import * as GA from "../ga"; import * as GAPoint from "../gapoints"; import * as GADirection from "../gadirections"; import * as GALine from "../galines"; import * as GATransform from "../gatransforms"; import { isPathALoop, isPointInPolygon, rotate } from "../math"; import { pointsOnBezierCurves } from "points-on-curve"; import { NonDeletedExcalidrawElement, ExcalidrawBindableElement, ExcalidrawElement, ExcalidrawRectangleElement, ExcalidrawDiamondElement, ExcalidrawTextElement, ExcalidrawEllipseElement, NonDeleted, } from "./types"; import { getElementAbsoluteCoords, getCurvePathOps, Bounds } from "./bounds"; import { Point } from "../types"; import { Drawable } from "roughjs/bin/core"; import { AppState } from "../types"; import { getShapeForElement } from "../renderer/renderElement"; const isElementDraggableFromInside = ( element: NonDeletedExcalidrawElement, ): boolean => { if (element.type === "arrow") { return false; } const isDraggableFromInside = element.backgroundColor !== "transparent"; if (element.type === "line" || element.type === "draw") { return isDraggableFromInside && isPathALoop(element.points); } return isDraggableFromInside; }; export const hitTest = ( element: NonDeletedExcalidrawElement, appState: AppState, x: number, y: number, ): boolean => { // How many pixels off the shape boundary we still consider a hit const threshold = 10 / appState.zoom.value; const point: Point = [x, y]; if (isElementSelected(appState, element)) { return isPointHittingElementBoundingBox(element, point, threshold); } return isHittingElementNotConsideringBoundingBox(element, appState, point); }; export const isHittingElementBoundingBoxWithoutHittingElement = ( element: NonDeletedExcalidrawElement, appState: AppState, x: number, y: number, ): boolean => { const threshold = 10 / appState.zoom.value; return ( !isHittingElementNotConsideringBoundingBox(element, appState, [x, y]) && isPointHittingElementBoundingBox(element, [x, y], threshold) ); }; const isHittingElementNotConsideringBoundingBox = ( element: NonDeletedExcalidrawElement, appState: AppState, point: Point, ): boolean => { const threshold = 10 / appState.zoom.value; const check = element.type === "text" ? isStrictlyInside : isElementDraggableFromInside(element) ? isInsideCheck : isNearCheck; return hitTestPointAgainstElement({ element, point, threshold, check }); }; const isElementSelected = ( appState: AppState, element: NonDeleted, ) => appState.selectedElementIds[element.id]; const isPointHittingElementBoundingBox = ( element: NonDeleted, [x, y]: Point, threshold: number, ) => { const [x1, y1, x2, y2] = getElementAbsoluteCoords(element); const elementCenterX = (x1 + x2) / 2; const elementCenterY = (y1 + y2) / 2; // reverse rotate to take element's angle into account. const [rotatedX, rotatedY] = rotate( x, y, elementCenterX, elementCenterY, -element.angle, ); return ( rotatedX > x1 - threshold && rotatedX < x2 + threshold && rotatedY > y1 - threshold && rotatedY < y2 + threshold ); }; export const bindingBorderTest = ( element: NonDeleted, { x, y }: { x: number; y: number }, ): boolean => { const threshold = maxBindingGap(element, element.width, element.height); const check = isOutsideCheck; const point: Point = [x, y]; return hitTestPointAgainstElement({ element, point, threshold, check }); }; export const maxBindingGap = ( element: ExcalidrawElement, elementWidth: number, elementHeight: number, ): number => { // Aligns diamonds with rectangles const shapeRatio = element.type === "diamond" ? 1 / Math.sqrt(2) : 1; const smallerDimension = shapeRatio * Math.min(elementWidth, elementHeight); // We make the bindable boundary bigger for bigger elements return Math.max(15, Math.min(0.25 * smallerDimension, 80)); }; type HitTestArgs = { element: NonDeletedExcalidrawElement; point: Point; threshold: number; check: (distance: number, threshold: number) => boolean; }; const hitTestPointAgainstElement = (args: HitTestArgs): boolean => { switch (args.element.type) { case "rectangle": case "text": case "diamond": case "ellipse": const distance = distanceToBindableElement(args.element, args.point); return args.check(distance, args.threshold); case "arrow": case "line": case "draw": return hitTestLinear(args); case "selection": console.warn( "This should not happen, we need to investigate why it does.", ); return false; } }; export const distanceToBindableElement = ( element: ExcalidrawBindableElement, point: Point, ): number => { switch (element.type) { case "rectangle": case "text": return distanceToRectangle(element, point); case "diamond": return distanceToDiamond(element, point); case "ellipse": return distanceToEllipse(element, point); } }; const isStrictlyInside = (distance: number, threshold: number): boolean => { return distance < 0; }; const isInsideCheck = (distance: number, threshold: number): boolean => { return distance < threshold; }; const isNearCheck = (distance: number, threshold: number): boolean => { return Math.abs(distance) < threshold; }; const isOutsideCheck = (distance: number, threshold: number): boolean => { return 0 <= distance && distance < threshold; }; const distanceToRectangle = ( element: ExcalidrawRectangleElement | ExcalidrawTextElement, point: Point, ): number => { const [, pointRel, hwidth, hheight] = pointRelativeToElement(element, point); return Math.max( GAPoint.distanceToLine(pointRel, GALine.equation(0, 1, -hheight)), GAPoint.distanceToLine(pointRel, GALine.equation(1, 0, -hwidth)), ); }; const distanceToDiamond = ( element: ExcalidrawDiamondElement, point: Point, ): number => { const [, pointRel, hwidth, hheight] = pointRelativeToElement(element, point); const side = GALine.equation(hheight, hwidth, -hheight * hwidth); return GAPoint.distanceToLine(pointRel, side); }; const distanceToEllipse = ( element: ExcalidrawEllipseElement, point: Point, ): number => { const [pointRel, tangent] = ellipseParamsForTest(element, point); return -GALine.sign(tangent) * GAPoint.distanceToLine(pointRel, tangent); }; const ellipseParamsForTest = ( element: ExcalidrawEllipseElement, point: Point, ): [GA.Point, GA.Line] => { const [, pointRel, hwidth, hheight] = pointRelativeToElement(element, point); const [px, py] = GAPoint.toTuple(pointRel); // We're working in positive quadrant, so start with `t = 45deg`, `tx=cos(t)` let tx = 0.707; let ty = 0.707; const a = hwidth; const b = hheight; // This is a numerical method to find the params tx, ty at which // the ellipse has the closest point to the given point [0, 1, 2, 3].forEach((_) => { const xx = a * tx; const yy = b * ty; const ex = ((a * a - b * b) * tx ** 3) / a; const ey = ((b * b - a * a) * ty ** 3) / b; const rx = xx - ex; const ry = yy - 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 closestPoint = GA.point(a * tx, b * ty); const tangent = GALine.orthogonalThrough(pointRel, closestPoint); return [pointRel, tangent]; }; const hitTestLinear = (args: HitTestArgs): boolean => { const { element, threshold } = args; if (!getShapeForElement(element)) { return false; } const [point, pointAbs, hwidth, hheight] = pointRelativeToElement( args.element, args.point, ); const side1 = GALine.equation(0, 1, -hheight); const side2 = GALine.equation(1, 0, -hwidth); if ( !isInsideCheck(GAPoint.distanceToLine(pointAbs, side1), threshold) || !isInsideCheck(GAPoint.distanceToLine(pointAbs, side2), threshold) ) { return false; } const [relX, relY] = GAPoint.toTuple(point); const shape = getShapeForElement(element) as Drawable[]; if (args.check === isInsideCheck) { const hit = shape.some((subshape) => hitTestCurveInside(subshape, relX, relY, element.strokeSharpness), ); if (hit) { return true; } } // hit test all "subshapes" of the linear element return shape.some((subshape) => hitTestRoughShape(subshape, relX, relY, threshold), ); }; // Returns: // 1. the point relative to the elements (x, y) position // 2. the point relative to the element's center with positive (x, y) // 3. half element width // 4. half element height // // Note that for linear elements the (x, y) position is not at the // top right corner of their boundary. // // Rectangles, diamonds and ellipses are symmetrical over axes, // and other elements have a rectangular boundary, // so we only need to perform hit tests for the positive quadrant. const pointRelativeToElement = ( element: ExcalidrawElement, pointTuple: Point, ): [GA.Point, GA.Point, number, number] => { const point = GAPoint.from(pointTuple); const elementCoords = getElementAbsoluteCoords(element); const center = coordsCenter(elementCoords); // GA has angle orientation opposite to `rotate` const rotate = GATransform.rotation(center, element.angle); const pointRotated = GATransform.apply(rotate, point); const pointRelToCenter = GA.sub(pointRotated, GADirection.from(center)); const pointRelToCenterAbs = GAPoint.abs(pointRelToCenter); const elementPos = GA.offset(element.x, element.y); const pointRelToPos = GA.sub(pointRotated, elementPos); const [ax, ay, bx, by] = elementCoords; const halfWidth = (bx - ax) / 2; const halfHeight = (by - ay) / 2; return [pointRelToPos, pointRelToCenterAbs, halfWidth, halfHeight]; }; // Returns point in absolute coordinates export const pointInAbsoluteCoords = ( element: ExcalidrawElement, // Point relative to the element position point: Point, ): Point => { const [x, y] = point; const [x1, y1, x2, y2] = getElementAbsoluteCoords(element); const cx = (x2 - x1) / 2; const cy = (y2 - y1) / 2; const [rotatedX, rotatedY] = rotate(x, y, cx, cy, element.angle); return [element.x + rotatedX, element.y + rotatedY]; }; const relativizationToElementCenter = ( element: ExcalidrawElement, ): GA.Transform => { const elementCoords = getElementAbsoluteCoords(element); const center = coordsCenter(elementCoords); // GA has angle orientation opposite to `rotate` const rotate = GATransform.rotation(center, element.angle); const translate = GA.reverse( GATransform.translation(GADirection.from(center)), ); return GATransform.compose(rotate, translate); }; const coordsCenter = ([ax, ay, bx, by]: Bounds): GA.Point => { return GA.point((ax + bx) / 2, (ay + by) / 2); }; // The focus distance is the oriented ratio between the size of // the `element` and the "focus image" of the element on which // all focus points lie, so it's a number between -1 and 1. // The line going through `a` and `b` is a tangent to the "focus image" // of the element. export const determineFocusDistance = ( element: ExcalidrawBindableElement, // Point on the line, in absolute coordinates a: Point, // Another point on the line, in absolute coordinates (closer to element) b: Point, ): number => { const relateToCenter = relativizationToElementCenter(element); const aRel = GATransform.apply(relateToCenter, GAPoint.from(a)); const bRel = GATransform.apply(relateToCenter, GAPoint.from(b)); const line = GALine.through(aRel, bRel); const q = element.height / element.width; const hwidth = element.width / 2; const hheight = element.height / 2; const n = line[2]; const m = line[3]; const c = line[1]; const mabs = Math.abs(m); const nabs = Math.abs(n); switch (element.type) { case "rectangle": case "text": return c / (hwidth * (nabs + q * mabs)); case "diamond": return mabs < nabs ? c / (nabs * hwidth) : c / (mabs * hheight); case "ellipse": return c / (hwidth * Math.sqrt(n ** 2 + q ** 2 * m ** 2)); } }; export const determineFocusPoint = ( element: ExcalidrawBindableElement, // The oriented, relative distance from the center of `element` of the // returned focusPoint focus: number, adjecentPoint: Point, ): Point => { if (focus === 0) { const elementCoords = getElementAbsoluteCoords(element); const center = coordsCenter(elementCoords); return GAPoint.toTuple(center); } const relateToCenter = relativizationToElementCenter(element); const adjecentPointRel = GATransform.apply( relateToCenter, GAPoint.from(adjecentPoint), ); const reverseRelateToCenter = GA.reverse(relateToCenter); let point; switch (element.type) { case "rectangle": case "text": case "diamond": point = findFocusPointForRectangulars(element, focus, adjecentPointRel); break; case "ellipse": point = findFocusPointForEllipse(element, focus, adjecentPointRel); break; } return GAPoint.toTuple(GATransform.apply(reverseRelateToCenter, point)); }; // Returns 2 or 0 intersection points between line going through `a` and `b` // and the `element`, in ascending order of distance from `a`. export const intersectElementWithLine = ( element: ExcalidrawBindableElement, // Point on the line, in absolute coordinates a: Point, // Another point on the line, in absolute coordinates b: Point, // If given, the element is inflated by this value gap: number = 0, ): Point[] => { const relateToCenter = relativizationToElementCenter(element); const aRel = GATransform.apply(relateToCenter, GAPoint.from(a)); const bRel = GATransform.apply(relateToCenter, GAPoint.from(b)); const line = GALine.through(aRel, bRel); const reverseRelateToCenter = GA.reverse(relateToCenter); const intersections = getSortedElementLineIntersections( element, line, aRel, gap, ); return intersections.map((point) => GAPoint.toTuple(GATransform.apply(reverseRelateToCenter, point)), ); }; const getSortedElementLineIntersections = ( element: ExcalidrawBindableElement, // Relative to element center line: GA.Line, // Relative to element center nearPoint: GA.Point, gap: number = 0, ): GA.Point[] => { let intersections: GA.Point[]; switch (element.type) { case "rectangle": case "text": case "diamond": const corners = getCorners(element); intersections = corners .flatMap((point, i) => { const edge: [GA.Point, GA.Point] = [point, corners[(i + 1) % 4]]; return intersectSegment(line, offsetSegment(edge, gap)); }) .concat( corners.flatMap((point) => getCircleIntersections(point, gap, line)), ); break; case "ellipse": intersections = getEllipseIntersections(element, gap, line); break; } if (intersections.length < 2) { // Ignore the "edge" case of only intersecting with a single corner return []; } const sortedIntersections = intersections.sort( (i1, i2) => GAPoint.distance(i1, nearPoint) - GAPoint.distance(i2, nearPoint), ); return [ sortedIntersections[0], sortedIntersections[sortedIntersections.length - 1], ]; }; const getCorners = ( element: | ExcalidrawRectangleElement | ExcalidrawDiamondElement | ExcalidrawTextElement, scale: number = 1, ): GA.Point[] => { const hx = (scale * element.width) / 2; const hy = (scale * element.height) / 2; switch (element.type) { case "rectangle": case "text": return [ GA.point(hx, hy), GA.point(hx, -hy), GA.point(-hx, -hy), GA.point(-hx, hy), ]; case "diamond": return [ GA.point(0, hy), GA.point(hx, 0), GA.point(0, -hy), GA.point(-hx, 0), ]; } }; // Returns intersection of `line` with `segment`, with `segment` moved by // `gap` in its polar direction. // If intersection conincides with second segment point returns empty array. const intersectSegment = ( line: GA.Line, segment: [GA.Point, GA.Point], ): GA.Point[] => { const [a, b] = segment; const aDist = GAPoint.distanceToLine(a, line); const bDist = GAPoint.distanceToLine(b, line); if (aDist * bDist >= 0) { // The intersection is outside segment `(a, b)` return []; } return [GAPoint.intersect(line, GALine.through(a, b))]; }; const offsetSegment = ( segment: [GA.Point, GA.Point], distance: number, ): [GA.Point, GA.Point] => { const [a, b] = segment; const offset = GATransform.translationOrthogonal( GADirection.fromTo(a, b), distance, ); return [GATransform.apply(offset, a), GATransform.apply(offset, b)]; }; const getEllipseIntersections = ( element: ExcalidrawEllipseElement, gap: number, line: GA.Line, ): GA.Point[] => { const a = element.width / 2 + gap; const b = element.height / 2 + gap; const m = line[2]; const n = line[3]; const c = line[1]; const squares = a * a * m * m + b * b * n * n; const discr = squares - c * c; if (squares === 0 || discr <= 0) { return []; } const discrRoot = Math.sqrt(discr); const xn = -a * a * m * c; const yn = -b * b * n * c; return [ GA.point( (xn + a * b * n * discrRoot) / squares, (yn - a * b * m * discrRoot) / squares, ), GA.point( (xn - a * b * n * discrRoot) / squares, (yn + a * b * m * discrRoot) / squares, ), ]; }; export const getCircleIntersections = ( center: GA.Point, radius: number, line: GA.Line, ): GA.Point[] => { if (radius === 0) { return GAPoint.distanceToLine(line, center) === 0 ? [center] : []; } const m = line[2]; const n = line[3]; const c = line[1]; const [a, b] = GAPoint.toTuple(center); const r = radius; const squares = m * m + n * n; const discr = r * r * squares - (m * a + n * b + c) ** 2; if (squares === 0 || discr <= 0) { return []; } const discrRoot = Math.sqrt(discr); const xn = a * n * n - b * m * n - m * c; const yn = b * m * m - a * m * n - n * c; return [ GA.point((xn + n * discrRoot) / squares, (yn - m * discrRoot) / squares), GA.point((xn - n * discrRoot) / squares, (yn + m * discrRoot) / squares), ]; }; // The focus point is the tangent point of the "focus image" of the // `element`, where the tangent goes through `point`. export const findFocusPointForEllipse = ( ellipse: ExcalidrawEllipseElement, // Between -1 and 1 (not 0) the relative size of the "focus image" of // the element on which the focus point lies relativeDistance: number, // The point for which we're trying to find the focus point, relative // to the ellipse center. point: GA.Point, ): GA.Point => { const relativeDistanceAbs = Math.abs(relativeDistance); const a = (ellipse.width * relativeDistanceAbs) / 2; const b = (ellipse.height * relativeDistanceAbs) / 2; const orientation = Math.sign(relativeDistance); const [px, pyo] = GAPoint.toTuple(point); // The calculation below can't handle py = 0 const py = pyo === 0 ? 0.0001 : pyo; const squares = px ** 2 * b ** 2 + py ** 2 * a ** 2; // Tangent mx + ny + 1 = 0 const m = (-px * b ** 2 + orientation * py * Math.sqrt(Math.max(0, squares - a ** 2 * b ** 2))) / squares; const n = (-m * px - 1) / py; const x = -(a ** 2 * m) / (n ** 2 * b ** 2 + m ** 2 * a ** 2); return GA.point(x, (-m * x - 1) / n); }; export const findFocusPointForRectangulars = ( element: | ExcalidrawRectangleElement | ExcalidrawDiamondElement | ExcalidrawTextElement, // Between -1 and 1 for how far away should the focus point be relative // to the size of the element. Sign determines orientation. relativeDistance: number, // The point for which we're trying to find the focus point, relative // to the element center. point: GA.Point, ): GA.Point => { const relativeDistanceAbs = Math.abs(relativeDistance); const orientation = Math.sign(relativeDistance); const corners = getCorners(element, relativeDistanceAbs); let maxDistance = 0; let tangentPoint: null | GA.Point = null; corners.forEach((corner) => { const distance = orientation * GALine.through(point, corner)[1]; if (distance > maxDistance) { maxDistance = distance; tangentPoint = corner; } }); return tangentPoint!; }; const pointInBezierEquation = ( p0: Point, p1: Point, p2: Point, p3: Point, [mx, my]: Point, lineThreshold: number, ) => { // B(t) = p0 * (1-t)^3 + 3p1 * t * (1-t)^2 + 3p2 * t^2 * (1-t) + p3 * t^3 const equation = (t: number, idx: number) => Math.pow(1 - t, 3) * p3[idx] + 3 * t * Math.pow(1 - t, 2) * p2[idx] + 3 * Math.pow(t, 2) * (1 - t) * p1[idx] + p0[idx] * Math.pow(t, 3); // go through t in increments of 0.01 let t = 0; while (t <= 1.0) { const tx = equation(t, 0); const ty = equation(t, 1); const diff = Math.sqrt(Math.pow(tx - mx, 2) + Math.pow(ty - my, 2)); if (diff < lineThreshold) { return true; } t += 0.01; } return false; }; const hitTestCurveInside = ( drawable: Drawable, x: number, y: number, sharpness: ExcalidrawElement["strokeSharpness"], ) => { const ops = getCurvePathOps(drawable); const points: Point[] = []; let odd = false; // select one line out of double lines for (const operation of ops) { if (operation.op === "move") { odd = !odd; if (odd) { points.push([operation.data[0], operation.data[1]]); } } else if (operation.op === "bcurveTo") { if (odd) { points.push([operation.data[0], operation.data[1]]); points.push([operation.data[2], operation.data[3]]); points.push([operation.data[4], operation.data[5]]); } } } if (points.length >= 4) { if (sharpness === "sharp") { return isPointInPolygon(points, x, y); } const polygonPoints = pointsOnBezierCurves(points as any, 10, 5); return isPointInPolygon(polygonPoints, x, y); } return false; }; const hitTestRoughShape = ( drawable: Drawable, x: number, y: number, lineThreshold: number, ) => { // read operations from first opSet const ops = getCurvePathOps(drawable); // set start position as (0,0) just in case // move operation does not exist (unlikely but it is worth safekeeping it) let currentP: Point = [0, 0]; return ops.some(({ op, data }, idx) => { // There are only four operation types: // move, bcurveTo, lineTo, and curveTo if (op === "move") { // change starting point currentP = (data as unknown) as Point; // move operation does not draw anything; so, it always // returns false } else if (op === "bcurveTo") { // create points from bezier curve // bezier curve stores data as a flattened array of three positions // [x1, y1, x2, y2, x3, y3] const p1 = [data[0], data[1]] as Point; const p2 = [data[2], data[3]] as Point; const p3 = [data[4], data[5]] as Point; const p0 = currentP; currentP = p3; // check if points are on the curve // cubic bezier curves require four parameters // the first parameter is the last stored position (p0) const retVal = pointInBezierEquation( p0, p1, p2, p3, [x, y], lineThreshold, ); // set end point of bezier curve as the new starting point for // upcoming operations as each operation is based on the last drawn // position of the previous operation return retVal; } else if (op === "lineTo") { // TODO: Implement this } else if (op === "qcurveTo") { // TODO: Implement this } return false; }); };