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import { vec2 } from 'gl-matrix';
import containsPoint from './containsPoint';
import getSignedArea from './getSignedArea';
import {
EPSILON,
IntersectionDirection,
pointsAreEqual,
PolylineNodeType,
robustSegmentIntersection,
type AugmentedPolyNode,
type IntersectionInfo,
} from './robustSegmentIntersection';
/**
* Calculates all unique intersection points between two polylines.
* Assumes polylines are closed (last point connects to first).
*
* @param polyline1 - The first polyline, an array of Point2.
* @param polyline2 - The second polyline, an array of Point2.
* @returns An array of unique intersection points (Types.Point2[]).
*/
export default function intersectPolylines(
mainPolyCoords: Types.Point2[],
clipPolyCoordsInput: Types.Point2[]
): Types.Point2[][] {
if (mainPolyCoords.length < 3 || clipPolyCoordsInput.length < 3) {
return []; // Not valid polygons
}
let clipPolyCoords = clipPolyCoordsInput.slice();
// 1. Ensure consistent winding for intersection (e.g., both CCW)
const mainArea = getSignedArea(mainPolyCoords);
const clipArea = getSignedArea(clipPolyCoords);
if (Math.abs(mainArea) < EPSILON || Math.abs(clipArea) < EPSILON) {
return []; // Degenerate polygon(s)
}
// Make both CCW (positive area) for easier reasoning, or both CW. Let's aim for CCW.
if (mainArea < 0) {
// mainPoly is CW, reverse it
mainPolyCoords = mainPolyCoords.slice().reverse();
}
if (clipArea < 0) {
// clipPoly is CW, reverse it
clipPolyCoords = clipPolyCoords.slice().reverse();
}
// After this, if original clipPolyCoordsInput was used for pointInPolygon, its winding matters.
// Let's use the potentially reversed clipPolyCoords for internal consistency in PIP tests.
const currentClipPolyForPIP = clipPolyCoords;
// 2. Find all intersections
const intersections: IntersectionInfo[] = [];
for (let i = 0; i < mainPolyCoords.length; i++) {
const p1 = mainPolyCoords[i];
const p2 = mainPolyCoords[(i + 1) % mainPolyCoords.length];
for (let j = 0; j < clipPolyCoords.length; j++) {
const q1 = clipPolyCoords[j];
const q2 = clipPolyCoords[(j + 1) % clipPolyCoords.length];
const intersectPt = robustSegmentIntersection(p1, p2, q1, q2);
if (intersectPt) {
const lenP = Math.sqrt(vec2.squaredDistance(p1, p2));
const lenQ = Math.sqrt(vec2.squaredDistance(q1, q2));
intersections.push({
coord: [...intersectPt],
seg1Idx: i, // Corresponds to mainPoly
seg2Idx: j, // Corresponds to clipPoly
alpha1:
lenP < EPSILON
? 0
: Math.sqrt(vec2.squaredDistance(p1, intersectPt)) / lenP,
alpha2:
lenQ < EPSILON
? 0
: Math.sqrt(vec2.squaredDistance(q1, intersectPt)) / lenQ,
});
}
}
}
// 3. Handle cases with no intersections
if (intersections.length === 0) {
// Check for full containment
if (
containsPoint(currentClipPolyForPIP, mainPolyCoords[0]) &&
mainPolyCoords.every((pt) => containsPoint(currentClipPolyForPIP, pt))
) {
return [[...mainPolyCoords.map((p) => [...p] as Types.Point2)]]; // Main is inside Clip
}
if (
containsPoint(mainPolyCoords, clipPolyCoords[0]) &&
clipPolyCoords.every((pt) => containsPoint(mainPolyCoords, pt))
) {
return [[...clipPolyCoords.map((p) => [...p] as Types.Point2)]]; // Clip is inside Main
}
return []; // No intersection, no containment
}
// 4. Build augmented polylines (linked lists of AugmentedPolyNode)
const buildAugmentedList = (
polyCoords: Types.Point2[],
polyIndex: 0 | 1, // 0 for main, 1 for clip
allIntersections: IntersectionInfo[]
): AugmentedPolyNode[] => {
const augmentedList: AugmentedPolyNode[] = [];
let nodeIdCounter = 0;
for (let i = 0; i < polyCoords.length; i++) {
const p1 = polyCoords[i];
augmentedList.push({
id: `${polyIndex}_v${nodeIdCounter++}`,
coordinates: [...p1],
type: PolylineNodeType.Vertex,
originalPolyIndex: polyIndex,
originalVertexIndex: i,
next: null,
prev: null,
isIntersection: false,
visited: false,
processedInPath: false, // Initialize new flag
intersectionDir: IntersectionDirection.Unknown, // Initialize
});
const segmentIntersections = allIntersections
.filter(
(isect) => (polyIndex === 0 ? isect.seg1Idx : isect.seg2Idx) === i
)
.sort(
(a, b) =>
(polyIndex === 0 ? a.alpha1 : a.alpha2) -
(polyIndex === 0 ? b.alpha1 : b.alpha2)
);
for (const isect of segmentIntersections) {
if (
augmentedList.length > 0 &&
pointsAreEqual(
augmentedList[augmentedList.length - 1].coordinates,
isect.coord
)
) {
const lastNode = augmentedList[augmentedList.length - 1];
if (!lastNode.isIntersection) {
lastNode.isIntersection = true;
lastNode.intersectionInfo = isect;
lastNode.alpha = polyIndex === 0 ? isect.alpha1 : isect.alpha2;
lastNode.type = PolylineNodeType.Intersection;
}
continue;
}
augmentedList.push({
id: `${polyIndex}_i${nodeIdCounter++}`,
coordinates: [...isect.coord],
type: PolylineNodeType.Intersection,
originalPolyIndex: polyIndex,
next: null,
prev: null,
isIntersection: true,
visited: false,
processedInPath: false, // Initialize
alpha: polyIndex === 0 ? isect.alpha1 : isect.alpha2,
intersectionInfo: isect,
intersectionDir: IntersectionDirection.Unknown, // Initialize
});
}
}
const finalList: AugmentedPolyNode[] = [];
if (augmentedList.length > 0) {
finalList.push(augmentedList[0]);
for (let i = 1; i < augmentedList.length; i++) {
if (
!pointsAreEqual(
augmentedList[i].coordinates,
finalList[finalList.length - 1].coordinates
)
) {
finalList.push(augmentedList[i]);
} else {
const lastNodeInFinal = finalList[finalList.length - 1];
if (
augmentedList[i].isIntersection &&
augmentedList[i].intersectionInfo
) {
lastNodeInFinal.isIntersection = true;
lastNodeInFinal.intersectionInfo =
augmentedList[i].intersectionInfo;
lastNodeInFinal.alpha = augmentedList[i].alpha;
lastNodeInFinal.type = PolylineNodeType.Intersection;
}
}
}
}
if (
finalList.length > 1 &&
pointsAreEqual(
finalList[0].coordinates,
finalList[finalList.length - 1].coordinates
)
) {
const firstNode = finalList[0];
const lastNodePopped = finalList.pop()!; // remove last, it's a duplicate of first
if (
lastNodePopped.isIntersection &&
!firstNode.isIntersection &&
lastNodePopped.intersectionInfo
) {
firstNode.isIntersection = true;
firstNode.intersectionInfo = lastNodePopped.intersectionInfo;
firstNode.alpha = lastNodePopped.alpha;
firstNode.type = PolylineNodeType.Intersection;
}
}
if (finalList.length > 0) {
for (let i = 0; i < finalList.length; i++) {
finalList[i].next = finalList[(i + 1) % finalList.length];
finalList[i].prev =
finalList[(i - 1 + finalList.length) % finalList.length];
}
}
return finalList;
};
const mainAugmented = buildAugmentedList(mainPolyCoords, 0, intersections);
const clipAugmented = buildAugmentedList(clipPolyCoords, 1, intersections);
if (mainAugmented.length === 0 || clipAugmented.length === 0) {
return [];
}
// 5. Pair intersection nodes and classify direction (Entry/Exit)
// For a node on mainAugmented, 'Entering' means mainPoly enters clipPoly.
// 'Exiting' means mainPoly exits clipPoly.
mainAugmented.forEach((mainNode) => {
if (mainNode.isIntersection && mainNode.intersectionInfo) {
const mainIntersectData = mainNode.intersectionInfo;
const partnerNode = clipAugmented.find(
(clipNode) =>
clipNode.isIntersection &&
clipNode.intersectionInfo &&
pointsAreEqual(clipNode.coordinates, mainNode.coordinates) &&
clipNode.intersectionInfo.seg1Idx === mainIntersectData.seg1Idx &&
clipNode.intersectionInfo.seg2Idx === mainIntersectData.seg2Idx
);
if (partnerNode) {
mainNode.partnerNode = partnerNode;
partnerNode.partnerNode = mainNode; // Bidirectional link
// Classify for mainNode:
// Point before mainNode on mainPoly: mainNode.prev.coordinates
// Point after mainNode on mainPoly: mainNode.next.coordinates
// Point after partnerNode on clipPoly: partnerNode.next.coordinates
// (Assumes both mainPoly and clipPoly are CCW after normalization)
// Vector from mainNode.prev to mainNode (arrival on main)
const v_arrival_main = vec2.subtract(
vec2.create(),
mainNode.coordinates,
mainNode.prev.coordinates
) as Types.Point2;
// Vector from mainNode (partner) to partnerNode.next (departure on clip)
const v_departure_clip = vec2.subtract(
vec2.create(),
partnerNode.next.coordinates,
partnerNode.coordinates
) as Types.Point2;
// Cross product determines if main is turning "into" or "out of" clip
// If main and clip are CCW:
// cross > 0: main turns left relative to clip's segment => Entering clip
// cross < 0: main turns right relative to clip's segment => Exiting clip
const crossZ =
v_arrival_main[0] * v_departure_clip[1] -
v_arrival_main[1] * v_departure_clip[0];
if (crossZ > EPSILON) {
mainNode.intersectionDir = IntersectionDirection.Entering;
partnerNode.intersectionDir = IntersectionDirection.Exiting; // From clip's perspective, main is coming in
} else if (crossZ < -EPSILON) {
mainNode.intersectionDir = IntersectionDirection.Exiting;
partnerNode.intersectionDir = IntersectionDirection.Entering; // From clip's perspective, main is leaving
} else {
// Collinear case at intersection - this is complex.
// A more robust method: check midpoint of segment mainNode.prev->mainNode against clipPoly
const midPrevMainSeg = [
(mainNode.prev.coordinates[0] + mainNode.coordinates[0]) / 2,
(mainNode.prev.coordinates[1] + mainNode.coordinates[1]) / 2,
];
if (
containsPoint(currentClipPolyForPIP, midPrevMainSeg as Types.Point2)
) {
// Previous segment was inside clip, so this intersection is an Exit for mainPoly
mainNode.intersectionDir = IntersectionDirection.Exiting;
partnerNode.intersectionDir = IntersectionDirection.Entering; // Mirror for clip
} else {
// Previous segment was outside clip, so this intersection is an Entry for mainPoly
mainNode.intersectionDir = IntersectionDirection.Entering;
partnerNode.intersectionDir = IntersectionDirection.Exiting; // Mirror for clip
}
}
} else {
// Demote if no partner: might be a vertex of one on edge of other, not a true crossing.
mainNode.isIntersection = false;
mainNode.intersectionInfo = undefined;
}
}
});
// 6. Trace result polygons for Intersection
const resultPolygons: Types.Point2[][] = [];
for (const startCand of mainAugmented) {
if (
!startCand.isIntersection ||
startCand.visited ||
startCand.intersectionDir !== IntersectionDirection.Entering
) {
continue; // Start only from unvisited "Entering" intersection points on the main polygon
}
let currentPathCoords: Types.Point2[] = [];
let currentNode: AugmentedPolyNode = startCand;
let onMainList = true; // Start on main list, about to jump to clip list
const pathStartNode = startCand; // Keep track of the very first node of this path
let safetyBreak = 0;
const maxIter = (mainAugmented.length + clipAugmented.length) * 2;
// Mark all nodes in this potential path with a temporary 'processedInPath' flag
// to handle complex cases where a node might be visited by one path attempt
// but should be available for another if the first attempt doesn't complete.
// Reset this flag before each new path attempt from a new startCand.
mainAugmented.forEach((n) => (n.processedInPath = false));
clipAugmented.forEach((n) => (n.processedInPath = false));
do {
if (safetyBreak++ > maxIter) {
console.warn(
'Intersection: Max iterations in path tracing.',
pathStartNode.id,
currentNode.id
);
currentPathCoords = []; // Discard incomplete path
break;
}
if (currentNode.processedInPath && currentNode !== pathStartNode) {
// Loop detected before closing properly
// This can happen in complex scenarios, especially with shared boundaries or self-intersections not handled upstream
console.warn(
'Intersection: Path processing loop detected, discarding path segment.',
pathStartNode.id,
currentNode.id
);
currentPathCoords = [];
break;
}
currentNode.processedInPath = true; // Mark as processed for *this* path attempt
currentNode.visited = true; // Mark as globally visited once part of any successful path or processed
if (
currentPathCoords.length === 0 ||
!pointsAreEqual(
currentPathCoords[currentPathCoords.length - 1],
currentNode.coordinates
)
) {
currentPathCoords.push([...currentNode.coordinates]);
}
let switchedList = false;
if (currentNode.isIntersection && currentNode.partnerNode) {
if (onMainList) {
// Currently on main list
// For intersection, if we are on main and hit an intersection, we always switch to clip.
// The type of intersection (Entry/Exit on mainNode) guided our *start*.
// Once tracing, main -> clip.
currentNode = currentNode.partnerNode;
onMainList = false;
switchedList = true;
} else {
// Currently on clip list
// If on clip and hit an intersection, we always switch back to main.
currentNode = currentNode.partnerNode;
onMainList = true;
switchedList = true;
}
}
if (!switchedList) {
currentNode = currentNode.next;
} else {
// After switching, we must advance on the *new* list
currentNode = currentNode.next;
}
} while (
currentNode !== pathStartNode ||
(onMainList && currentNode.originalPolyIndex !== 0) ||
(!onMainList && currentNode.originalPolyIndex !== 1)
);
// The loop condition is tricky: back to pathStartNode AND on its original list type.
// More simply: `while (currentNode !== pathStartNode || (onMainList !== (pathStartNode.originalPolyIndex === 0)))`
// This means if pathStartNode was on main, we must be onMainList when we return to it.
if (safetyBreak > maxIter || currentPathCoords.length === 0) {
// Path was discarded or didn't form
} else if (
currentPathCoords.length > 0 &&
pointsAreEqual(
currentPathCoords[0],
currentPathCoords[currentPathCoords.length - 1]
)
) {
currentPathCoords.pop(); // Remove redundant closing point
}
if (currentPathCoords.length >= 3) {
// Ensure the resulting polygon has the correct winding (e.g., CCW)
// This is important if multiple disjoint intersection areas are formed.
// The tracing rule should naturally produce this if inputs are CCW.
const resultArea = getSignedArea(currentPathCoords);
if (mainArea > 0 && resultArea < 0) {
// If main was CCW, result should be CCW
currentPathCoords.reverse();
} else if (mainArea < 0 && resultArea > 0) {
// If main was CW, result should be CW
currentPathCoords.reverse();
}
resultPolygons.push(currentPathCoords.map((p) => [...p]));
}
}
return resultPolygons;
}
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