// (c) Copyright 2016, Sean Connelly (@voidqk), http://syntheti.cc // MIT License // Project Home: https://github.com/voidqk/polybooljs // // this is the core work-horse // var LinkedList = require('./linked-list'); function Intersecter(selfIntersection, eps, buildLog){ // selfIntersection is true/false depending on the phase of the overall algorithm // // segment creation // function segmentNew(start, end){ return { id: buildLog ? buildLog.segmentId() : -1, start: start, end: end, myFill: { above: null, // is there fill above us? below: null // is there fill below us? }, otherFill: null }; } function segmentCopy(start, end, seg){ return { id: buildLog ? buildLog.segmentId() : -1, start: start, end: end, myFill: { above: seg.myFill.above, below: seg.myFill.below }, otherFill: null }; } // // event logic // var event_root = LinkedList.create(); function eventCompare(p1_isStart, p1_1, p1_2, p2_isStart, p2_1, p2_2){ // compare the selected points first var comp = eps.pointsCompare(p1_1, p2_1); if (comp !== 0) return comp; // the selected points are the same if (eps.pointsSame(p1_2, p2_2)) // if the non-selected points are the same too... return 0; // then the segments are equal if (p1_isStart !== p2_isStart) // if one is a start and the other isn't... return p1_isStart ? 1 : -1; // favor the one that isn't the start // otherwise, we'll have to calculate which one is below the other manually return eps.pointAboveOrOnLine(p1_2, p2_isStart ? p2_1 : p2_2, // order matters p2_isStart ? p2_2 : p2_1 ) ? 1 : -1; } function eventAdd(ev, other_pt){ event_root.insertBefore(ev, function(here){ // should ev be inserted before here? var comp = eventCompare( ev .isStart, ev .pt, other_pt, here.isStart, here.pt, here.other.pt ); return comp < 0; }); } function eventAddSegmentStart(seg, primary){ var ev_start = LinkedList.node({ isStart: true, pt: seg.start, seg: seg, primary: primary, other: null, status: null }); eventAdd(ev_start, seg.end); return ev_start; } function eventAddSegmentEnd(ev_start, seg, primary){ var ev_end = LinkedList.node({ isStart: false, pt: seg.end, seg: seg, primary: primary, other: ev_start, status: null }); ev_start.other = ev_end; eventAdd(ev_end, ev_start.pt); } function eventAddSegment(seg, primary){ var ev_start = eventAddSegmentStart(seg, primary); eventAddSegmentEnd(ev_start, seg, primary); return ev_start; } function eventUpdateEnd(ev, end){ // slides an end backwards // (start)------------(end) to: // (start)---(end) if (buildLog) buildLog.segmentChop(ev.seg, end); ev.other.remove(); ev.seg.end = end; ev.other.pt = end; eventAdd(ev.other, ev.pt); } function eventDivide(ev, pt){ var ns = segmentCopy(pt, ev.seg.end, ev.seg); eventUpdateEnd(ev, pt); return eventAddSegment(ns, ev.primary); } function calculate(primaryPolyInverted, secondaryPolyInverted){ // if selfIntersection is true then there is no secondary polygon, so that isn't used // // status logic // var status_root = LinkedList.create(); function statusCompare(ev1, ev2){ var a1 = ev1.seg.start; var a2 = ev1.seg.end; var b1 = ev2.seg.start; var b2 = ev2.seg.end; if (eps.pointsCollinear(a1, b1, b2)){ if (eps.pointsCollinear(a2, b1, b2)) return 1;//eventCompare(true, a1, a2, true, b1, b2); return eps.pointAboveOrOnLine(a2, b1, b2) ? 1 : -1; } return eps.pointAboveOrOnLine(a1, b1, b2) ? 1 : -1; } function statusFindSurrounding(ev){ return status_root.findTransition(function(here){ var comp = statusCompare(ev, here.ev); return comp > 0; }); } function checkIntersection(ev1, ev2){ // returns the segment equal to ev1, or false if nothing equal var seg1 = ev1.seg; var seg2 = ev2.seg; var a1 = seg1.start; var a2 = seg1.end; var b1 = seg2.start; var b2 = seg2.end; if (buildLog) buildLog.checkIntersection(seg1, seg2); var i = eps.linesIntersect(a1, a2, b1, b2); if (i === false){ // segments are parallel or coincident // if points aren't collinear, then the segments are parallel, so no intersections if (!eps.pointsCollinear(a1, a2, b1)) return false; // otherwise, segments are on top of each other somehow (aka coincident) if (eps.pointsSame(a1, b2) || eps.pointsSame(a2, b1)) return false; // segments touch at endpoints... no intersection var a1_equ_b1 = eps.pointsSame(a1, b1); var a2_equ_b2 = eps.pointsSame(a2, b2); if (a1_equ_b1 && a2_equ_b2) return ev2; // segments are exactly equal var a1_between = !a1_equ_b1 && eps.pointBetween(a1, b1, b2); var a2_between = !a2_equ_b2 && eps.pointBetween(a2, b1, b2); // handy for debugging: // buildLog.log({ // a1_equ_b1: a1_equ_b1, // a2_equ_b2: a2_equ_b2, // a1_between: a1_between, // a2_between: a2_between // }); if (a1_equ_b1){ if (a2_between){ // (a1)---(a2) // (b1)----------(b2) eventDivide(ev2, a2); } else{ // (a1)----------(a2) // (b1)---(b2) eventDivide(ev1, b2); } return ev2; } else if (a1_between){ if (!a2_equ_b2){ // make a2 equal to b2 if (a2_between){ // (a1)---(a2) // (b1)-----------------(b2) eventDivide(ev2, a2); } else{ // (a1)----------(a2) // (b1)----------(b2) eventDivide(ev1, b2); } } // (a1)---(a2) // (b1)----------(b2) eventDivide(ev2, a1); } } else{ // otherwise, lines intersect at i.pt, which may or may not be between the endpoints // is A divided between its endpoints? (exclusive) if (i.alongA === 0){ if (i.alongB === -1) // yes, at exactly b1 eventDivide(ev1, b1); else if (i.alongB === 0) // yes, somewhere between B's endpoints eventDivide(ev1, i.pt); else if (i.alongB === 1) // yes, at exactly b2 eventDivide(ev1, b2); } // is B divided between its endpoints? (exclusive) if (i.alongB === 0){ if (i.alongA === -1) // yes, at exactly a1 eventDivide(ev2, a1); else if (i.alongA === 0) // yes, somewhere between A's endpoints (exclusive) eventDivide(ev2, i.pt); else if (i.alongA === 1) // yes, at exactly a2 eventDivide(ev2, a2); } } return false; } // // main event loop // var segments = []; while (!event_root.isEmpty()){ var ev = event_root.getHead(); if (buildLog) buildLog.vert(ev.pt[0]); if (ev.isStart){ if (buildLog) buildLog.segmentNew(ev.seg, ev.primary); var surrounding = statusFindSurrounding(ev); var above = surrounding.before ? surrounding.before.ev : null; var below = surrounding.after ? surrounding.after.ev : null; if (buildLog){ buildLog.tempStatus( ev.seg, above ? above.seg : false, below ? below.seg : false ); } function checkBothIntersections(){ if (above){ var eve = checkIntersection(ev, above); if (eve) return eve; } if (below) return checkIntersection(ev, below); return false; } var eve = checkBothIntersections(); if (eve){ // ev and eve are equal // we'll keep eve and throw away ev // merge ev.seg's fill information into eve.seg if (selfIntersection){ var toggle; // are we a toggling edge? if (ev.seg.myFill.below === null) toggle = true; else toggle = ev.seg.myFill.above !== ev.seg.myFill.below; // merge two segments that belong to the same polygon // think of this as sandwiching two segments together, where `eve.seg` is // the bottom -- this will cause the above fill flag to toggle if (toggle) eve.seg.myFill.above = !eve.seg.myFill.above; } else{ // merge two segments that belong to different polygons // each segment has distinct knowledge, so no special logic is needed // note that this can only happen once per segment in this phase, because we // are guaranteed that all self-intersections are gone eve.seg.otherFill = ev.seg.myFill; } if (buildLog) buildLog.segmentUpdate(eve.seg); ev.other.remove(); ev.remove(); } if (event_root.getHead() !== ev){ // something was inserted before us in the event queue, so loop back around and // process it before continuing if (buildLog) buildLog.rewind(ev.seg); continue; } // // calculate fill flags // if (selfIntersection){ var toggle; // are we a toggling edge? if (ev.seg.myFill.below === null) // if we are a new segment... toggle = true; // then we toggle else // we are a segment that has previous knowledge from a division toggle = ev.seg.myFill.above !== ev.seg.myFill.below; // calculate toggle // next, calculate whether we are filled below us if (!below){ // if nothing is below us... // we are filled below us if the polygon is inverted ev.seg.myFill.below = primaryPolyInverted; } else{ // otherwise, we know the answer -- it's the same if whatever is below // us is filled above it ev.seg.myFill.below = below.seg.myFill.above; } // since now we know if we're filled below us, we can calculate whether // we're filled above us by applying toggle to whatever is below us if (toggle) ev.seg.myFill.above = !ev.seg.myFill.below; else ev.seg.myFill.above = ev.seg.myFill.below; } else{ // now we fill in any missing transition information, since we are all-knowing // at this point if (ev.seg.otherFill === null){ // if we don't have other information, then we need to figure out if we're // inside the other polygon var inside; if (!below){ // if nothing is below us, then we're inside if the other polygon is // inverted inside = ev.primary ? secondaryPolyInverted : primaryPolyInverted; } else{ // otherwise, something is below us // so copy the below segment's other polygon's above if (ev.primary === below.primary) inside = below.seg.otherFill.above; else inside = below.seg.myFill.above; } ev.seg.otherFill = { above: inside, below: inside }; } } if (buildLog){ buildLog.status( ev.seg, above ? above.seg : false, below ? below.seg : false ); } // insert the status and remember it for later removal ev.other.status = surrounding.insert(LinkedList.node({ ev: ev })); } else{ var st = ev.status; if (st === null){ throw new Error('PolyBool: Zero-length segment detected; your epsilon is ' + 'probably too small or too large'); } // removing the status will create two new adjacent edges, so we'll need to check // for those if (status_root.exists(st.prev) && status_root.exists(st.next)) checkIntersection(st.prev.ev, st.next.ev); if (buildLog) buildLog.statusRemove(st.ev.seg); // remove the status st.remove(); // if we've reached this point, we've calculated everything there is to know, so // save the segment for reporting if (!ev.primary){ // make sure `seg.myFill` actually points to the primary polygon though var s = ev.seg.myFill; ev.seg.myFill = ev.seg.otherFill; ev.seg.otherFill = s; } segments.push(ev.seg); } // remove the event and continue event_root.getHead().remove(); } if (buildLog) buildLog.done(); return segments; } // return the appropriate API depending on what we're doing if (!selfIntersection){ // performing combination of polygons, so only deal with already-processed segments return { calculate: function(segments1, inverted1, segments2, inverted2){ // segmentsX come from the self-intersection API, or this API // invertedX is whether we treat that list of segments as an inverted polygon or not // returns segments that can be used for further operations segments1.forEach(function(seg){ eventAddSegment(segmentCopy(seg.start, seg.end, seg), true); }); segments2.forEach(function(seg){ eventAddSegment(segmentCopy(seg.start, seg.end, seg), false); }); return calculate(inverted1, inverted2); } }; } // otherwise, performing self-intersection, so deal with regions return { addRegion: function(region){ // regions are a list of points: // [ [0, 0], [100, 0], [50, 100] ] // you can add multiple regions before running calculate var pt1; var pt2 = region[region.length - 1]; for (var i = 0; i < region.length; i++){ pt1 = pt2; pt2 = region[i]; var forward = eps.pointsCompare(pt1, pt2); if (forward === 0) // points are equal, so we have a zero-length segment continue; // just skip it eventAddSegment( segmentNew( forward < 0 ? pt1 : pt2, forward < 0 ? pt2 : pt1 ), true ); } }, calculate: function(inverted){ // is the polygon inverted? // returns segments return calculate(inverted, false); } }; } module.exports = Intersecter;