .filter((i): i is Point => !!i);
};

const distanceToEllipse = <Point extends LocalPoint | GlobalPoint>(
  p: Point,
  ellipse: Ellipse<Point>,
) => {
  const { angle, halfWidth, halfHeight, center } = ellipse;
  const a = halfWidth;
  const b = halfHeight;
  const translatedPoint = vectorAdd(
    vectorFromPoint(p),
    vectorScale(vectorFromPoint(center), -1),
  );
  const [rotatedPointX, rotatedPointY] = pointRotateRads(
    pointFromVector(translatedPoint),
    pointFrom(0, 0),
    -angle as Radians,
  );

  const px = Math.abs(rotatedPointX);
  const py = Math.abs(rotatedPointY);

  let tx = 0.707;
  let ty = 0.707;

  for (let i = 0; i < 3; i++) {
    const x = a * tx;
    const y = b * ty;

    const ex = ((a * a - b * b) * tx ** 3) / a;
    const ey = ((b * b - a * a) * ty ** 3) / b;

    const rx = x - ex;
    const ry = y - ey;

    const qx = px - ex;
    const qy = py - ey;

    const r = Math.hypot(ry, rx);
    const q = Math.hypot(qy, qx);

    tx = Math.min(1, Math.max(0, ((qx * r) / q + ex) / a));
    ty = Math.min(1, Math.max(0, ((qy * r) / q + ey) / b));
    const t = Math.hypot(ty, tx);
    tx /= t;
    ty /= t;
  }

  const [minX, minY] = [
    a * tx * Math.sign(rotatedPointX),
    b * ty * Math.sign(rotatedPointY),
  ];

  return pointDistance(
    pointFrom(rotatedPointX, rotatedPointY),
    pointFrom(minX, minY),
  );
};

export const pointOnEllipse = <Point extends LocalPoint | GlobalPoint>(
  point: Point,
  ellipse: Ellipse<Point>,
  threshold = PRECISION,
) => {
  return distanceToEllipse(point, ellipse) <= threshold;
};

export const pointInEllipse = <Point extends LocalPoint | GlobalPoint>(
  p: Point,
  ellipse: Ellipse<Point>,
) => {
  const { center, angle, halfWidth, halfHeight } = ellipse;
  const translatedPoint = vectorAdd(
    vectorFromPoint(p),
    vectorScale(vectorFromPoint(center), -1),
  );
  const [rotatedPointX, rotatedPointY] = pointRotateRads(
    pointFromVector(translatedPoint),
    pointFrom(0, 0),
    -angle as Radians,
  );

  return (
    (rotatedPointX / halfWidth) * (rotatedPointX / halfWidth) +
      (rotatedPointY / halfHeight) * (rotatedPointY / halfHeight) <=
    1
  );
};

export const ellipseAxes = <Point extends LocalPoint | GlobalPoint>(
  ellipse: Ellipse<Point>,
) => {
  const widthGreaterThanHeight = ellipse.halfWidth > ellipse.halfHeight;

  const majorAxis = widthGreaterThanHeight
    ? ellipse.halfWidth * 2
    : ellipse.halfHeight * 2;
  const minorAxis = widthGreaterThanHeight
    ? ellipse.halfHeight * 2
    : ellipse.halfWidth * 2;

  return {
    majorAxis,
    minorAxis,
  };
};

export const ellipseFocusToCenter = <Point extends LocalPoint | GlobalPoint>(
  ellipse: Ellipse<Point>,
) => {
  const { majorAxis, minorAxis } = ellipseAxes(ellipse);

  return Math.sqrt(majorAxis ** 2 - minorAxis ** 2);
};

export const ellipseExtremes = <Point extends LocalPoint | GlobalPoint>(
  ellipse: Ellipse<Point>,
) => {
  const { center, angle } = ellipse;
  const { majorAxis, minorAxis } = ellipseAxes(ellipse);

  const cos = Math.cos(angle);
  const sin = Math.sin(angle);

  const sqSum = majorAxis ** 2 + minorAxis ** 2;
  const sqDiff = (majorAxis ** 2 - minorAxis ** 2) * Math.cos(2 * angle);

  const yMax = Math.sqrt((sqSum - sqDiff) / 2);
  const xAtYMax =
    (yMax * sqSum * sin * cos) /
    (majorAxis ** 2 * sin ** 2 + minorAxis ** 2 * cos ** 2);

  const xMax = Math.sqrt((sqSum + sqDiff) / 2);
  const yAtXMax =
    (xMax * sqSum * sin * cos) /
    (majorAxis ** 2 * cos ** 2 + minorAxis ** 2 * sin ** 2);
  const centerVector = vectorFromPoint(center);

  return [
    vectorAdd(vector(xAtYMax, yMax), centerVector),
    vectorAdd(vectorScale(vector(xAtYMax, yMax), -1), centerVector),
    vectorAdd(vector(xMax, yAtXMax), centerVector),
    vectorAdd(vector(xMax, yAtXMax), centerVector),
  ];
};