// Geometry helpers shared by all typed renderers. Every function here is
// pure; renderers own their layout tables and pass measured rects
// ({x, y, width, height, cx, cy}) in.

import { recordDiagnostic } from './diagnostics.mjs';

// In degraded mode (no ajv) a type-wrong top-level field reaches the renderer.
// Coerce non-arrays to [] so the module-level Maps build without throwing and
// the friendly validator checks (which run later) report the real problem.
export function asArray(value) {
  return Array.isArray(value) ? value : [];
}

// A computed coordinate must be a finite number; NaN/undefined would silently
// write `<rect x="NaN">` into the output. Used by the validators as a backstop.
export function isFinitePoint(...coords) {
  return coords.every((c) => Number.isFinite(c));
}

// Separation the layout solver guarantees and separation this check re-derives
// travel through different arithmetic, so a pair the solver placed at exactly
// its minimum can land a few ulps short of this comparison. In #583 the CLI's
// own receipt has the pair `793.6 + 160 + 8` read as 2**-43 past a5's left edge
// at 961.5999999999999 — one ulp at that magnitude. 0.0001 is the numeric
// tolerance the route and layout geometry in this file already compares with.
const NUMERIC_CLEARANCE_PX = 0.0001;

export function rectsOverlap(a, b, gap = 0) {
  // Non-finite geometry means "unknown", not "overlapping". Every comparison
  // below is false for NaN, so without this guard the negation reports a
  // collision for every pair. Callers surface non-finite pos/size through their
  // own diagnostic; reporting it again as an overlap buries that message under
  // one bogus separation hint per pair.
  if (!isFinitePoint(a.x, a.y, a.width, a.height, b.x, b.y, b.width, b.height)) {
    return false;
  }
  return !(
    a.x + a.width + gap <= b.x + NUMERIC_CLEARANCE_PX ||
    b.x + b.width + gap <= a.x + NUMERIC_CLEARANCE_PX ||
    a.y + a.height + gap <= b.y + NUMERIC_CLEARANCE_PX ||
    b.y + b.height + gap <= a.y + NUMERIC_CLEARANCE_PX
  );
}

export function segmentIntersectsRect(segment, rect, gap = 0) {
  const box = {
    x1: rect.x - gap,
    y1: rect.y - gap,
    x2: rect.x + rect.width + gap,
    y2: rect.y + rect.height + gap
  };
  const [a, b] = [segment.start, segment.end];
  if (pointInBox(a, box) || pointInBox(b, box)) return true;
  return (
    segmentsIntersect(a, b, [box.x1, box.y1], [box.x2, box.y1]) ||
    segmentsIntersect(a, b, [box.x2, box.y1], [box.x2, box.y2]) ||
    segmentsIntersect(a, b, [box.x2, box.y2], [box.x1, box.y2]) ||
    segmentsIntersect(a, b, [box.x1, box.y2], [box.x1, box.y1])
  );
}

export function segmentRectClearance(segment, rect) {
  if (!segment || !rect) return null;
  const { start, end } = segment;
  if (!Array.isArray(start) || !Array.isArray(end) || start.length !== 2 || end.length !== 2) return null;
  if (!isFinitePoint(start[0], start[1], end[0], end[1], rect.x, rect.y, rect.width, rect.height)) return null;
  if (rect.width < 0 || rect.height < 0) return null;
  if (segmentIntersectsRect(segment, rect)) return 0;

  const right = rect.x + rect.width;
  const bottom = rect.y + rect.height;
  let clearance = Math.min(pointRectDistance(start, rect), pointRectDistance(end, rect));
  const corners = [rect.x, rect.y, right, rect.y, right, bottom, rect.x, bottom];
  for (let index = 0; index < 8; index += 2) {
    const distance = pointSegmentDistanceXY(corners[index], corners[index + 1], start, end);
    if (distance < clearance) clearance = distance;
  }
  return clearance;
}

// The same clearance, but the caller already knows the threshold it compares
// against: when an axis gap alone proves the distance cannot be smaller, the
// exact distance is never computed and Infinity is returned.
export function segmentRectClearanceWithin(segment, rect, limit) {
  if (!segment || !rect) return segmentRectClearance(segment, rect);
  const { start, end } = segment;
  if (!Array.isArray(start) || !Array.isArray(end) || start.length !== 2 || end.length !== 2) return null;
  if (!isFinitePoint(start[0], start[1], end[0], end[1], rect.x, rect.y, rect.width, rect.height)) return null;
  if (rect.width < 0 || rect.height < 0) return null;
  if (segmentIntersectsRect(segment, rect)) return 0;
  const minX = Math.min(start[0], end[0]);
  const maxX = Math.max(start[0], end[0]);
  const minY = Math.min(start[1], end[1]);
  const maxY = Math.max(start[1], end[1]);
  const gapX = Math.max(rect.x - maxX, minX - (rect.x + rect.width));
  const gapY = Math.max(rect.y - maxY, minY - (rect.y + rect.height));
  if (Math.max(gapX, gapY) > limit) return Number.POSITIVE_INFINITY;
  return segmentRectClearance(segment, rect);
}

export function segmentRectIntersectionLength(segment, rect) {
  if (!segment || !rect) return null;
  const { start, end } = segment;
  if (!Array.isArray(start) || !Array.isArray(end) || start.length !== 2 || end.length !== 2) return null;
  if (!isFinitePoint(...start, ...end, rect.x, rect.y, rect.width, rect.height)) return null;
  if (rect.width < 0 || rect.height < 0) return null;

  const dx = end[0] - start[0];
  const dy = end[1] - start[1];
  const length = Math.hypot(dx, dy);
  if (length <= 0.0000001) return 0;
  const bounds = [
    [-dx, start[0] - rect.x],
    [dx, rect.x + rect.width - start[0]],
    [-dy, start[1] - rect.y],
    [dy, rect.y + rect.height - start[1]],
  ];
  let enter = 0;
  let leave = 1;
  for (const [direction, distance] of bounds) {
    if (Math.abs(direction) <= 0.0000001) {
      if (distance < -0.0000001) return 0;
      continue;
    }
    const ratio = distance / direction;
    if (direction < 0) enter = Math.max(enter, ratio);
    else leave = Math.min(leave, ratio);
    if (enter > leave + 0.0000001) return 0;
  }
  return length * Math.max(0, leave - enter);
}

const ROUTE_INDEX_CELL_SIZE = 128;
const ROUTE_INDEX_MAX_CELLS_PER_ROUTE = 256;

function routeBounds(route) {
  let x1 = Infinity;
  let y1 = Infinity;
  let x2 = -Infinity;
  let y2 = -Infinity;
  for (const [x, y] of route.points) {
    x1 = Math.min(x1, x);
    y1 = Math.min(y1, y);
    x2 = Math.max(x2, x);
    y2 = Math.max(y2, y);
  }
  return { x1, y1, x2, y2 };
}

function createRouteCandidateIndex(routes) {
  const cells = new Map();
  const globalRouteIndexes = [];

  routes.forEach((route, routeIndex) => {
    const bounds = routeBounds(route);
    const x1 = Math.floor(bounds.x1 / ROUTE_INDEX_CELL_SIZE);
    const y1 = Math.floor(bounds.y1 / ROUTE_INDEX_CELL_SIZE);
    const x2 = Math.floor(bounds.x2 / ROUTE_INDEX_CELL_SIZE);
    const y2 = Math.floor(bounds.y2 / ROUTE_INDEX_CELL_SIZE);
    if (![x1, y1, x2, y2].every(Number.isSafeInteger)) {
      globalRouteIndexes.push(routeIndex);
      return;
    }
    const cellCount = (x2 - x1 + 1) * (y2 - y1 + 1);

    // Very long routes are cheaper to test once per label than to duplicate
    // across a large part of the index.
    if (!Number.isSafeInteger(cellCount) || cellCount > ROUTE_INDEX_MAX_CELLS_PER_ROUTE) {
      globalRouteIndexes.push(routeIndex);
      return;
    }
    for (let y = y1; y <= y2; y += 1) {
      for (let x = x1; x <= x2; x += 1) {
        const key = `${x}:${y}`;
        const bucket = cells.get(key);
        if (bucket) bucket.push(routeIndex);
        else cells.set(key, [routeIndex]);
      }
    }
  });

  return function candidates(rect, threshold) {
    const x1 = Math.floor((rect.x - threshold) / ROUTE_INDEX_CELL_SIZE);
    const y1 = Math.floor((rect.y - threshold) / ROUTE_INDEX_CELL_SIZE);
    const x2 = Math.floor((rect.x + rect.width + threshold) / ROUTE_INDEX_CELL_SIZE);
    const y2 = Math.floor((rect.y + rect.height + threshold) / ROUTE_INDEX_CELL_SIZE);
    const cellCount = (x2 - x1 + 1) * (y2 - y1 + 1);

    // A huge threshold offers no selectivity and can overflow cell iteration.
    if (![x1, y1, x2, y2].every(Number.isSafeInteger)
      || !Number.isSafeInteger(cellCount)
      || cellCount > Math.max(64, cells.size * 4)) return routes;

    const routeIndexes = new Set(globalRouteIndexes);
    for (let y = y1; y <= y2; y += 1) {
      for (let x = x1; x <= x2; x += 1) {
        for (const routeIndex of cells.get(`${x}:${y}`) || []) routeIndexes.add(routeIndex);
      }
    }
    return [...routeIndexes]
      .sort((left, right) => left - right)
      .map((routeIndex) => routes[routeIndex]);
  };
}

export function collectLabelRouteClearance({ labels, routedRelations, threshold }) {
  if (!Number.isFinite(threshold) || threshold < 0) return [];
  if (threshold === 0) return [];
  const routeCandidates = asArray(routedRelations).map((entry, fallbackIndex) => {
    const relation = entry?.relation || entry;
    const points = normalizeRoutePoints(entry?.points || relation?.routePoints);
    if (!relation || points.length < 2) return null;
    return {
      relation,
      relationIndex: Number.isInteger(entry?.relationIndex) ? entry.relationIndex : fallbackIndex,
      points,
    };
  }).filter(Boolean);
  const seenRoutes = new Set();
  const routes = routeCandidates.filter((route) => {
    const identity = relationshipIdentity(route.relation, route.relationIndex);
    if (seenRoutes.has(identity)) return false;
    seenRoutes.add(identity);
    return true;
  });
  const hits = [];
  const seenLabels = new Set();
  const candidateRoutes = createRouteCandidateIndex(routes);

  for (const [fallbackIndex, label] of asArray(labels).entries()) {
    const rect = label?.rect || label;
    if (!rect || !isFinitePoint(rect.x, rect.y, rect.width, rect.height) || rect.width < 0 || rect.height < 0) continue;
    const relationIndex = Number.isInteger(label?.relationIndex) ? label.relationIndex : fallbackIndex;
    const labelIdentity = relationshipIdentity(label?.relation, relationIndex);
    if (seenLabels.has(labelIdentity)) continue;
    seenLabels.add(labelIdentity);
    for (const route of candidateRoutes(rect, threshold)) {
      if (relationIndex === route.relationIndex || sameRelationship(label?.relation, route.relation)) continue;
      let nearest = null;
      for (let segmentIndex = 0; segmentIndex < route.points.length - 1; segmentIndex += 1) {
        const start = route.points[segmentIndex];
        const end = route.points[segmentIndex + 1];
        const clearance = segmentRectClearance({ start, end }, rect);
        if (clearance == null) continue;
        if (!nearest || clearance < nearest.clearance) {
          nearest = {
            clearance,
            intersectionLength: segmentRectIntersectionLength({ start, end }, rect),
            segmentIndex,
            start,
            end,
          };
        }
      }
      if (!nearest || nearest.clearance + 0.0001 >= threshold) continue;
      hits.push({
        label,
        labelRelation: label?.relation,
        labelRelationIndex: relationIndex,
        otherRelation: route.relation,
        otherRelationIndex: route.relationIndex,
        rect,
        ...nearest,
        threshold,
      });
    }
  }
  return hits;
}

export function minimumLabelRouteClearance(measurements) {
  if (!asArray(measurements).length) return null;
  const minimum = measurements.reduce(
    (value, hit) => Math.min(value, hit.clearance),
    Infinity,
  );
  return Math.round(minimum * 10) / 10;
}

function relationshipIdentity(relation, relationIndex) {
  if (relation?.key !== undefined) return `key:${relation.key}`;
  if (relation?.id) return `id:${relation.from || ''}\u0000${relation.to || ''}\u0000${relation.id}`;
  return `index:${relationIndex}`;
}

function sameRelationship(left, right) {
  if (!left || !right) return false;
  if (left === right) return true;
  if (left.key !== undefined && right.key !== undefined) return left.key === right.key;
  return Boolean(left.id && right.id && left.id === right.id && left.from === right.from && left.to === right.to);
}

function relationshipSubject(diagramType, relationCollection, relationIndex, relation) {
  return {
    diagramType,
    collection: relationCollection,
    index: relationIndex,
    ...(relation?.id ? { id: relation.id } : {}),
    ...(relation?.from ? { from: relation.from } : {}),
    ...(relation?.to ? { to: relation.to } : {}),
  };
}

const AUTHORED_PLAN_KEYS = ['route', 'via', 'channelX', 'channelY', 'fromSide', 'toSide', 'bias', 'labelAt', 'labelDx', 'labelDy', 'labelSegment'];

// Re-planning advice only applies when the failing relation actually carries
// authored controls; telling an author to remove controls that do not exist
// just sends them hunting for a field that was never written.
function rePlanHint(relations, fallback) {
  const controls = new Set();
  for (const relation of asArray(relations)) {
    for (const key of AUTHORED_PLAN_KEYS) if (relation?.[key] !== undefined) controls.add(key);
  }
  if (!controls.size) return fallback;
  return `if the authored ${[...controls].join('/')} are not required by the user, remove them so the renderer can re-plan; otherwise preserve that intent and ${fallback}`;
}

const ENDPOINT_SIDE_RULES = {
  left: {
    axis: 'horizontal',
    sourceSign: -1,
    targetSign: 1,
    sourceDirection: 'leftward',
    targetDirection: 'rightward from the left',
  },
  right: {
    axis: 'horizontal',
    sourceSign: 1,
    targetSign: -1,
    sourceDirection: 'rightward',
    targetDirection: 'leftward from the right',
  },
  top: {
    axis: 'vertical',
    sourceSign: -1,
    targetSign: 1,
    sourceDirection: 'upward',
    targetDirection: 'downward from above',
  },
  bottom: {
    axis: 'vertical',
    sourceSign: 1,
    targetSign: -1,
    sourceDirection: 'downward',
    targetDirection: 'upward from below',
  },
};

function endpointSideIssue(points, endpoint, side) {
  const rule = ENDPOINT_SIDE_RULES[side];
  if (!rule) return null;
  const normalized = normalizeRoutePoints(points);
  if (normalized.length < 2) return null;
  const segmentIndex = endpoint === 'source' ? 0 : normalized.length - 2;
  const start = normalized[segmentIndex];
  const end = normalized[segmentIndex + 1];
  const dx = end[0] - start[0];
  const dy = end[1] - start[1];
  const along = rule.axis === 'horizontal' ? dx : dy;
  const across = rule.axis === 'horizontal' ? dy : dx;
  const expectedSign = endpoint === 'source' ? rule.sourceSign : rule.targetSign;
  if (Math.abs(across) <= 0.0001 && along * expectedSign > 0.0001) return null;
  return {
    endpoint,
    side,
    segmentIndex,
    start,
    end,
    expectedAxis: rule.axis,
    expectedDirection: endpoint === 'source' ? rule.sourceDirection : rule.targetDirection,
  };
}

// A side is a direction contract, not just a point on a box border. This pure
// predicate lets automatic routers prefer a dogleg whose first and final
// segments leave/enter the chosen sides perpendicularly.
export function routeHonorsEndpointSides(points, fromSide, toSide) {
  return !endpointSideIssue(points, 'source', fromSide)
    && !endpointSideIssue(points, 'target', toSide);
}
// Explicit fromSide/toSide are authored geometry, so a tangent or backwards
// endpoint segment changes their meaning. Fail this universally instead of
// leaving a malformed arrow for visual review to discover. Named routes and
// authored via points already carry their own geometry semantics: when they
// omit endpoint sides, do not invent a relative-position side and then reject
// the route for disagreeing with that invention. Pure automatic routes may
// still be checked against renderer-inferred sides.
export function cleanEndpointSideProblems({
  relations,
  endpointIds,
  pathFor,
  diagramType,
  relationCollection,
  fromSideFor,
  toSideFor,
  shouldCheckRelation = () => true,
  routeHint = 'align the first/final via segment with fromSide/toSide, change the side, or remove explicit routing so auto can choose a perpendicular approach',
}) {
  const problems = [];
  for (const [relationIndex, relation] of asArray(relations).entries()) {
    if (!relation || !endpointIds?.has(relation.from) || !endpointIds?.has(relation.to)) continue;
    if (!shouldCheckRelation(relation, relationIndex)) continue;
    const points = pathFor(relation)?.points;
    if (!Array.isArray(points) || points.length < 2) continue;
    const authoredFromSide = relation.fromSide && relation.fromSide !== 'auto' ? relation.fromSide : null;
    const authoredToSide = relation.toSide && relation.toSide !== 'auto' ? relation.toSide : null;
    const hasAuthoredRouteGeometry = Boolean(
      (relation.route && relation.route !== 'auto') || Array.isArray(relation.via),
    );
    const inferredFromSide = !hasAuthoredRouteGeometry && typeof fromSideFor === 'function'
      ? fromSideFor(relation)
      : null;
    const inferredToSide = !hasAuthoredRouteGeometry && typeof toSideFor === 'function'
      ? toSideFor(relation)
      : null;
    const fromSide = authoredFromSide ?? inferredFromSide;
    const toSide = authoredToSide ?? inferredToSide;
    const checks = [
      fromSide
        ? { ...endpointSideIssue(points, 'source', fromSide), sideOrigin: authoredFromSide ? 'authored' : 'inferred' }
        : null,
      toSide
        ? { ...endpointSideIssue(points, 'target', toSide), sideOrigin: authoredToSide ? 'authored' : 'inferred' }
        : null,
    ].filter((issue) => issue?.endpoint);
    for (const issue of checks) {
      const relationId = relation.id ? ` id "${relation.id}"` : '';
      const authoredField = issue.endpoint === 'source' ? 'fromSide' : 'toSide';
      const sideField = issue.sideOrigin === 'inferred' ? `inferred ${authoredField}` : authoredField;
      const segmentRole = issue.endpoint === 'source' ? 'first' : 'final';
      const from = issue.start.map((value) => Math.round(value * 10) / 10).join(', ');
      const to = issue.end.map((value) => Math.round(value * 10) / 10).join(', ');
      const message = `[clean-flow/endpoint-side-direction] ${diagramType} ${relationCollection}[${relationIndex}]${relationId} "${relation.from}" -> "${relation.to}" ${segmentRole} segment ${issue.segmentIndex} [${from}] -> [${to}] does not honor ${sideField} "${issue.side}" — it must run ${issue.expectedAxis} ${issue.expectedDirection}; ${routeHint}.`;
      recordDiagnostic({
        code: 'clean-flow/endpoint-side-direction',
        severity: 'error',
        message,
        subject: relationshipSubject(diagramType, relationCollection, relationIndex, relation),
        evidence: {
          endpoint: issue.endpoint,
          authoredField,
          sideOrigin: issue.sideOrigin,
          side: issue.side,
          segmentIndex: issue.segmentIndex,
          from: issue.start,
          to: issue.end,
          expectedAxis: issue.expectedAxis,
          expectedDirection: issue.expectedDirection,
        },
        supportedFixes: [routeHint],
      });
      problems.push(message);
    }
  }
  return problems;
}

// One mechanical quality gate for every renderer-owned relationship path.
// A renderer supplies its semantic obstacle set; source/target boxes are
// always exempt because paths are expected to terminate on their boundaries.
// Containers, lifelines, and other intentionally pass-through geometry should
// simply not be supplied as obstacles.
export function cleanFlowProblems({
  relations,
  obstacles,
  pathFor,
  diagramType,
  relationCollection,
  obstacleKind,
  clearance = 2,
  routeHint = 'adjust fromSide/toSide, set route/via or channel coordinates, or move the obstacle'
}) {
  // A relationship hidden behind an unrelated opaque node changes the
  // diagram's meaning, so this is a correctness invariant rather than an
  // opt-in composition preference. Keep it active even when the author omits
  // quality_profile; standard/showcase still control stricter visual budgets.
  const problems = [];
  const obstacleList = [...obstacles];
  const obstacleIds = new Set(obstacleList.map((obstacle) => obstacle?.id));
  for (const [relationIndex, relation] of asArray(relations).entries()) {
    if (!relation || typeof relation.from !== 'string' || typeof relation.to !== 'string') continue;
    if (!obstacleIds.has(relation.from) || !obstacleIds.has(relation.to)) continue;
    const points = pathFor(relation)?.points;
    if (!Array.isArray(points) || points.length < 2) continue;
    if (!points.every((point) => Array.isArray(point) && point.length === 2 && isFinitePoint(...point))) continue;

    const endpointIds = new Set([relation.from, relation.to]);
    for (const obstacle of obstacleList) {
      if (!obstacle || endpointIds.has(obstacle.id)) continue;
      if (!isFinitePoint(obstacle.x, obstacle.y, obstacle.width, obstacle.height)) continue;
      let hitSegment = -1;
      for (let segmentIndex = 0; segmentIndex < points.length - 1; segmentIndex += 1) {
        if (segmentIntersectsRect({ start: points[segmentIndex], end: points[segmentIndex + 1] }, obstacle, clearance)) {
          hitSegment = segmentIndex;
          break;
        }
      }
      if (hitSegment === -1) continue;
      const from = points[hitSegment].map(Math.round).join(', ');
      const to = points[hitSegment + 1].map(Math.round).join(', ');
      const relationId = relation.id ? ` id "${relation.id}"` : '';
      const hint = rePlanHint([relation], routeHint);
      const message = `[clean-flow/edge-through-node] ${diagramType} ${relationCollection}[${relationIndex}]${relationId} "${relation.from}" -> "${relation.to}" crosses ${obstacleKind} "${obstacle.id}" (unrelated to this relationship) on segment ${hitSegment} [${from}] -> [${to}] (${clearance}px clearance) — ${hint}.`;
      recordDiagnostic({
        code: 'clean-flow/edge-through-node',
        severity: 'error',
        message,
        subject: relationshipSubject(diagramType, relationCollection, relationIndex, relation),
        evidence: {
          obstacleKind,
          obstacleId: obstacle.id,
          segmentIndex: hitSegment,
          from: points[hitSegment],
          to: points[hitSegment + 1],
          clearancePx: clearance,
        },
        supportedFixes: [hint],
      });
      problems.push(message);
    }
  }
  return problems;
}

// Build a read-only analysis copy of a polyline with straight-through
// waypoints removed. A waypoint on a forward-collinear run is not a visual
// endpoint, so treating it as one would hide a proper X that lands exactly on
// that waypoint. Reversals and real bends stay split: their shared point can
// still be an authored touch rather than a crossing. The source points are
// retained on every merged segment so diagnostics can name the authored
// segment that contains a hit without changing rendered/receipt geometry.
export function forwardCollinearAnalysisSegments(points) {
  const segments = [];
  for (let segmentIndex = 0; segmentIndex < asArray(points).length - 1; segmentIndex += 1) {
    const authoredStart = points[segmentIndex];
    const authoredEnd = points[segmentIndex + 1];
    const start = Array.isArray(authoredStart) ? [...authoredStart] : authoredStart;
    const end = Array.isArray(authoredEnd) ? [...authoredEnd] : authoredEnd;
    const sourceSegment = { start, end, segmentIndex };
    const previous = segments.at(-1);
    if (previous && segmentsContinueForward(previous.start, previous.end, start, end)) {
      previous.end = end;
      previous.sourceSegments.push(sourceSegment);
      continue;
    }
    segments.push({
      start,
      end,
      segmentIndex,
      sourceSegments: [sourceSegment],
    });
  }
  return segments;
}

export function sourceSegmentIndexAtPoint(segment, point) {
  const source = asArray(segment?.sourceSegments).find(({ start, end }) => (
    pointLiesOnSegment(point, start, end)
  ));
  return source?.segmentIndex ?? segment?.segmentIndex ?? 0;
}

function authoredAnalysisSegments(points) {
  return asArray(points).slice(0, -1).map((start, segmentIndex) => ({
    start,
    end: points[segmentIndex + 1],
    segmentIndex,
    sourceSegments: [{ start, end: points[segmentIndex + 1], segmentIndex }],
  }));
}

function segmentsContinueForward(firstStart, firstEnd, secondStart, secondEnd) {
  if (![firstStart, firstEnd, secondStart, secondEnd].every((point) => (
    Array.isArray(point) && point.length === 2 && isFinitePoint(...point)
  ))) return false;
  const epsilon = 0.0001;
  if (Math.abs(firstEnd[0] - secondStart[0]) > epsilon
    || Math.abs(firstEnd[1] - secondStart[1]) > epsilon) return false;
  const firstVector = [firstEnd[0] - firstStart[0], firstEnd[1] - firstStart[1]];
  const secondVector = [secondEnd[0] - secondStart[0], secondEnd[1] - secondStart[1]];
  const firstLength = Math.hypot(...firstVector);
  const secondLength = Math.hypot(...secondVector);
  if (firstLength <= epsilon || secondLength <= epsilon) return false;
  const cross = firstVector[0] * secondVector[1] - firstVector[1] * secondVector[0];
  if (Math.abs(cross) > epsilon) return false;
  const dot = firstVector[0] * secondVector[0] + firstVector[1] * secondVector[1];
  return dot > epsilon;
}

function pointLiesOnSegment(point, start, end) {
  if (![point, start, end].every((candidate) => (
    Array.isArray(candidate) && candidate.length === 2 && isFinitePoint(...candidate)
  ))) return false;
  const epsilon = 0.0001;
  const length = Math.hypot(end[0] - start[0], end[1] - start[1]);
  if (length <= epsilon) return Math.hypot(point[0] - start[0], point[1] - start[1]) <= epsilon;
  if (Math.abs(crossProduct(start, end, point)) > epsilon * length) return false;
  return point[0] >= Math.min(start[0], end[0]) - epsilon
    && point[0] <= Math.max(start[0], end[0]) + epsilon
    && point[1] >= Math.min(start[1], end[1]) - epsilon
    && point[1] <= Math.max(start[1], end[1]) + epsilon;
}

// Authored shared endpoints retain their junction interpretation by default.
// Renderers can opt their automatic routes into proper interior X checks;
// endpoint touches and collinear trunks still are not proper crossings.
export function cleanCrossingProblems({
  relations,
  endpointIds,
  pathFor,
  diagramType,
  relationCollection,
  profile = 'standard',
  profileIsAuthoritative = false,
  mergeForwardCollinearWaypoints = false,
  includeSharedEndpoints = () => false,
  crossingResolved = () => false,
  warnInStandard = false,
  onDiagnostic = recordDiagnostic,
  routeHint = 'adjust route/via or channel coordinates so the relationships use separate corridors'
}) {
  const severity = qualityProfileForGate(profile, profileIsAuthoritative) === 'showcase' ? 'error' : 'warning';
  if (severity === 'warning' && !warnInStandard) return [];
  const routed = asArray(relations).map((relation, index) => {
    if (!relation || !endpointIds.has(relation.from) || !endpointIds.has(relation.to)) return null;
    const points = pathFor(relation)?.points;
    if (!Array.isArray(points) || points.length < 2) return null;
    if (!points.every((point) => Array.isArray(point) && point.length === 2 && isFinitePoint(...point))) return null;
    return {
      relation,
      index,
      points,
      analysisSegments: mergeForwardCollinearWaypoints
        ? forwardCollinearAnalysisSegments(points)
        : authoredAnalysisSegments(points),
    };
  }).filter(Boolean);
  const problems = [];

  for (let leftIndex = 0; leftIndex < routed.length; leftIndex += 1) {
    const left = routed[leftIndex];
    for (let rightIndex = leftIndex + 1; rightIndex < routed.length; rightIndex += 1) {
      const right = routed[rightIndex];
      if ([left.relation.from, left.relation.to].some((id) => id === right.relation.from || id === right.relation.to)
          && !includeSharedEndpoints(left.relation, right.relation)) continue;

      let hit = null;
      for (const leftSegment of left.analysisSegments) {
        if (hit) break;
        for (const rightSegment of right.analysisSegments) {
          const point = properSegmentIntersection(
            leftSegment.start,
            leftSegment.end,
            rightSegment.start,
            rightSegment.end
          );
          if (point) {
            hit = {
              point,
              leftSegment: sourceSegmentIndexAtPoint(leftSegment, point),
              rightSegment: sourceSegmentIndexAtPoint(rightSegment, point),
            };
            break;
          }
        }
      }
      if (!hit) continue;
      if (crossingResolved(left.relation, right.relation, hit)) continue;

      const describe = ({ relation, index }) => {
        const id = relation.id ? ` id "${relation.id}"` : '';
        return `${relationCollection}[${index}]${id} "${relation.from}" -> "${relation.to}"`;
      };
      const point = hit.point.map((value) => Math.round(value * 10) / 10).join(', ');
      const hint = rePlanHint([left.relation, right.relation], routeHint);
      const message = `[composition/proper-crossing] ${severity === 'error' ? 'showcase' : 'standard'} ${diagramType} ${describe(left)} crosses ${describe(right)} at [${point}] (segments ${hit.leftSegment} and ${hit.rightSegment}) — ${hint}.`;
      onDiagnostic({
        code: 'composition/proper-crossing',
        severity,
        message,
        subject: relationshipSubject(diagramType, relationCollection, left.index, left.relation),
        evidence: {
          otherRelationship: relationshipSubject(diagramType, relationCollection, right.index, right.relation),
          point: hit.point,
          segmentIndex: hit.leftSegment,
          otherSegmentIndex: hit.rightSegment,
        },
        supportedFixes: [hint],
      });
      if (severity === 'error') problems.push(message);
    }
  }
  return problems;
}

// Two unrelated relationships that occupy the same visible corridor can read
// as one authored branch or merge even when neither relationship crosses a
// node or forms a proper X. Keep authored shared endpoints exempt by default;
// automatic architecture routes opt in because they promise separate ports.
// Workflow v2 opts into shared-endpoint checks with a bounded terminal-trunk
// exception. Other callers keep their existing authored-junction contract.
// The counterflow-only opt-in serves older workflow exports without a root
// readable-v2 contract; full shared-endpoint checking takes precedence.
// Tiny overlaps below the route rhythm
// floor are ignored to avoid turning sub-pixel rounding into a quality debt.
export function collectAmbiguousCorridors({
  routedRelations,
  minOverlapPx = 8,
  includeSharedEndpoints = () => false,
  includeSharedEndpointCounterflow = () => false,
  allowShortWorkflowTrunks = false,
}) {
  const routed = asArray(routedRelations).map((entry, fallbackIndex) => {
    const relation = entry?.relation;
    if (!relation || typeof relation.from !== 'string' || typeof relation.to !== 'string') return null;
    const points = normalizeRoutePoints(entry?.points);
    if (points.length < 2) return null;
    return {
      relation,
      relationIndex: Number.isInteger(entry.relationIndex) ? entry.relationIndex : fallbackIndex,
      points,
    };
  }).filter(Boolean);
  const hits = [];

  for (let leftIndex = 0; leftIndex < routed.length; leftIndex += 1) {
    const left = routed[leftIndex];
    for (let rightIndex = leftIndex + 1; rightIndex < routed.length; rightIndex += 1) {
      const right = routed[rightIndex];
      const sharedEndpoint = [left.relation.from, left.relation.to].some((id) => id === right.relation.from || id === right.relation.to);
      const counterflowOnly = sharedEndpoint && !includeSharedEndpoints(left.relation, right.relation);
      if (counterflowOnly && !includeSharedEndpointCounterflow(left.relation, right.relation)) continue;

      let longest = null;
      for (let leftSegment = 0; leftSegment < left.points.length - 1; leftSegment += 1) {
        for (let rightSegment = 0; rightSegment < right.points.length - 1; rightSegment += 1) {
          const overlap = collinearAxisOverlap(
            left.points[leftSegment],
            left.points[leftSegment + 1],
            right.points[rightSegment],
            right.points[rightSegment + 1],
          );
          if (!overlap || overlap.length + 0.0001 < minOverlapPx) continue;
          if (allowShortWorkflowTrunks && shortWorkflowTrunk(left, right, leftSegment, rightSegment, overlap.length)) continue;
          if (counterflowOnly) {
            const leftDelta = left.points[leftSegment + 1].map((value, axis) => value - left.points[leftSegment][axis]);
            const rightDelta = right.points[rightSegment + 1].map((value, axis) => value - right.points[rightSegment][axis]);
            if (leftDelta[0] * rightDelta[0] + leftDelta[1] * rightDelta[1] >= 0) continue;
          }
          if (!longest || overlap.length > longest.overlapLength + 0.0001) {
            longest = {
              left,
              right,
              leftSegment,
              rightSegment,
              overlapLength: overlap.length,
              overlapStart: overlap.start,
              overlapEnd: overlap.end,
            };
          }
        }
      }
      if (longest) hits.push(longest);
    }
  }
  return hits;
}

function shortWorkflowTrunk(left, right, leftSegment, rightSegment, length) {
  if (length > 24 + 0.0001) return false;
  const a = left.relation, b = right.relation;
  const variant = (edge) => edge.variant || 'default';
  const width = (edge) => edge.width || (variant(edge) === 'emphasis' ? 1.8 : 1.4);
  if (variant(a) !== variant(b) || width(a) !== width(b) || (a.role || '') !== (b.role || '')) return false;
  const same = (p, q) => Math.abs(p[0] - q[0]) < 0.0001 && Math.abs(p[1] - q[1]) < 0.0001;
  const source = a.from === b.from && leftSegment === 0 && rightSegment === 0
    && same(left.points[0], right.points[0]);
  const target = a.to === b.to && leftSegment === left.points.length - 2 && rightSegment === right.points.length - 2
    && same(left.points.at(-1), right.points.at(-1));
  if (!source && !target) return false;
  const p = left.points[leftSegment], q = left.points[leftSegment + 1];
  const r = right.points[rightSegment], s = right.points[rightSegment + 1];
  return (q[0] - p[0]) * (s[0] - r[0]) + (q[1] - p[1]) * (s[1] - r[1]) > 0;
}

// Bundled arrow markers are 7 stroke-widths across the direction of travel.
// Callers select the automatic routes they own; explicit junctions are preserved.
export function collectArrowheadCollisions({ routedRelations, allowShortWorkflowTrunks = false }) {
  const incoming = new Map();
  const hits = [];
  for (const entry of asArray(routedRelations)) {
    const points = normalizeRoutePoints(entry.points);
    if (points.length < 2 || !entry.relation?.to) continue;
    const tip = points.at(-1);
    const previous = points.at(-2);
    const vertical = Math.abs(tip[0] - previous[0]) < 0.0001;
    const axis = vertical ? 0 : 1;
    const direction = Math.sign(tip[1 - axis] - previous[1 - axis]);
    const halfWidth = 3.5 * (entry.relation.width || (entry.relation.variant === 'emphasis' ? 1.8 : 1.5));
    const key = `${entry.relation.to}\u0000${axis}\u0000${direction}`;
    const siblings = incoming.get(key) || [];
    const current = { ...entry, tip, halfWidth };
    for (const sibling of siblings) {
      if (Math.abs(tip[1 - axis] - sibling.tip[1 - axis]) > 0.0001) continue;
      const distance = Math.abs(tip[axis] - sibling.tip[axis]);
      const minimum = halfWidth + sibling.halfWidth;
      if (allowShortWorkflowTrunks) {
        const left = { ...sibling, points: normalizeRoutePoints(sibling.points) };
        const right = { ...entry, points };
        const overlap = collinearAxisOverlap(left.points.at(-2), left.points.at(-1), points.at(-2), tip);
        if (overlap && shortWorkflowTrunk(left, right, left.points.length - 2, points.length - 2, overlap.length)) continue;
      }
      if (distance < minimum - 0.0001) hits.push({ left: sibling, right: current, distance, minimum });
    }
    siblings.push(current);
    incoming.set(key, siblings);
  }
  return hits;
}

export function cleanAmbiguousCorridorProblems({
  relations,
  endpointIds,
  pathFor,
  diagramType,
  relationCollection,
  profile = 'standard',
  profileIsAuthoritative = false,
  routeHint = 'adjust route/via or channel coordinates so the relationships use separate corridors',
  minOverlapPx = 8,
  includeSharedEndpoints = () => false,
  includeSharedEndpointCounterflow = () => false,
  allowShortWorkflowTrunks = false,
  onDiagnostic = recordDiagnostic,
}) {
  const severity = qualityProfileForGate(profile, profileIsAuthoritative) === 'showcase' ? 'error' : 'warning';
  if (severity === 'warning' && !allowShortWorkflowTrunks) return [];
  const routedRelations = collectEligibleRoutedRelations({ relations, endpointIds, pathFor });

  return collectAmbiguousCorridors({ routedRelations, minOverlapPx, includeSharedEndpoints, includeSharedEndpointCounterflow, allowShortWorkflowTrunks }).map((hit) => {
    const describe = ({ relation, relationIndex }) => {
      const id = relation.id ? ` id "${relation.id}"` : '';
      return `${relationCollection}[${relationIndex}]${id} "${relation.from}" -> "${relation.to}"`;
    };
    const length = Math.round(hit.overlapLength * 10) / 10;
    const from = hit.overlapStart.map((value) => Math.round(value * 10) / 10).join(', ');
    const to = hit.overlapEnd.map((value) => Math.round(value * 10) / 10).join(', ');
    const hint = rePlanHint([hit.left.relation, hit.right.relation], routeHint);
    const message = `[composition/ambiguous-corridor] ${severity === 'error' ? 'showcase' : 'standard'} ${diagramType} ${describe(hit.left)} shares a ${length}px corridor with ${describe(hit.right)} at [${from}] -> [${to}] (segments ${hit.leftSegment} and ${hit.rightSegment}; minimum ${minOverlapPx}px) — ${hint}.`;
    onDiagnostic({
      code: 'composition/ambiguous-corridor',
      severity,
      message,
      subject: relationshipSubject(diagramType, relationCollection, hit.left.relationIndex, hit.left.relation),
      evidence: {
        otherRelationship: relationshipSubject(diagramType, relationCollection, hit.right.relationIndex, hit.right.relation),
        overlapLengthPx: length,
        minimumPx: minOverlapPx,
        from: hit.overlapStart,
        to: hit.overlapEnd,
        segmentIndex: hit.leftSegment,
        otherSegmentIndex: hit.rightSegment,
      },
      supportedFixes: [hint],
    });
    return severity === 'error' ? message : null;
  }).filter(Boolean);
}

// Relationship paths may cross a structural frame, but they must not borrow a
// frame side as a routing corridor. Rounded rectangle corners are trimmed from
// the modeled straight sides so a short corner touch is not mistaken for a
// border run. Any positive straight overlap beyond the numeric epsilon is a
// hard failure in every quality profile; 16px belongs only to the separate,
// neutral short-segment metric and is not a corridor exemption.
export function collectBorderRuns({ routedRelations, frames }) {
  const hits = [];
  for (const routed of asArray(routedRelations)) {
    const routeSegments = Array.isArray(routed?.segments)
      ? routed.segments
      : asArray(routed?.points).slice(0, -1).map((start, index) => ({ start, end: routed.points[index + 1] }));
    if (!routeSegments.length) continue;
    if (!routeSegments.every((segment) => (
      Array.isArray(segment?.start) && segment.start.length === 2 && isFinitePoint(...segment.start)
      && Array.isArray(segment?.end) && segment.end.length === 2 && isFinitePoint(...segment.end)
    ))) continue;
    for (const [frameIndex, frame] of asArray(frames).entries()) {
      for (const border of frameBorderSegments(frame)) {
        const overlaps = [];
        for (let segmentIndex = 0; segmentIndex < routeSegments.length; segmentIndex += 1) {
          const segment = routeSegments[segmentIndex];
          const overlap = collinearAxisOverlap(
            segment.start,
            segment.end,
            border.start,
            border.end,
          );
          if (!overlap || overlap.length <= 0.0001) continue;
          overlaps.push({ ...overlap, segmentIndex });
        }
        if (!overlaps.length) continue;
        const merged = mergeBorderOverlaps(overlaps, border);
        const longest = [...merged].sort((left, right) => right.length - left.length || left.low - right.low)[0];
        hits.push({
          ...routed,
          frame,
          frameIndex,
          side: border.side,
          segmentIndex: overlaps.reduce((min, overlap) => Math.min(min, overlap.segmentIndex), Infinity),
          overlapLength: merged.reduce((total, overlap) => total + overlap.length, 0),
          overlapStart: longest.start,
          overlapEnd: longest.end,
        });
      }
    }
  }
  return hits;
}

export function cleanBorderRunProblems({
  relations,
  endpointIds,
  frames,
  pathFor,
  diagramType,
  relationCollection,
  profile,
  profileIsAuthoritative = false,
  routeHint = 'adjust route/via or channel coordinates so the relationship crosses the frame perpendicularly through a clear opening'
}) {
  if (!qualityProfileForGate(profile, profileIsAuthoritative)) return [];
  const routedRelations = collectEligibleRoutedRelations({ relations, endpointIds, pathFor });
  return collectBorderRuns({ routedRelations, frames }).map((hit) => {
    const relation = hit.relation || {};
    const relationId = relation.id ? ` id "${relation.id}"` : '';
    const frameKind = hit.frame?.kind || hit.frame?.shape || 'frame';
    const frameIdentity = hit.frame?.label || hit.frame?.id || hit.frameIndex;
    const length = Math.round(hit.overlapLength * 10) / 10;
    const from = hit.overlapStart.map((value) => Math.round(value * 10) / 10).join(', ');
    const to = hit.overlapEnd.map((value) => Math.round(value * 10) / 10).join(', ');
    const hint = rePlanHint([relation], routeHint);
    const message = `[composition/container-border-run] ${diagramType} ${relationCollection}[${hit.relationIndex}]${relationId} "${relation.from}" -> "${relation.to}" follows ${frameKind} "${frameIdentity}" ${hit.side} border for ${length}px on segment ${hit.segmentIndex} [${from}] -> [${to}] — ${hint}.`;
    recordDiagnostic({
      code: 'composition/container-border-run',
      severity: 'error',
      message,
      subject: relationshipSubject(diagramType, relationCollection, hit.relationIndex, relation),
      evidence: {
        frameKind,
        frameId: hit.frame?.id,
        frameLabel: hit.frame?.label,
        side: hit.side,
        segmentIndex: hit.segmentIndex,
        overlapLengthPx: length,
        from: hit.overlapStart,
        to: hit.overlapEnd,
      },
      supportedFixes: [hint],
    });
    return message;
  });
}

export function routeBudgetMetrics({
  routedRelations,
  bendsPerRelationship = 2,
  stretch = 1.35,
  segmentPx = 16,
  microSegmentPx = 8,
}) {
  let maxBends = 0;
  let routesOverSuggestedBends = 0;
  let maxStretch = null;
  let routesOverSuggestedStretch = 0;
  let minSegmentPx = null;
  let minInteriorSegmentPx = null;
  let shortSegmentCount = 0;
  let shortEndpointSegmentCount = 0;
  let shortInteriorSegmentCount = 0;
  let microSegmentCount = 0;

  for (const routed of asArray(routedRelations)) {
    const points = normalizeRoutePoints(routed?.points);
    if (points.length < 2) continue;
    const bends = Math.max(0, points.length - 2);
    maxBends = Math.max(maxBends, bends);
    if (bends > bendsPerRelationship) routesOverSuggestedBends += 1;

    let routeLength = 0;
    for (let index = 0; index < points.length - 1; index += 1) {
      const length = Math.abs(points[index + 1][0] - points[index][0]) + Math.abs(points[index + 1][1] - points[index][1]);
      if (length <= 0.0001) continue;
      const position = segmentPosition(index, points.length - 1);
      routeLength += length;
      minSegmentPx = minSegmentPx == null ? length : Math.min(minSegmentPx, length);
      if (position === 'interior') {
        minInteriorSegmentPx = minInteriorSegmentPx == null ? length : Math.min(minInteriorSegmentPx, length);
      }
      if (length < segmentPx) {
        shortSegmentCount += 1;
        if (position === 'interior') shortInteriorSegmentCount += 1;
        else shortEndpointSegmentCount += 1;
      }
      if (length < microSegmentPx) microSegmentCount += 1;
    }
    const direct = Math.abs(points.at(-1)[0] - points[0][0]) + Math.abs(points.at(-1)[1] - points[0][1]);
    if (direct > 0.0001) {
      const routeStretch = routeLength / direct;
      maxStretch = maxStretch == null ? routeStretch : Math.max(maxStretch, routeStretch);
      if (routeStretch > stretch + 0.0001) routesOverSuggestedStretch += 1;
    }
  }

  return {
    maxBends,
    routesOverSuggestedBends,
    maxStretch,
    routesOverSuggestedStretch,
    minSegmentPx,
    minInteriorSegmentPx,
    shortSegmentCount,
    shortEndpointSegmentCount,
    shortInteriorSegmentCount,
    microSegmentCount,
  };
}

export function collectRouteRhythmIssues({
  routedRelations,
  interiorSegmentPx = 16,
  microSegmentPx = 8,
}) {
  const issues = [];
  for (const [fallbackIndex, routed] of asArray(routedRelations).entries()) {
    const points = normalizeRoutePoints(routed?.points);
    if (points.length < 2) continue;
    for (let segmentIndex = 0; segmentIndex < points.length - 1; segmentIndex += 1) {
      const start = points[segmentIndex];
      const end = points[segmentIndex + 1];
      const length = Math.abs(end[0] - start[0]) + Math.abs(end[1] - start[1]);
      if (length <= 0.0001) continue;
      const position = segmentPosition(segmentIndex, points.length - 1);
      const code = length < microSegmentPx - 0.0001
        ? 'composition/micro-segment'
        : position === 'interior' && length < interiorSegmentPx - 0.0001
          ? 'composition/short-interior-segment'
          : null;
      if (!code) continue;
      issues.push({
        code,
        relation: routed.relation,
        relationIndex: Number.isInteger(routed.relationIndex) ? routed.relationIndex : fallbackIndex,
        segmentIndex,
        position,
        length,
        start,
        end,
      });
    }
  }
  return issues;
}

export function cleanRouteRhythmProblems({
  relations,
  endpointIds,
  pathFor,
  diagramType,
  relationCollection,
  profile,
  profileIsAuthoritative = false,
  routeHint = 'move the channel/via point to remove the cramped turn or give the route more corridor space',
  interiorSegmentPx = 16,
  microSegmentPx = 8,
}) {
  if (qualityProfileForGate(profile, profileIsAuthoritative) !== 'showcase') return [];
  const routedRelations = collectEligibleRoutedRelations({ relations, endpointIds, pathFor });
  return collectRouteRhythmIssues({ routedRelations, interiorSegmentPx, microSegmentPx }).map((hit) => {
    const relation = hit.relation || {};
    const relationId = relation.id ? ` id "${relation.id}"` : '';
    const length = Math.round(hit.length * 10) / 10;
    const from = hit.start.map((value) => Math.round(value * 10) / 10).join(', ');
    const to = hit.end.map((value) => Math.round(value * 10) / 10).join(', ');
    const rule = hit.code === 'composition/micro-segment'
      ? `is below the ${microSegmentPx}px micro-segment floor`
      : `is below the ${interiorSegmentPx}px interior-segment floor`;
    const hint = rePlanHint([relation], routeHint);
    const message = `[${hit.code}] showcase ${diagramType} ${relationCollection}[${hit.relationIndex}]${relationId} "${relation.from}" -> "${relation.to}" has a ${length}px ${hit.position} segment ${hit.segmentIndex} [${from}] -> [${to}] that ${rule} — ${hint}.`;
    recordDiagnostic({
      code: hit.code,
      severity: 'error',
      message,
      subject: relationshipSubject(diagramType, relationCollection, hit.relationIndex, relation),
      evidence: {
        segmentIndex: hit.segmentIndex,
        position: hit.position,
        lengthPx: length,
        minimumPx: hit.code === 'composition/micro-segment' ? microSegmentPx : interiorSegmentPx,
        from: hit.start,
        to: hit.end,
      },
      supportedFixes: [hint],
    });
    return message;
  });
}

export function cleanLabelRouteClearanceProblems({
  relations,
  labels,
  endpointIds,
  pathFor,
  diagramType,
  relationCollection,
  profile,
  profileIsAuthoritative = false,
  threshold = 4,
  routeHint = 'adjust labelAt, labelDx, labelDy, or labelSegment; otherwise adjust the other relationship route/via/channel',
}) {
  if (qualityProfileForGate(profile, profileIsAuthoritative) !== 'showcase') return [];
  const routedRelations = collectEligibleRoutedRelations({ relations, endpointIds, pathFor });
  return collectLabelRouteClearance({ labels, routedRelations, threshold }).map((hit) => {
    const describe = (relation, relationIndex) => {
      const relationId = relation?.id ? ` id "${relation.id}"` : '';
      const relationLabel = relation?.label ? ` label "${relation.label}"` : '';
      return `${relationCollection}[${relationIndex}]${relationId} "${relation?.from}" -> "${relation?.to}"${relationLabel}`;
    };
    const clearance = Math.round(hit.clearance * 10) / 10;
    const from = hit.start.map((value) => Math.round(value * 10) / 10).join(', ');
    const to = hit.end.map((value) => Math.round(value * 10) / 10).join(', ');
    const hint = rePlanHint([hit.labelRelation, hit.otherRelation], routeHint);
    const message = `[composition/label-route-clearance] showcase ${diagramType} label "${hit.label?.label || hit.labelRelation?.label || ''}" on ${describe(hit.labelRelation, hit.labelRelationIndex)} is ${clearance}px from ${describe(hit.otherRelation, hit.otherRelationIndex)} segment ${hit.segmentIndex} [${from}] -> [${to}] (label rect ${formatRect(hit.rect)}; minimum ${threshold}px) — ${hint}.`;
    recordDiagnostic({
      code: 'composition/label-route-clearance',
      severity: 'error',
      message,
      subject: relationshipSubject(diagramType, relationCollection, hit.labelRelationIndex, hit.labelRelation),
      evidence: {
        label: hit.label?.label || hit.labelRelation?.label || '',
        otherRelationship: relationshipSubject(diagramType, relationCollection, hit.otherRelationIndex, hit.otherRelation),
        segmentIndex: hit.segmentIndex,
        clearancePx: clearance,
        minimumPx: threshold,
        labelRect: hit.rect,
        from: hit.start,
        to: hit.end,
      },
      supportedFixes: [hint],
    });
    return message;
  });
}

// How far [start, start + size) leaves [0, extent), per end of one axis. This
// is the single definition of "inside the canvas" that both the containment
// rule and the repair hints measure against; an unknown extent bounds nothing.
function axisCanvasOverflow(start, size, extent, origin = 0) {
  if (!Number.isFinite(extent)) return { start: 0, end: 0 };
  return { start: origin - start, end: start + size - (origin + extent) };
}

// THE CANVAS CONTAINMENT RATIONALE (referenced from the other call sites).
//
// The SVG canvas clips whatever leaves the viewBox, so an edge label that
// overhangs an edge ships as truncated text while every post-render check on
// the emitted markup still passes: clipped text is still well-formed markup.
// Renderers with a fixed canvas already bound their nodes, lanes, and legends
// against it; edge label rects were the exception.
//
// Not applied to readable-v2 workflows: that compiler grows its canvas around
// pinned label rects and rejects an authored viewBox that cannot hold the
// result, so the only gap growth cannot close is the origin its own rule
// already guards. Architecture's auto canvas grows the same way, which leaves
// this rule reporting authored viewBoxes and the origin side.
//
// Showcase only: a standard document authored before the rule exists may
// overhang by a few pixels, and failing it there would break compatibility
// instead of repairing a diagram.
export function collectLabelCanvasOverflow({ labels, viewBox, tolerance = 0.5 }) {
  // Renderers author origin-zero canvases (meta.viewBox is [width, height] by
  // schema), but `check` re-measures foreign artifacts whose SVG viewBox may
  // carry a legal non-zero min-x/min-y; those pass all four numbers.
  const box = asArray(viewBox);
  const [originX, originY, canvasWidth, canvasHeight] = box.length === 4 ? box : [0, 0, box[0], box[1]];
  if (!isFinitePoint(originX, originY, canvasWidth, canvasHeight)) return [];
  const hits = [];
  for (const [fallbackIndex, label] of asArray(labels).entries()) {
    const rect = label?.rect || label;
    if (!rect || !isFinitePoint(rect.x, rect.y, rect.width, rect.height)) continue;
    // `check` parses foreign markup, so a malformed negative-size rect is
    // skipped like the other label collectors do — its flipped interval would
    // otherwise read as contained.
    if (rect.width < 0 || rect.height < 0) continue;
    const horizontal = axisCanvasOverflow(rect.x, rect.width, canvasWidth, originX);
    const vertical = axisCanvasOverflow(rect.y, rect.height, canvasHeight, originY);
    const overflow = {
      left: horizontal.start,
      right: horizontal.end,
      top: vertical.start,
      bottom: vertical.end,
    };
    const sides = Object.keys(overflow).filter((side) => overflow[side] > tolerance);
    if (!sides.length) continue;
    hits.push({
      label,
      relation: label?.relation,
      relationIndex: Number.isInteger(label?.relationIndex) ? label.relationIndex : fallbackIndex,
      rect,
      viewBox: [canvasWidth, canvasHeight],
      viewBoxOrigin: [originX, originY],
      sides,
      overflowPx: Object.fromEntries(sides.map((side) => [side, Math.round(overflow[side] * 10) / 10])),
      tolerance,
    });
  }
  return hits;
}

export function describeLabelCanvasOverflow(hit) {
  return hit.sides.map((side) => `${side} edge by ${hit.overflowPx[side]}px`).join(' and ');
}

export function cleanLabelCanvasContainmentProblems({
  labels,
  viewBox,
  diagramType,
  relationCollection,
  profile,
  profileIsAuthoritative = false,
  routeHint = 'adjust labelAt, labelDx, labelDy, or labelSegment; otherwise enlarge meta.viewBox',
  // Label widths are estimated from the text, not measured, so sub-pixel
  // overhang is rounding noise rather than a visible truncation.
  tolerance = 0.5,
}) {
  if (qualityProfileForGate(profile, profileIsAuthoritative) !== 'showcase') return [];
  return collectLabelCanvasOverflow({ labels, viewBox, tolerance }).map((hit) => {
    const relation = hit.relation;
    const relationId = relation?.id ? ` id "${relation.id}"` : '';
    const labelText = hit.label?.label || relation?.label || '';
    const hint = rePlanHint([relation], routeHint);
    const message = `[composition/label-canvas-containment] showcase ${diagramType} label "${labelText}" on ${relationCollection}[${hit.relationIndex}]${relationId} "${relation?.from}" -> "${relation?.to}" extends past the ${describeLabelCanvasOverflow(hit)} (label rect ${formatRect(hit.rect)}; viewBox ${hit.viewBox[0]}x${hit.viewBox[1]}) — ${hint}.`;
    recordDiagnostic({
      code: 'composition/label-canvas-containment',
      severity: 'error',
      message,
      subject: relationshipSubject(diagramType, relationCollection, hit.relationIndex, relation),
      evidence: {
        label: labelText,
        labelRect: { x: hit.rect.x, y: hit.rect.y, width: hit.rect.width, height: hit.rect.height },
        viewBox: hit.viewBox,
        overflowPx: hit.overflowPx,
        tolerancePx: hit.tolerance,
      },
      supportedFixes: [hint],
    });
    return message;
  });
}

function qualityProfileForGate(profile, profileIsAuthoritative) {
  return profileIsAuthoritative
    ? profile
    : process.env.ARCHIFY_QUALITY_PROFILE || profile;
}

function collectEligibleRoutedRelations({ relations, endpointIds, pathFor }) {
  return asArray(relations).map((relation, relationIndex) => {
    if (!relation || typeof relation.from !== 'string' || typeof relation.to !== 'string') return null;
    if (endpointIds && (!endpointIds.has(relation.from) || !endpointIds.has(relation.to))) return null;
    return { relation, relationIndex, points: pathFor(relation)?.points };
  }).filter(Boolean);
}

function segmentPosition(index, segmentCount) {
  if (index === 0) return 'source-stub';
  if (index === segmentCount - 1) return 'target-stub';
  return 'interior';
}

// Normalizing a route is pure, and the same route array is normalized again by
// every predicate that inspects it. Keyed by the array itself, so a rebuilt
// route simply gets a new entry. The result's outer array is frozen. Callers
// must also treat input arrays and their coordinate pairs as immutable, since
// edits in place cannot invalidate this identity-based cache.
const NORMALIZED_ROUTE_POINTS = new WeakMap();

// Assembling a route from an anchor, corridor points and an anchor is the same
// normalization without the intermediate array, and the result is seeded in the
// cache so later predicates do not normalize it again.
export function joinRoutePoints(start, via, end) {
  const normalized = [];
  const accept = (point) => {
    if (!Array.isArray(point) || point.length !== 2 || !isFinitePoint(point[0], point[1])) return;
    const previous = normalized.at(-1);
    if (previous
      && Math.abs(point[0] - previous[0]) <= 0.0001
      && Math.abs(point[1] - previous[1]) <= 0.0001) return;
    while (normalized.length >= 2 && collinearForward(normalized.at(-2), normalized.at(-1), point)) normalized.pop();
    normalized.push(point);
  };
  accept(start);
  for (const point of Array.isArray(via) ? via : []) accept(point);
  accept(end);
  Object.freeze(normalized);
  NORMALIZED_ROUTE_POINTS.set(normalized, normalized);
  return normalized;
}

export function normalizeRoutePoints(points) {
  if (Array.isArray(points)) {
    const cached = NORMALIZED_ROUTE_POINTS.get(points);
    if (cached) return cached;
  }
  const normalized = [];
  for (const point of Array.isArray(points) ? points : []) {
    if (!Array.isArray(point) || point.length !== 2 || !isFinitePoint(point[0], point[1])) continue;
    const previous = normalized.at(-1);
    if (previous
      && Math.abs(point[0] - previous[0]) <= 0.0001
      && Math.abs(point[1] - previous[1]) <= 0.0001) continue;
    while (normalized.length >= 2 && collinearForward(normalized.at(-2), normalized.at(-1), point)) normalized.pop();
    normalized.push(point);
  }
  if (Array.isArray(points)) {
    Object.freeze(normalized);
    NORMALIZED_ROUTE_POINTS.set(points, normalized);
  }
  return normalized;
}

function pointRectDistance(point, rect) {
  const dx = Math.max(rect.x - point[0], 0, point[0] - (rect.x + rect.width));
  const dy = Math.max(rect.y - point[1], 0, point[1] - (rect.y + rect.height));
  return Math.hypot(dx, dy);
}

function pointSegmentDistanceXY(px, py, start, end) {
  const dx = end[0] - start[0];
  const dy = end[1] - start[1];
  const lengthSquared = dx * dx + dy * dy;
  if (lengthSquared <= 0.0000001) return Math.hypot(px - start[0], py - start[1]);
  const t = Math.max(0, Math.min(1, ((px - start[0]) * dx + (py - start[1]) * dy) / lengthSquared));
  return Math.hypot(px - (start[0] + t * dx), py - (start[1] + t * dy));
}

function pointSegmentDistance(point, start, end) {
  return pointSegmentDistanceXY(point[0], point[1], start, end);
}

function collinearForward(a, b, c) {
  if (Math.abs(crossProduct(a, b, c)) > 0.0001) return false;
  return (b[0] - a[0]) * (c[0] - b[0]) + (b[1] - a[1]) * (c[1] - b[1]) >= -0.0001;
}

export function frameBorderSegments(frame) {
  if (!frame || typeof frame !== 'object') return [];
  if (frame.shape === 'line') {
    const start = frame.start || [frame.x1, frame.y1];
    const end = frame.end || [frame.x2, frame.y2];
    return isFinitePoint(...start, ...end) ? [{ side: 'line', start, end }] : [];
  }
  if (!isFinitePoint(frame.x, frame.y, frame.width, frame.height) || frame.width <= 0 || frame.height <= 0) return [];
  const radius = Math.max(0, Math.min(Number(frame.radius) || 0, frame.width / 2, frame.height / 2));
  const left = frame.x;
  const right = frame.x + frame.width;
  const top = frame.y;
  const bottom = frame.y + frame.height;
  return [
    { side: 'top', start: [left + radius, top], end: [right - radius, top] },
    { side: 'right', start: [right, top + radius], end: [right, bottom - radius] },
    { side: 'bottom', start: [right - radius, bottom], end: [left + radius, bottom] },
    { side: 'left', start: [left, bottom - radius], end: [left, top + radius] },
  ].filter(({ start, end }) => Math.hypot(end[0] - start[0], end[1] - start[1]) > 0.0001);
}

function mergeBorderOverlaps(overlaps, border) {
  const horizontal = Math.abs(border.start[1] - border.end[1]) <= 0.0001;
  const axis = horizontal ? 0 : 1;
  const fixed = horizontal ? border.start[1] : border.start[0];
  const sorted = overlaps.map((overlap) => ({
    low: Math.min(overlap.start[axis], overlap.end[axis]),
    high: Math.max(overlap.start[axis], overlap.end[axis]),
  })).sort((left, right) => left.low - right.low || left.high - right.high);
  const merged = [];
  for (const interval of sorted) {
    const previous = merged.at(-1);
    if (previous && interval.low <= previous.high + 0.0001) previous.high = Math.max(previous.high, interval.high);
    else merged.push({ ...interval });
  }
  return merged.map((interval) => ({
    ...interval,
    length: interval.high - interval.low,
    start: horizontal ? [interval.low, fixed] : [fixed, interval.low],
    end: horizontal ? [interval.high, fixed] : [fixed, interval.high],
  }));
}

function collinearAxisOverlap(a, b, c, d) {
  const epsilon = 0.0001;
  const horizontal = Math.abs(a[1] - b[1]) <= epsilon
    && Math.abs(c[1] - d[1]) <= epsilon
    && Math.abs(a[1] - c[1]) <= epsilon;
  const vertical = Math.abs(a[0] - b[0]) <= epsilon
    && Math.abs(c[0] - d[0]) <= epsilon
    && Math.abs(a[0] - c[0]) <= epsilon;
  if (!horizontal && !vertical) return null;
  const axis = horizontal ? 0 : 1;
  const low = Math.max(Math.min(a[axis], b[axis]), Math.min(c[axis], d[axis]));
  const high = Math.min(Math.max(a[axis], b[axis]), Math.max(c[axis], d[axis]));
  if (high - low <= epsilon) return null;
  const fixed = horizontal ? a[1] : a[0];
  return {
    length: high - low,
    start: horizontal ? [low, fixed] : [fixed, low],
    end: horizontal ? [high, fixed] : [fixed, high],
  };
}

export function properSegmentIntersection(a, b, c, d) {
  const abC = crossProduct(a, b, c);
  const abD = crossProduct(a, b, d);
  const cdA = crossProduct(c, d, a);
  const cdB = crossProduct(c, d, b);
  const epsilon = 0.0001;
  const opposite = (left, right) => (left > epsilon && right < -epsilon) || (left < -epsilon && right > epsilon);
  if (!opposite(abC, abD) || !opposite(cdA, cdB)) return null;

  const denominator = (a[0] - b[0]) * (c[1] - d[1]) - (a[1] - b[1]) * (c[0] - d[0]);
  if (Math.abs(denominator) < epsilon) return null;
  const ab = a[0] * b[1] - a[1] * b[0];
  const cd = c[0] * d[1] - c[1] * d[0];
  return [
    (ab * (c[0] - d[0]) - (a[0] - b[0]) * cd) / denominator,
    (ab * (c[1] - d[1]) - (a[1] - b[1]) * cd) / denominator
  ];
}

function crossProduct(a, b, c) {
  return (b[0] - a[0]) * (c[1] - a[1]) - (b[1] - a[1]) * (c[0] - a[0]);
}

function pointInBox(point, box) {
  return point[0] >= box.x1 && point[0] <= box.x2 && point[1] >= box.y1 && point[1] <= box.y2;
}

function segmentsIntersect(a, b, c, d) {
  const o1 = orientation(a, b, c);
  const o2 = orientation(a, b, d);
  const o3 = orientation(c, d, a);
  const o4 = orientation(c, d, b);

  if (o1 === 0 && onSegment(a, c, b)) return true;
  if (o2 === 0 && onSegment(a, d, b)) return true;
  if (o3 === 0 && onSegment(c, a, d)) return true;
  if (o4 === 0 && onSegment(c, b, d)) return true;

  return o1 !== o2 && o3 !== o4;
}

function orientation(a, b, c) {
  const value = (b[1] - a[1]) * (c[0] - b[0]) - (b[0] - a[0]) * (c[1] - b[1]);
  if (Math.abs(value) < 0.0001) return 0;
  return value > 0 ? 1 : 2;
}

function onSegment(a, b, c) {
  return (
    b[0] <= Math.max(a[0], c[0]) &&
    b[0] >= Math.min(a[0], c[0]) &&
    b[1] <= Math.max(a[1], c[1]) &&
    b[1] >= Math.min(a[1], c[1])
  );
}

export function anchor(rect, side) {
  switch (side) {
    case 'left': return [rect.x, rect.cy];
    case 'right': return [rect.x + rect.width, rect.cy];
    case 'top': return [rect.cx, rect.y];
    case 'bottom': return [rect.cx, rect.y + rect.height];
    default:
      return [rect.x + rect.width, rect.cy];
  }
}

const PORT_OUTWARD_VECTOR = {
  left: [-1, 0],
  right: [1, 0],
  top: [0, -1],
  bottom: [0, 1],
};

// Automatic port spreading can put otherwise parallel anchors only a few
// pixels apart. A conventional midpoint dogleg then violates the renderer's
// own 8px/16px route-rhythm floors. Return a full outside-channel route when
// that happens, or null when the normal automatic route remains appropriate.
export function automaticPortRhythmBridge(
  start,
  end,
  fromSide,
  toSide,
  { endpointStubPx = 24, interiorSegmentPx = 16, accept } = {},
) {
  if (!Array.isArray(start) || !Array.isArray(end)
      || start.length !== 2 || end.length !== 2
      || !isFinitePoint(...start, ...end)) return null;
  const fromVector = PORT_OUTWARD_VECTOR[fromSide];
  const toVector = PORT_OUTWARD_VECTOR[toSide];
  if (!fromVector || !toVector) return null;

  const opposedFacingGap = (
    (fromSide === 'right' && toSide === 'left' && end[0] > start[0])
    || (fromSide === 'left' && toSide === 'right' && start[0] > end[0])
  ) ? Math.abs(end[0] - start[0]) : (
    (fromSide === 'bottom' && toSide === 'top' && end[1] > start[1])
    || (fromSide === 'top' && toSide === 'bottom' && start[1] > end[1])
  ) ? Math.abs(end[1] - start[1]) : null;
  const boundedStubPx = opposedFacingGap != null
    && opposedFacingGap - endpointStubPx * 2 < interiorSegmentPx
    ? Math.max(8, Math.min(endpointStubPx, (opposedFacingGap - interiorSegmentPx) / 2))
    : null;
  const stubDistances = [endpointStubPx];
  if (boundedStubPx != null && boundedStubPx >= 8 && boundedStubPx !== endpointStubPx) {
    stubDistances.push(boundedStubPx);
  }
  const candidates = [];
  const verticalSides = new Set(['top', 'bottom']);
  const horizontalSides = new Set(['left', 'right']);

  for (const stubPx of stubDistances) {
    const startStub = [
      start[0] + fromVector[0] * stubPx,
      start[1] + fromVector[1] * stubPx,
    ];
    const endStub = [
      end[0] + toVector[0] * stubPx,
      end[1] + toVector[1] * stubPx,
    ];
    if (verticalSides.has(fromSide) && verticalSides.has(toSide)
        && Math.abs(start[0] - end[0]) < interiorSegmentPx) {
      for (const channelX of [
        Math.max(start[0], end[0]) + interiorSegmentPx,
        Math.min(start[0], end[0]) - interiorSegmentPx,
      ]) {
        candidates.push([
          start,
          startStub,
          [channelX, startStub[1]],
          [channelX, endStub[1]],
          endStub,
          end,
        ]);
      }
    }
    if (horizontalSides.has(fromSide) && horizontalSides.has(toSide)
        && Math.abs(start[1] - end[1]) < interiorSegmentPx) {
      for (const channelY of [
        Math.max(start[1], end[1]) + interiorSegmentPx,
        Math.min(start[1], end[1]) - interiorSegmentPx,
      ]) {
        candidates.push([
          start,
          startStub,
          [startStub[0], channelY],
          [endStub[0], channelY],
          endStub,
          end,
        ]);
      }
    }
  }

  return candidates
    .map((points) => normalizeRoutePoints(points))
    .find((points) => (
      routeHonorsEndpointSides(points, fromSide, toSide)
      && collectRouteRhythmIssues({ routedRelations: [{ points }], interiorSegmentPx }).length === 0
      && (typeof accept !== 'function' || accept(points))
    )) || null;
}

// Keep conservative auto-routed fan-out/fan-in relationships visually
// distinct without changing authored route controls. The returned map only
// contains endpoints that belong to a shared automatic midpoint anchor.
export function automaticPortSpread(relations, boxes, { gutter = 16, maxSpacing = 14, sideFor, spacingFor } = {}) {
  const groups = new Map();
  const spread = new Map();

  const add = (relation, endpoint, rect, side, counterpart) => {
    const key = `${rect.id}\u0000${side}`;
    const items = groups.get(key) || [];
    items.push({ relation, endpoint, rect, side, counterpart });
    groups.set(key, items);
  };

  for (const relation of asArray(relations)) {
    if (!relation || (relation.route && relation.route !== 'auto')) continue;
    if (relation.via || relation.channelX !== undefined || relation.channelY !== undefined || relation.labelAt) continue;
    const from = boxes.get(relation.from);
    const to = boxes.get(relation.to);
    if (!from || !to) continue;
    const fromSide = chosenSide(
      relation.fromSide,
      sideFor?.(relation, 'source') || defaultFromSide(from, to),
    );
    const toSide = chosenSide(
      relation.toSide,
      sideFor?.(relation, 'target') || defaultToSide(from, to),
    );
    add(relation, 'from', from, fromSide, to);
    add(relation, 'to', to, toSide, from);
  }

  for (const items of groups.values()) {
    if (items.length < 2) continue;
    const verticalSide = items[0].side === 'left' || items[0].side === 'right';
    items.sort((a, b) => {
      const aCoordinate = verticalSide ? a.counterpart.cy : a.counterpart.cx;
      const bCoordinate = verticalSide ? b.counterpart.cy : b.counterpart.cx;
      if (aCoordinate !== bCoordinate) return aCoordinate - bCoordinate;
      const aKey = `${a.relation.id || ''}\u0000${a.relation.from}\u0000${a.relation.to}\u0000${a.relation.label || ''}`;
      const bKey = `${b.relation.id || ''}\u0000${b.relation.from}\u0000${b.relation.to}\u0000${b.relation.label || ''}`;
      return aKey < bKey ? -1 : aKey > bKey ? 1 : 0;
    });

    const extent = verticalSide ? items[0].rect.height : items[0].rect.width;
    const usable = Math.max(0, extent - gutter * 2);
    const spacing = Math.min(maxSpacing, usable / (items.length - 1));
    if (!(spacing > 0)) continue;

    // Width-aware callers reserve the whole group together. Moving a single
    // port around the legacy 14px slots can wrongly report a full side while
    // its still-unrouted neighbours could have fitted farther apart.
    let offsets;
    if (spacingFor) {
      const gaps = items.slice(1).map((item, index) => Math.max(maxSpacing,
        spacingFor(items[index].relation, item.relation)));
      const span = gaps.reduce((sum, gap) => sum + gap, 0);
      if (span <= usable && gaps.some((gap) => gap > maxSpacing)) {
        let offset = -span / 2;
        offsets = [offset, ...gaps.map((gap) => (offset += gap))];
      }
    }

    for (const [index, item] of items.entries()) {
      const offset = offsets?.[index] ?? (index - (items.length - 1) / 2) * spacing;
      const point = anchor(item.rect, item.side);
      if (verticalSide) point[1] += offset;
      else point[0] += offset;
      const endpoints = spread.get(item.relation) || {};
      endpoints[item.endpoint] = point;
      spread.set(item.relation, endpoints);
    }
  }

  return spread;
}

// A centre delta on the horizontal axis does not by itself mean the route
// leaves sideways: a hub above an offset spoke has both a horizontal and a
// larger vertical delta, and the router draws the vertical dogleg. Compare the
// deltas so the inferred side matches the axis the route actually uses. Equal
// deltas select horizontal sides; dx === 0 preserves the previous vertical
// result, while a vertical-dominant nonzero dx selects vertical sides.
export function defaultFromSide(from, to) {
  const dx = to.cx - from.cx;
  const dy = to.cy - from.cy;
  if (dx !== 0 && Math.abs(dx) >= Math.abs(dy)) return dx < 0 ? 'left' : 'right';
  return dy > 0 ? 'bottom' : 'top';
}

export function defaultToSide(from, to) {
  const dx = to.cx - from.cx;
  const dy = to.cy - from.cy;
  if (dx !== 0 && Math.abs(dx) >= Math.abs(dy)) return dx < 0 ? 'right' : 'left';
  return dy > 0 ? 'top' : 'bottom';
}

// Non-architecture renderers retain their established horizontal-first
// endpoint contract. Architecture opts into dominant-axis inference above so
// a vertical hub-and-spoke route can use perpendicular automatic ports.
export function legacyDefaultFromSide(from, to) {
  if (to.cx < from.cx) return 'left';
  if (to.cx > from.cx) return 'right';
  if (to.cy > from.cy) return 'bottom';
  return 'top';
}

export function legacyDefaultToSide(from, to) {
  if (to.cx < from.cx) return 'right';
  if (to.cx > from.cx) return 'left';
  if (to.cy > from.cy) return 'top';
  return 'bottom';
}

export function chosenSide(side, fallback) {
  return side && side !== 'auto' ? side : fallback;
}

export function polylinePath(points) {
  return points.map(([x, y], index) => `${index === 0 ? 'M' : 'L'} ${x} ${y}`).join(' ');
}

export function routePointsValue(points) {
  return asArray(points)
    .filter((point) => Array.isArray(point) && point.length === 2 && isFinitePoint(...point))
    .map(([x, y]) => `${x},${y}`)
    .join(';');
}

// Only a direct, explicitly authored diagonal needs an artifact-check exception.
// Nonempty via takes precedence; empty via adds no intermediate geometry.
export function authoredStraightRouteAttrs(relation, points) {
  if (relation.route !== 'straight' || relation.via?.length || points.length !== 2) return '';
  const [start, end] = points;
  return Math.abs(start[0] - end[0]) > 0.01 && Math.abs(start[1] - end[1]) > 0.01
    ? ' data-composition-route="straight"'
    : '';
}

export function roundedPath(points, radius) {
  if (points.length < 3 || radius <= 0) {
    return polylinePath(points);
  }

  const commands = [`M ${points[0][0]} ${points[0][1]}`];
  for (let i = 1; i < points.length - 1; i += 1) {
    const [px, py] = points[i - 1];
    const [cx, cy] = points[i];
    const [nx, ny] = points[i + 1];
    const prevLen = Math.hypot(cx - px, cy - py);
    const nextLen = Math.hypot(nx - cx, ny - cy);
    const r = Math.min(radius, prevLen / 2, nextLen / 2);
    if (r < 1) {
      commands.push(`L ${cx} ${cy}`);
      continue;
    }
    const before = [cx - ((cx - px) / prevLen) * r, cy - ((cy - py) / prevLen) * r];
    const after = [cx + ((nx - cx) / nextLen) * r, cy + ((ny - cy) / nextLen) * r];
    commands.push(`L ${before[0]} ${before[1]}`);
    commands.push(`Q ${cx} ${cy} ${after[0]} ${after[1]}`);
  }
  const [endX, endY] = points[points.length - 1];
  commands.push(`L ${endX} ${endY}`);
  return commands.join(' ');
}

// Shared by edges/flows/transitions: all carry the same optional
// labelAt/labelDx/labelDy/labelSegment knobs.
export function labelPoint(item, points) {
  if (item.labelAt) return item.labelAt;
  if (points.length === 2) {
    return [
      (points[0][0] + points[1][0]) / 2 + (item.labelDx || 0),
      points[0][1] - 10 + (item.labelDy || 0)
    ];
  }
  const segmentIndex = Math.min(points.length - 2, Math.max(0, item.labelSegment ?? 1));
  const a = points[segmentIndex];
  const b = points[segmentIndex + 1];
  return [(a[0] + b[0]) / 2 + (item.labelDx || 0), (a[1] + b[1]) / 2 - 10 + (item.labelDy || 0)];
}

export const componentFill = {
  frontend: 'c-frontend',
  backend: 'c-backend',
  database: 'c-database',
  cloud: 'c-cloud',
  security: 'c-security',
  messagebus: 'c-messagebus',
  external: 'c-external'
};

export const componentText = {
  frontend: 't-frontend',
  backend: 't-backend',
  database: 't-database',
  cloud: 't-cloud',
  security: 't-security',
  messagebus: 't-messagebus',
  external: 't-external'
};

export const arrowClassMap = {
  default: ['a-default', 'arrowhead'],
  emphasis: ['a-emphasis', 'arrowhead-emphasis'],
  security: ['a-security', 'arrowhead-security'],
  dashed: ['a-dashed', 'arrowhead-dashed']
};

// Structural phase/group accents retain their existing semantic colors.
export function variantAccent(variant) {
  return variant === 'security' ? 't-security'
    : variant === 'emphasis' ? 't-backend'
      : variant === 'dashed' ? 't-messagebus' : 't-muted';
}

// Relationship labels use the same theme token as their path. Keep this map
// edge-specific: node-kind text colors only coincide with some path colors in
// the classic preset and must not define the relationship's visual meaning.
export function edgeLabelAccent(variant) {
  return variant === 'security'
    ? 't-edge-security'
    : variant === 'emphasis'
      ? 't-edge-emphasis'
      : variant === 'dashed'
        ? 't-edge-dashed'
        : 't-edge-default';
}

export function formatRect(r) {
  return `[${Math.round(r.x)}, ${Math.round(r.y)}, ${Math.round(r.width)}, ${Math.round(r.height)}]`;
}

function formatValue(n) {
  return String(Math.round(n));
}

// A label anchor is the text origin, so keeping a suggestion on the canvas
// means moving the whole rect: offset is `rect - anchor` on that axis.
function anchorFitsCanvas(anchorValue, offset, size, extent) {
  const overflow = axisCanvasOverflow(anchorValue + offset, size, extent);
  return overflow.start <= 0 && overflow.end <= 0;
}

// Suggestions are emitted as integers, so the real-valued bounds are tightened
// inward with ceil/floor first: every integer between them keeps the whole rect
// on the canvas, which a bound like 616.7 would not. Returns null when the rect
// is wider than the canvas and no anchor can contain it.
function clampAnchorToCanvas(anchorValue, offset, size, extent) {
  const rounded = Math.round(anchorValue);
  if (!Number.isFinite(extent)) return rounded;
  const min = Math.ceil(-offset);
  const max = Math.floor(extent - size - offset);
  return max < min ? null : Math.min(Math.max(rounded, min), max);
}

/**
 * Actionable hint when an edge label rect hits a node/component box (#7).
 * Every suggested value is a replacement for the authored field, not an
 * increment, and has to survive being applied to the document:
 * - the absolute form is nudged along x so the rect stays on the canvas, and a
 *   vertical placement that cannot fit is dropped rather than clamped, since
 *   clamping it back would push the label onto the obstacle it must clear;
 * - the relative form is offered only when labelDx/labelDy actually move this
 *   label (labelPoint returns an authored labelAt as-is) and only when the
 *   replacements, computed from the document's own labelDx/labelDy, land the
 *   rect inside the canvas.
 * The authored values therefore come from `labelRect.relation`, the authored
 * relationship the renderer already attaches to every label record.
 * `obstacles` is every box the callers' own overlap loop tests (defaults to
 * the named obstacle alone): a placement that merely traded the named obstacle
 * for its neighbor would fail the same rule again when applied.
 */
export function suggestLabelObstacleFix(labelRect, lx, ly, obstacle, obstacleKind = 'component', viewBox, obstacles) {
  // Renderer canvases are origin-zero [width, height] by schema, but read a
  // 4-number [min-x, min-y, width, height] the same way the containment
  // collector does — degraded no-ajv runs must not clamp against the origin
  // pair as if it were the canvas size.
  const box = asArray(viewBox);
  const [canvasWidth, canvasHeight] = box.length === 4 ? box.slice(2) : box;
  const xOffset = labelRect.x - lx;
  const yOffset = labelRect.y - ly;
  const anchorX = clampAnchorToCanvas(lx, xOffset, labelRect.width, canvasWidth);
  // The placement anchors are derived from the label's own rect, not from the
  // obstacle alone: an obstacle-only "above" anchor assumes the 14px
  // single-line rect and lands a 27px two-line rect (dataflow classification,
  // lifecycle note) back on the obstacle it must clear. The overlap filter
  // uses the callers' own detection call, so a surviving hint cannot re-raise
  // the problem it repairs.
  const blockers = obstacles ? [...obstacles] : [obstacle];
  const placements = [
    { name: 'below', y: Math.round(obstacle.y + obstacle.height + 4 - yOffset) },
    { name: 'above', y: Math.round(obstacle.y - 4 - labelRect.height - yOffset) },
  ].filter(({ y }) => anchorX !== null
    && anchorFitsCanvas(y, yOffset, labelRect.height, canvasHeight)
    && blockers.every((blocker) => !rectsOverlap(
      { x: anchorX + xOffset, y: y + yOffset, width: labelRect.width, height: labelRect.height },
      blocker,
      -2,
    )));
  const lines = [
    `  label rect: ${formatRect(labelRect)}`,
    `  ${obstacleKind} "${obstacle.id}" rect: ${formatRect(obstacle)}`,
  ];
  if (!placements.length) {
    // Only the vertical slots beside the named obstacle were tried, so an
    // unclaimed spot elsewhere may still exist — never assert that none does.
    lines.push(anchorX === null
      ? `  Suggested fix: the ${Math.round(labelRect.width)}px label rect cannot fit the ${canvasWidth}x${canvasHeight} viewBox at any anchor — shorten the label or enlarge meta.viewBox`
      : `  Suggested fix: no placement directly above or below "${obstacle.id}" stays clear inside the ${canvasWidth}x${canvasHeight} viewBox — move the label to an open area with labelAt, shorten the label, move the ${obstacleKind}, or enlarge meta.viewBox`);
    return lines.join('\n');
  }
  const authored = labelRect.relation || {};
  const authoredDx = Number.isFinite(authored.labelDx) ? authored.labelDx : 0;
  const authoredDy = Number.isFinite(authored.labelDy) ? authored.labelDy : 0;
  const relativeHint = (y) => {
    if (Array.isArray(authored.labelAt)) return null;
    // Both replacements are measured from the automatic label point that the
    // authored offsets are applied to, and against the unrounded anchor: a
    // rounded base would shift the applied label by up to a pixel.
    const dx = Math.round(authoredDx + anchorX - lx);
    const dy = Math.round(authoredDy + y - ly);
    // labelDx is authored as a number, so an authored fraction must not read as
    // a needed nudge once the replacement is rounded to an integer.
    const movesX = Math.abs(dx - authoredDx) >= 0.5;
    const landsAtX = lx - authoredDx + (movesX ? dx : authoredDx);
    const landsAtY = ly - authoredDy + dy;
    if (!anchorFitsCanvas(landsAtX, xOffset, labelRect.width, canvasWidth)) return null;
    if (!anchorFitsCanvas(landsAtY, yOffset, labelRect.height, canvasHeight)) return null;
    return movesX
      ? `set labelDx ${formatValue(dx)} with labelDy ${formatValue(dy)}`
      : `set labelDy ${formatValue(dy)}`;
  };
  const hint = placements
    .map(({ name, y }) => {
      const relative = relativeHint(y);
      return `set labelAt [${anchorX}, ${y}]${relative ? ` or ${relative}` : ''} (${name})`;
    })
    .join('; or ');
  lines.push(`  Suggested fix: ${hint}`);
  return lines.join('\n');
}

/** Hint when two edge labels collide. */
export function suggestLabelPairFix(a, b) {
  return [
    `  "${a.label}" ${formatRect(a)}; "${b.label}" ${formatRect(b)}`,
    '  Suggested fix: adjust labelDx/labelDy/labelSegment, or route one relationship through a separate corridor',
  ].join('\n');
}

/** Hint when two components/nodes are too close. */
export function suggestComponentSeparation(a, b, minGap = 8) {
  const rightX = Math.round(a.x + a.width + minGap);
  const belowY = Math.round(a.y + a.height + minGap);
  return [
    `  "${a.id}" ${formatRect(a)}; "${b.id}" ${formatRect(b)}`,
    `  Suggested fix: move "${b.id}" pos to [${rightX}, ${Math.round(b.y)}] (right of "${a.id}") or [${Math.round(b.x)}, ${belowY}] (below)`,
  ].join('\n');
}