node-red-contrib-tak-registration
Version:
A Node-RED node to register to TAK and to help wrap files as datapackages to send to TAK
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JavaScript
import SplayTree from 'splaytree';
import { orient2d } from 'robust-predicates';
/**
* A bounding box has the format:
*
* { ll: { x: xmin, y: ymin }, ur: { x: xmax, y: ymax } }
*
*/
const isInBbox = (bbox, point) => {
return bbox.ll.x <= point.x && point.x <= bbox.ur.x && bbox.ll.y <= point.y && point.y <= bbox.ur.y;
};
/* Returns either null, or a bbox (aka an ordered pair of points)
* If there is only one point of overlap, a bbox with identical points
* will be returned */
const getBboxOverlap = (b1, b2) => {
// check if the bboxes overlap at all
if (b2.ur.x < b1.ll.x || b1.ur.x < b2.ll.x || b2.ur.y < b1.ll.y || b1.ur.y < b2.ll.y) return null;
// find the middle two X values
const lowerX = b1.ll.x < b2.ll.x ? b2.ll.x : b1.ll.x;
const upperX = b1.ur.x < b2.ur.x ? b1.ur.x : b2.ur.x;
// find the middle two Y values
const lowerY = b1.ll.y < b2.ll.y ? b2.ll.y : b1.ll.y;
const upperY = b1.ur.y < b2.ur.y ? b1.ur.y : b2.ur.y;
// put those middle values together to get the overlap
return {
ll: {
x: lowerX,
y: lowerY
},
ur: {
x: upperX,
y: upperY
}
};
};
/* Javascript doesn't do integer math. Everything is
* floating point with percision Number.EPSILON.
*
* https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number/EPSILON
*/
let epsilon = Number.EPSILON;
// IE Polyfill
if (epsilon === undefined) epsilon = Math.pow(2, -52);
const EPSILON_SQ = epsilon * epsilon;
/* FLP comparator */
const cmp = (a, b) => {
// check if they're both 0
if (-epsilon < a && a < epsilon) {
if (-epsilon < b && b < epsilon) {
return 0;
}
}
// check if they're flp equal
const ab = a - b;
if (ab * ab < EPSILON_SQ * a * b) {
return 0;
}
// normal comparison
return a < b ? -1 : 1;
};
/**
* This class rounds incoming values sufficiently so that
* floating points problems are, for the most part, avoided.
*
* Incoming points are have their x & y values tested against
* all previously seen x & y values. If either is 'too close'
* to a previously seen value, it's value is 'snapped' to the
* previously seen value.
*
* All points should be rounded by this class before being
* stored in any data structures in the rest of this algorithm.
*/
class PtRounder {
constructor() {
this.reset();
}
reset() {
this.xRounder = new CoordRounder();
this.yRounder = new CoordRounder();
}
round(x, y) {
return {
x: this.xRounder.round(x),
y: this.yRounder.round(y)
};
}
}
class CoordRounder {
constructor() {
this.tree = new SplayTree();
// preseed with 0 so we don't end up with values < Number.EPSILON
this.round(0);
}
// Note: this can rounds input values backwards or forwards.
// You might ask, why not restrict this to just rounding
// forwards? Wouldn't that allow left endpoints to always
// remain left endpoints during splitting (never change to
// right). No - it wouldn't, because we snap intersections
// to endpoints (to establish independence from the segment
// angle for t-intersections).
round(coord) {
const node = this.tree.add(coord);
const prevNode = this.tree.prev(node);
if (prevNode !== null && cmp(node.key, prevNode.key) === 0) {
this.tree.remove(coord);
return prevNode.key;
}
const nextNode = this.tree.next(node);
if (nextNode !== null && cmp(node.key, nextNode.key) === 0) {
this.tree.remove(coord);
return nextNode.key;
}
return coord;
}
}
// singleton available by import
const rounder = new PtRounder();
/* Cross Product of two vectors with first point at origin */
const crossProduct = (a, b) => a.x * b.y - a.y * b.x;
/* Dot Product of two vectors with first point at origin */
const dotProduct = (a, b) => a.x * b.x + a.y * b.y;
/* Comparator for two vectors with same starting point */
const compareVectorAngles = (basePt, endPt1, endPt2) => {
const res = orient2d(basePt.x, basePt.y, endPt1.x, endPt1.y, endPt2.x, endPt2.y);
if (res > 0) return -1;
if (res < 0) return 1;
return 0;
};
const length = v => Math.sqrt(dotProduct(v, v));
/* Get the sine of the angle from pShared -> pAngle to pShaed -> pBase */
const sineOfAngle = (pShared, pBase, pAngle) => {
const vBase = {
x: pBase.x - pShared.x,
y: pBase.y - pShared.y
};
const vAngle = {
x: pAngle.x - pShared.x,
y: pAngle.y - pShared.y
};
return crossProduct(vAngle, vBase) / length(vAngle) / length(vBase);
};
/* Get the cosine of the angle from pShared -> pAngle to pShaed -> pBase */
const cosineOfAngle = (pShared, pBase, pAngle) => {
const vBase = {
x: pBase.x - pShared.x,
y: pBase.y - pShared.y
};
const vAngle = {
x: pAngle.x - pShared.x,
y: pAngle.y - pShared.y
};
return dotProduct(vAngle, vBase) / length(vAngle) / length(vBase);
};
/* Get the x coordinate where the given line (defined by a point and vector)
* crosses the horizontal line with the given y coordiante.
* In the case of parrallel lines (including overlapping ones) returns null. */
const horizontalIntersection = (pt, v, y) => {
if (v.y === 0) return null;
return {
x: pt.x + v.x / v.y * (y - pt.y),
y: y
};
};
/* Get the y coordinate where the given line (defined by a point and vector)
* crosses the vertical line with the given x coordiante.
* In the case of parrallel lines (including overlapping ones) returns null. */
const verticalIntersection = (pt, v, x) => {
if (v.x === 0) return null;
return {
x: x,
y: pt.y + v.y / v.x * (x - pt.x)
};
};
/* Get the intersection of two lines, each defined by a base point and a vector.
* In the case of parrallel lines (including overlapping ones) returns null. */
const intersection$1 = (pt1, v1, pt2, v2) => {
// take some shortcuts for vertical and horizontal lines
// this also ensures we don't calculate an intersection and then discover
// it's actually outside the bounding box of the line
if (v1.x === 0) return verticalIntersection(pt2, v2, pt1.x);
if (v2.x === 0) return verticalIntersection(pt1, v1, pt2.x);
if (v1.y === 0) return horizontalIntersection(pt2, v2, pt1.y);
if (v2.y === 0) return horizontalIntersection(pt1, v1, pt2.y);
// General case for non-overlapping segments.
// This algorithm is based on Schneider and Eberly.
// http://www.cimec.org.ar/~ncalvo/Schneider_Eberly.pdf - pg 244
const kross = crossProduct(v1, v2);
if (kross == 0) return null;
const ve = {
x: pt2.x - pt1.x,
y: pt2.y - pt1.y
};
const d1 = crossProduct(ve, v1) / kross;
const d2 = crossProduct(ve, v2) / kross;
// take the average of the two calculations to minimize rounding error
const x1 = pt1.x + d2 * v1.x,
x2 = pt2.x + d1 * v2.x;
const y1 = pt1.y + d2 * v1.y,
y2 = pt2.y + d1 * v2.y;
const x = (x1 + x2) / 2;
const y = (y1 + y2) / 2;
return {
x: x,
y: y
};
};
class SweepEvent {
// for ordering sweep events in the sweep event queue
static compare(a, b) {
// favor event with a point that the sweep line hits first
const ptCmp = SweepEvent.comparePoints(a.point, b.point);
if (ptCmp !== 0) return ptCmp;
// the points are the same, so link them if needed
if (a.point !== b.point) a.link(b);
// favor right events over left
if (a.isLeft !== b.isLeft) return a.isLeft ? 1 : -1;
// we have two matching left or right endpoints
// ordering of this case is the same as for their segments
return Segment.compare(a.segment, b.segment);
}
// for ordering points in sweep line order
static comparePoints(aPt, bPt) {
if (aPt.x < bPt.x) return -1;
if (aPt.x > bPt.x) return 1;
if (aPt.y < bPt.y) return -1;
if (aPt.y > bPt.y) return 1;
return 0;
}
// Warning: 'point' input will be modified and re-used (for performance)
constructor(point, isLeft) {
if (point.events === undefined) point.events = [this];else point.events.push(this);
this.point = point;
this.isLeft = isLeft;
// this.segment, this.otherSE set by factory
}
link(other) {
if (other.point === this.point) {
throw new Error("Tried to link already linked events");
}
const otherEvents = other.point.events;
for (let i = 0, iMax = otherEvents.length; i < iMax; i++) {
const evt = otherEvents[i];
this.point.events.push(evt);
evt.point = this.point;
}
this.checkForConsuming();
}
/* Do a pass over our linked events and check to see if any pair
* of segments match, and should be consumed. */
checkForConsuming() {
// FIXME: The loops in this method run O(n^2) => no good.
// Maintain little ordered sweep event trees?
// Can we maintaining an ordering that avoids the need
// for the re-sorting with getLeftmostComparator in geom-out?
// Compare each pair of events to see if other events also match
const numEvents = this.point.events.length;
for (let i = 0; i < numEvents; i++) {
const evt1 = this.point.events[i];
if (evt1.segment.consumedBy !== undefined) continue;
for (let j = i + 1; j < numEvents; j++) {
const evt2 = this.point.events[j];
if (evt2.consumedBy !== undefined) continue;
if (evt1.otherSE.point.events !== evt2.otherSE.point.events) continue;
evt1.segment.consume(evt2.segment);
}
}
}
getAvailableLinkedEvents() {
// point.events is always of length 2 or greater
const events = [];
for (let i = 0, iMax = this.point.events.length; i < iMax; i++) {
const evt = this.point.events[i];
if (evt !== this && !evt.segment.ringOut && evt.segment.isInResult()) {
events.push(evt);
}
}
return events;
}
/**
* Returns a comparator function for sorting linked events that will
* favor the event that will give us the smallest left-side angle.
* All ring construction starts as low as possible heading to the right,
* so by always turning left as sharp as possible we'll get polygons
* without uncessary loops & holes.
*
* The comparator function has a compute cache such that it avoids
* re-computing already-computed values.
*/
getLeftmostComparator(baseEvent) {
const cache = new Map();
const fillCache = linkedEvent => {
const nextEvent = linkedEvent.otherSE;
cache.set(linkedEvent, {
sine: sineOfAngle(this.point, baseEvent.point, nextEvent.point),
cosine: cosineOfAngle(this.point, baseEvent.point, nextEvent.point)
});
};
return (a, b) => {
if (!cache.has(a)) fillCache(a);
if (!cache.has(b)) fillCache(b);
const {
sine: asine,
cosine: acosine
} = cache.get(a);
const {
sine: bsine,
cosine: bcosine
} = cache.get(b);
// both on or above x-axis
if (asine >= 0 && bsine >= 0) {
if (acosine < bcosine) return 1;
if (acosine > bcosine) return -1;
return 0;
}
// both below x-axis
if (asine < 0 && bsine < 0) {
if (acosine < bcosine) return -1;
if (acosine > bcosine) return 1;
return 0;
}
// one above x-axis, one below
if (bsine < asine) return -1;
if (bsine > asine) return 1;
return 0;
};
}
}
// Give segments unique ID's to get consistent sorting of
// segments and sweep events when all else is identical
let segmentId = 0;
class Segment {
/* This compare() function is for ordering segments in the sweep
* line tree, and does so according to the following criteria:
*
* Consider the vertical line that lies an infinestimal step to the
* right of the right-more of the two left endpoints of the input
* segments. Imagine slowly moving a point up from negative infinity
* in the increasing y direction. Which of the two segments will that
* point intersect first? That segment comes 'before' the other one.
*
* If neither segment would be intersected by such a line, (if one
* or more of the segments are vertical) then the line to be considered
* is directly on the right-more of the two left inputs.
*/
static compare(a, b) {
const alx = a.leftSE.point.x;
const blx = b.leftSE.point.x;
const arx = a.rightSE.point.x;
const brx = b.rightSE.point.x;
// check if they're even in the same vertical plane
if (brx < alx) return 1;
if (arx < blx) return -1;
const aly = a.leftSE.point.y;
const bly = b.leftSE.point.y;
const ary = a.rightSE.point.y;
const bry = b.rightSE.point.y;
// is left endpoint of segment B the right-more?
if (alx < blx) {
// are the two segments in the same horizontal plane?
if (bly < aly && bly < ary) return 1;
if (bly > aly && bly > ary) return -1;
// is the B left endpoint colinear to segment A?
const aCmpBLeft = a.comparePoint(b.leftSE.point);
if (aCmpBLeft < 0) return 1;
if (aCmpBLeft > 0) return -1;
// is the A right endpoint colinear to segment B ?
const bCmpARight = b.comparePoint(a.rightSE.point);
if (bCmpARight !== 0) return bCmpARight;
// colinear segments, consider the one with left-more
// left endpoint to be first (arbitrary?)
return -1;
}
// is left endpoint of segment A the right-more?
if (alx > blx) {
if (aly < bly && aly < bry) return -1;
if (aly > bly && aly > bry) return 1;
// is the A left endpoint colinear to segment B?
const bCmpALeft = b.comparePoint(a.leftSE.point);
if (bCmpALeft !== 0) return bCmpALeft;
// is the B right endpoint colinear to segment A?
const aCmpBRight = a.comparePoint(b.rightSE.point);
if (aCmpBRight < 0) return 1;
if (aCmpBRight > 0) return -1;
// colinear segments, consider the one with left-more
// left endpoint to be first (arbitrary?)
return 1;
}
// if we get here, the two left endpoints are in the same
// vertical plane, ie alx === blx
// consider the lower left-endpoint to come first
if (aly < bly) return -1;
if (aly > bly) return 1;
// left endpoints are identical
// check for colinearity by using the left-more right endpoint
// is the A right endpoint more left-more?
if (arx < brx) {
const bCmpARight = b.comparePoint(a.rightSE.point);
if (bCmpARight !== 0) return bCmpARight;
}
// is the B right endpoint more left-more?
if (arx > brx) {
const aCmpBRight = a.comparePoint(b.rightSE.point);
if (aCmpBRight < 0) return 1;
if (aCmpBRight > 0) return -1;
}
if (arx !== brx) {
// are these two [almost] vertical segments with opposite orientation?
// if so, the one with the lower right endpoint comes first
const ay = ary - aly;
const ax = arx - alx;
const by = bry - bly;
const bx = brx - blx;
if (ay > ax && by < bx) return 1;
if (ay < ax && by > bx) return -1;
}
// we have colinear segments with matching orientation
// consider the one with more left-more right endpoint to be first
if (arx > brx) return 1;
if (arx < brx) return -1;
// if we get here, two two right endpoints are in the same
// vertical plane, ie arx === brx
// consider the lower right-endpoint to come first
if (ary < bry) return -1;
if (ary > bry) return 1;
// right endpoints identical as well, so the segments are idential
// fall back on creation order as consistent tie-breaker
if (a.id < b.id) return -1;
if (a.id > b.id) return 1;
// identical segment, ie a === b
return 0;
}
/* Warning: a reference to ringWindings input will be stored,
* and possibly will be later modified */
constructor(leftSE, rightSE, rings, windings) {
this.id = ++segmentId;
this.leftSE = leftSE;
leftSE.segment = this;
leftSE.otherSE = rightSE;
this.rightSE = rightSE;
rightSE.segment = this;
rightSE.otherSE = leftSE;
this.rings = rings;
this.windings = windings;
// left unset for performance, set later in algorithm
// this.ringOut, this.consumedBy, this.prev
}
static fromRing(pt1, pt2, ring) {
let leftPt, rightPt, winding;
// ordering the two points according to sweep line ordering
const cmpPts = SweepEvent.comparePoints(pt1, pt2);
if (cmpPts < 0) {
leftPt = pt1;
rightPt = pt2;
winding = 1;
} else if (cmpPts > 0) {
leftPt = pt2;
rightPt = pt1;
winding = -1;
} else throw new Error(`Tried to create degenerate segment at [${pt1.x}, ${pt1.y}]`);
const leftSE = new SweepEvent(leftPt, true);
const rightSE = new SweepEvent(rightPt, false);
return new Segment(leftSE, rightSE, [ring], [winding]);
}
/* When a segment is split, the rightSE is replaced with a new sweep event */
replaceRightSE(newRightSE) {
this.rightSE = newRightSE;
this.rightSE.segment = this;
this.rightSE.otherSE = this.leftSE;
this.leftSE.otherSE = this.rightSE;
}
bbox() {
const y1 = this.leftSE.point.y;
const y2 = this.rightSE.point.y;
return {
ll: {
x: this.leftSE.point.x,
y: y1 < y2 ? y1 : y2
},
ur: {
x: this.rightSE.point.x,
y: y1 > y2 ? y1 : y2
}
};
}
/* A vector from the left point to the right */
vector() {
return {
x: this.rightSE.point.x - this.leftSE.point.x,
y: this.rightSE.point.y - this.leftSE.point.y
};
}
isAnEndpoint(pt) {
return pt.x === this.leftSE.point.x && pt.y === this.leftSE.point.y || pt.x === this.rightSE.point.x && pt.y === this.rightSE.point.y;
}
/* Compare this segment with a point.
*
* A point P is considered to be colinear to a segment if there
* exists a distance D such that if we travel along the segment
* from one * endpoint towards the other a distance D, we find
* ourselves at point P.
*
* Return value indicates:
*
* 1: point lies above the segment (to the left of vertical)
* 0: point is colinear to segment
* -1: point lies below the segment (to the right of vertical)
*/
comparePoint(point) {
if (this.isAnEndpoint(point)) return 0;
const lPt = this.leftSE.point;
const rPt = this.rightSE.point;
const v = this.vector();
// Exactly vertical segments.
if (lPt.x === rPt.x) {
if (point.x === lPt.x) return 0;
return point.x < lPt.x ? 1 : -1;
}
// Nearly vertical segments with an intersection.
// Check to see where a point on the line with matching Y coordinate is.
const yDist = (point.y - lPt.y) / v.y;
const xFromYDist = lPt.x + yDist * v.x;
if (point.x === xFromYDist) return 0;
// General case.
// Check to see where a point on the line with matching X coordinate is.
const xDist = (point.x - lPt.x) / v.x;
const yFromXDist = lPt.y + xDist * v.y;
if (point.y === yFromXDist) return 0;
return point.y < yFromXDist ? -1 : 1;
}
/**
* Given another segment, returns the first non-trivial intersection
* between the two segments (in terms of sweep line ordering), if it exists.
*
* A 'non-trivial' intersection is one that will cause one or both of the
* segments to be split(). As such, 'trivial' vs. 'non-trivial' intersection:
*
* * endpoint of segA with endpoint of segB --> trivial
* * endpoint of segA with point along segB --> non-trivial
* * endpoint of segB with point along segA --> non-trivial
* * point along segA with point along segB --> non-trivial
*
* If no non-trivial intersection exists, return null
* Else, return null.
*/
getIntersection(other) {
// If bboxes don't overlap, there can't be any intersections
const tBbox = this.bbox();
const oBbox = other.bbox();
const bboxOverlap = getBboxOverlap(tBbox, oBbox);
if (bboxOverlap === null) return null;
// We first check to see if the endpoints can be considered intersections.
// This will 'snap' intersections to endpoints if possible, and will
// handle cases of colinearity.
const tlp = this.leftSE.point;
const trp = this.rightSE.point;
const olp = other.leftSE.point;
const orp = other.rightSE.point;
// does each endpoint touch the other segment?
// note that we restrict the 'touching' definition to only allow segments
// to touch endpoints that lie forward from where we are in the sweep line pass
const touchesOtherLSE = isInBbox(tBbox, olp) && this.comparePoint(olp) === 0;
const touchesThisLSE = isInBbox(oBbox, tlp) && other.comparePoint(tlp) === 0;
const touchesOtherRSE = isInBbox(tBbox, orp) && this.comparePoint(orp) === 0;
const touchesThisRSE = isInBbox(oBbox, trp) && other.comparePoint(trp) === 0;
// do left endpoints match?
if (touchesThisLSE && touchesOtherLSE) {
// these two cases are for colinear segments with matching left
// endpoints, and one segment being longer than the other
if (touchesThisRSE && !touchesOtherRSE) return trp;
if (!touchesThisRSE && touchesOtherRSE) return orp;
// either the two segments match exactly (two trival intersections)
// or just on their left endpoint (one trivial intersection
return null;
}
// does this left endpoint matches (other doesn't)
if (touchesThisLSE) {
// check for segments that just intersect on opposing endpoints
if (touchesOtherRSE) {
if (tlp.x === orp.x && tlp.y === orp.y) return null;
}
// t-intersection on left endpoint
return tlp;
}
// does other left endpoint matches (this doesn't)
if (touchesOtherLSE) {
// check for segments that just intersect on opposing endpoints
if (touchesThisRSE) {
if (trp.x === olp.x && trp.y === olp.y) return null;
}
// t-intersection on left endpoint
return olp;
}
// trivial intersection on right endpoints
if (touchesThisRSE && touchesOtherRSE) return null;
// t-intersections on just one right endpoint
if (touchesThisRSE) return trp;
if (touchesOtherRSE) return orp;
// None of our endpoints intersect. Look for a general intersection between
// infinite lines laid over the segments
const pt = intersection$1(tlp, this.vector(), olp, other.vector());
// are the segments parrallel? Note that if they were colinear with overlap,
// they would have an endpoint intersection and that case was already handled above
if (pt === null) return null;
// is the intersection found between the lines not on the segments?
if (!isInBbox(bboxOverlap, pt)) return null;
// round the the computed point if needed
return rounder.round(pt.x, pt.y);
}
/**
* Split the given segment into multiple segments on the given points.
* * Each existing segment will retain its leftSE and a new rightSE will be
* generated for it.
* * A new segment will be generated which will adopt the original segment's
* rightSE, and a new leftSE will be generated for it.
* * If there are more than two points given to split on, new segments
* in the middle will be generated with new leftSE and rightSE's.
* * An array of the newly generated SweepEvents will be returned.
*
* Warning: input array of points is modified
*/
split(point) {
const newEvents = [];
const alreadyLinked = point.events !== undefined;
const newLeftSE = new SweepEvent(point, true);
const newRightSE = new SweepEvent(point, false);
const oldRightSE = this.rightSE;
this.replaceRightSE(newRightSE);
newEvents.push(newRightSE);
newEvents.push(newLeftSE);
const newSeg = new Segment(newLeftSE, oldRightSE, this.rings.slice(), this.windings.slice());
// when splitting a nearly vertical downward-facing segment,
// sometimes one of the resulting new segments is vertical, in which
// case its left and right events may need to be swapped
if (SweepEvent.comparePoints(newSeg.leftSE.point, newSeg.rightSE.point) > 0) {
newSeg.swapEvents();
}
if (SweepEvent.comparePoints(this.leftSE.point, this.rightSE.point) > 0) {
this.swapEvents();
}
// in the point we just used to create new sweep events with was already
// linked to other events, we need to check if either of the affected
// segments should be consumed
if (alreadyLinked) {
newLeftSE.checkForConsuming();
newRightSE.checkForConsuming();
}
return newEvents;
}
/* Swap which event is left and right */
swapEvents() {
const tmpEvt = this.rightSE;
this.rightSE = this.leftSE;
this.leftSE = tmpEvt;
this.leftSE.isLeft = true;
this.rightSE.isLeft = false;
for (let i = 0, iMax = this.windings.length; i < iMax; i++) {
this.windings[i] *= -1;
}
}
/* Consume another segment. We take their rings under our wing
* and mark them as consumed. Use for perfectly overlapping segments */
consume(other) {
let consumer = this;
let consumee = other;
while (consumer.consumedBy) consumer = consumer.consumedBy;
while (consumee.consumedBy) consumee = consumee.consumedBy;
const cmp = Segment.compare(consumer, consumee);
if (cmp === 0) return; // already consumed
// the winner of the consumption is the earlier segment
// according to sweep line ordering
if (cmp > 0) {
const tmp = consumer;
consumer = consumee;
consumee = tmp;
}
// make sure a segment doesn't consume it's prev
if (consumer.prev === consumee) {
const tmp = consumer;
consumer = consumee;
consumee = tmp;
}
for (let i = 0, iMax = consumee.rings.length; i < iMax; i++) {
const ring = consumee.rings[i];
const winding = consumee.windings[i];
const index = consumer.rings.indexOf(ring);
if (index === -1) {
consumer.rings.push(ring);
consumer.windings.push(winding);
} else consumer.windings[index] += winding;
}
consumee.rings = null;
consumee.windings = null;
consumee.consumedBy = consumer;
// mark sweep events consumed as to maintain ordering in sweep event queue
consumee.leftSE.consumedBy = consumer.leftSE;
consumee.rightSE.consumedBy = consumer.rightSE;
}
/* The first segment previous segment chain that is in the result */
prevInResult() {
if (this._prevInResult !== undefined) return this._prevInResult;
if (!this.prev) this._prevInResult = null;else if (this.prev.isInResult()) this._prevInResult = this.prev;else this._prevInResult = this.prev.prevInResult();
return this._prevInResult;
}
beforeState() {
if (this._beforeState !== undefined) return this._beforeState;
if (!this.prev) this._beforeState = {
rings: [],
windings: [],
multiPolys: []
};else {
const seg = this.prev.consumedBy || this.prev;
this._beforeState = seg.afterState();
}
return this._beforeState;
}
afterState() {
if (this._afterState !== undefined) return this._afterState;
const beforeState = this.beforeState();
this._afterState = {
rings: beforeState.rings.slice(0),
windings: beforeState.windings.slice(0),
multiPolys: []
};
const ringsAfter = this._afterState.rings;
const windingsAfter = this._afterState.windings;
const mpsAfter = this._afterState.multiPolys;
// calculate ringsAfter, windingsAfter
for (let i = 0, iMax = this.rings.length; i < iMax; i++) {
const ring = this.rings[i];
const winding = this.windings[i];
const index = ringsAfter.indexOf(ring);
if (index === -1) {
ringsAfter.push(ring);
windingsAfter.push(winding);
} else windingsAfter[index] += winding;
}
// calcualte polysAfter
const polysAfter = [];
const polysExclude = [];
for (let i = 0, iMax = ringsAfter.length; i < iMax; i++) {
if (windingsAfter[i] === 0) continue; // non-zero rule
const ring = ringsAfter[i];
const poly = ring.poly;
if (polysExclude.indexOf(poly) !== -1) continue;
if (ring.isExterior) polysAfter.push(poly);else {
if (polysExclude.indexOf(poly) === -1) polysExclude.push(poly);
const index = polysAfter.indexOf(ring.poly);
if (index !== -1) polysAfter.splice(index, 1);
}
}
// calculate multiPolysAfter
for (let i = 0, iMax = polysAfter.length; i < iMax; i++) {
const mp = polysAfter[i].multiPoly;
if (mpsAfter.indexOf(mp) === -1) mpsAfter.push(mp);
}
return this._afterState;
}
/* Is this segment part of the final result? */
isInResult() {
// if we've been consumed, we're not in the result
if (this.consumedBy) return false;
if (this._isInResult !== undefined) return this._isInResult;
const mpsBefore = this.beforeState().multiPolys;
const mpsAfter = this.afterState().multiPolys;
switch (operation.type) {
case "union":
{
// UNION - included iff:
// * On one side of us there is 0 poly interiors AND
// * On the other side there is 1 or more.
const noBefores = mpsBefore.length === 0;
const noAfters = mpsAfter.length === 0;
this._isInResult = noBefores !== noAfters;
break;
}
case "intersection":
{
// INTERSECTION - included iff:
// * on one side of us all multipolys are rep. with poly interiors AND
// * on the other side of us, not all multipolys are repsented
// with poly interiors
let least;
let most;
if (mpsBefore.length < mpsAfter.length) {
least = mpsBefore.length;
most = mpsAfter.length;
} else {
least = mpsAfter.length;
most = mpsBefore.length;
}
this._isInResult = most === operation.numMultiPolys && least < most;
break;
}
case "xor":
{
// XOR - included iff:
// * the difference between the number of multipolys represented
// with poly interiors on our two sides is an odd number
const diff = Math.abs(mpsBefore.length - mpsAfter.length);
this._isInResult = diff % 2 === 1;
break;
}
case "difference":
{
// DIFFERENCE included iff:
// * on exactly one side, we have just the subject
const isJustSubject = mps => mps.length === 1 && mps[0].isSubject;
this._isInResult = isJustSubject(mpsBefore) !== isJustSubject(mpsAfter);
break;
}
default:
throw new Error(`Unrecognized operation type found ${operation.type}`);
}
return this._isInResult;
}
}
class RingIn {
constructor(geomRing, poly, isExterior) {
if (!Array.isArray(geomRing) || geomRing.length === 0) {
throw new Error("Input geometry is not a valid Polygon or MultiPolygon");
}
this.poly = poly;
this.isExterior = isExterior;
this.segments = [];
if (typeof geomRing[0][0] !== "number" || typeof geomRing[0][1] !== "number") {
throw new Error("Input geometry is not a valid Polygon or MultiPolygon");
}
const firstPoint = rounder.round(geomRing[0][0], geomRing[0][1]);
this.bbox = {
ll: {
x: firstPoint.x,
y: firstPoint.y
},
ur: {
x: firstPoint.x,
y: firstPoint.y
}
};
let prevPoint = firstPoint;
for (let i = 1, iMax = geomRing.length; i < iMax; i++) {
if (typeof geomRing[i][0] !== "number" || typeof geomRing[i][1] !== "number") {
throw new Error("Input geometry is not a valid Polygon or MultiPolygon");
}
let point = rounder.round(geomRing[i][0], geomRing[i][1]);
// skip repeated points
if (point.x === prevPoint.x && point.y === prevPoint.y) continue;
this.segments.push(Segment.fromRing(prevPoint, point, this));
if (point.x < this.bbox.ll.x) this.bbox.ll.x = point.x;
if (point.y < this.bbox.ll.y) this.bbox.ll.y = point.y;
if (point.x > this.bbox.ur.x) this.bbox.ur.x = point.x;
if (point.y > this.bbox.ur.y) this.bbox.ur.y = point.y;
prevPoint = point;
}
// add segment from last to first if last is not the same as first
if (firstPoint.x !== prevPoint.x || firstPoint.y !== prevPoint.y) {
this.segments.push(Segment.fromRing(prevPoint, firstPoint, this));
}
}
getSweepEvents() {
const sweepEvents = [];
for (let i = 0, iMax = this.segments.length; i < iMax; i++) {
const segment = this.segments[i];
sweepEvents.push(segment.leftSE);
sweepEvents.push(segment.rightSE);
}
return sweepEvents;
}
}
class PolyIn {
constructor(geomPoly, multiPoly) {
if (!Array.isArray(geomPoly)) {
throw new Error("Input geometry is not a valid Polygon or MultiPolygon");
}
this.exteriorRing = new RingIn(geomPoly[0], this, true);
// copy by value
this.bbox = {
ll: {
x: this.exteriorRing.bbox.ll.x,
y: this.exteriorRing.bbox.ll.y
},
ur: {
x: this.exteriorRing.bbox.ur.x,
y: this.exteriorRing.bbox.ur.y
}
};
this.interiorRings = [];
for (let i = 1, iMax = geomPoly.length; i < iMax; i++) {
const ring = new RingIn(geomPoly[i], this, false);
if (ring.bbox.ll.x < this.bbox.ll.x) this.bbox.ll.x = ring.bbox.ll.x;
if (ring.bbox.ll.y < this.bbox.ll.y) this.bbox.ll.y = ring.bbox.ll.y;
if (ring.bbox.ur.x > this.bbox.ur.x) this.bbox.ur.x = ring.bbox.ur.x;
if (ring.bbox.ur.y > this.bbox.ur.y) this.bbox.ur.y = ring.bbox.ur.y;
this.interiorRings.push(ring);
}
this.multiPoly = multiPoly;
}
getSweepEvents() {
const sweepEvents = this.exteriorRing.getSweepEvents();
for (let i = 0, iMax = this.interiorRings.length; i < iMax; i++) {
const ringSweepEvents = this.interiorRings[i].getSweepEvents();
for (let j = 0, jMax = ringSweepEvents.length; j < jMax; j++) {
sweepEvents.push(ringSweepEvents[j]);
}
}
return sweepEvents;
}
}
class MultiPolyIn {
constructor(geom, isSubject) {
if (!Array.isArray(geom)) {
throw new Error("Input geometry is not a valid Polygon or MultiPolygon");
}
try {
// if the input looks like a polygon, convert it to a multipolygon
if (typeof geom[0][0][0] === "number") geom = [geom];
} catch (ex) {
// The input is either malformed or has empty arrays.
// In either case, it will be handled later on.
}
this.polys = [];
this.bbox = {
ll: {
x: Number.POSITIVE_INFINITY,
y: Number.POSITIVE_INFINITY
},
ur: {
x: Number.NEGATIVE_INFINITY,
y: Number.NEGATIVE_INFINITY
}
};
for (let i = 0, iMax = geom.length; i < iMax; i++) {
const poly = new PolyIn(geom[i], this);
if (poly.bbox.ll.x < this.bbox.ll.x) this.bbox.ll.x = poly.bbox.ll.x;
if (poly.bbox.ll.y < this.bbox.ll.y) this.bbox.ll.y = poly.bbox.ll.y;
if (poly.bbox.ur.x > this.bbox.ur.x) this.bbox.ur.x = poly.bbox.ur.x;
if (poly.bbox.ur.y > this.bbox.ur.y) this.bbox.ur.y = poly.bbox.ur.y;
this.polys.push(poly);
}
this.isSubject = isSubject;
}
getSweepEvents() {
const sweepEvents = [];
for (let i = 0, iMax = this.polys.length; i < iMax; i++) {
const polySweepEvents = this.polys[i].getSweepEvents();
for (let j = 0, jMax = polySweepEvents.length; j < jMax; j++) {
sweepEvents.push(polySweepEvents[j]);
}
}
return sweepEvents;
}
}
class RingOut {
/* Given the segments from the sweep line pass, compute & return a series
* of closed rings from all the segments marked to be part of the result */
static factory(allSegments) {
const ringsOut = [];
for (let i = 0, iMax = allSegments.length; i < iMax; i++) {
const segment = allSegments[i];
if (!segment.isInResult() || segment.ringOut) continue;
let prevEvent = null;
let event = segment.leftSE;
let nextEvent = segment.rightSE;
const events = [event];
const startingPoint = event.point;
const intersectionLEs = [];
/* Walk the chain of linked events to form a closed ring */
while (true) {
prevEvent = event;
event = nextEvent;
events.push(event);
/* Is the ring complete? */
if (event.point === startingPoint) break;
while (true) {
const availableLEs = event.getAvailableLinkedEvents();
/* Did we hit a dead end? This shouldn't happen.
* Indicates some earlier part of the algorithm malfunctioned. */
if (availableLEs.length === 0) {
const firstPt = events[0].point;
const lastPt = events[events.length - 1].point;
throw new Error(`Unable to complete output ring starting at [${firstPt.x},` + ` ${firstPt.y}]. Last matching segment found ends at` + ` [${lastPt.x}, ${lastPt.y}].`);
}
/* Only one way to go, so cotinue on the path */
if (availableLEs.length === 1) {
nextEvent = availableLEs[0].otherSE;
break;
}
/* We must have an intersection. Check for a completed loop */
let indexLE = null;
for (let j = 0, jMax = intersectionLEs.length; j < jMax; j++) {
if (intersectionLEs[j].point === event.point) {
indexLE = j;
break;
}
}
/* Found a completed loop. Cut that off and make a ring */
if (indexLE !== null) {
const intersectionLE = intersectionLEs.splice(indexLE)[0];
const ringEvents = events.splice(intersectionLE.index);
ringEvents.unshift(ringEvents[0].otherSE);
ringsOut.push(new RingOut(ringEvents.reverse()));
continue;
}
/* register the intersection */
intersectionLEs.push({
index: events.length,
point: event.point
});
/* Choose the left-most option to continue the walk */
const comparator = event.getLeftmostComparator(prevEvent);
nextEvent = availableLEs.sort(comparator)[0].otherSE;
break;
}
}
ringsOut.push(new RingOut(events));
}
return ringsOut;
}
constructor(events) {
this.events = events;
for (let i = 0, iMax = events.length; i < iMax; i++) {
events[i].segment.ringOut = this;
}
this.poly = null;
}
getGeom() {
// Remove superfluous points (ie extra points along a straight line),
let prevPt = this.events[0].point;
const points = [prevPt];
for (let i = 1, iMax = this.events.length - 1; i < iMax; i++) {
const pt = this.events[i].point;
const nextPt = this.events[i + 1].point;
if (compareVectorAngles(pt, prevPt, nextPt) === 0) continue;
points.push(pt);
prevPt = pt;
}
// ring was all (within rounding error of angle calc) colinear points
if (points.length === 1) return null;
// check if the starting point is necessary
const pt = points[0];
const nextPt = points[1];
if (compareVectorAngles(pt, prevPt, nextPt) === 0) points.shift();
points.push(points[0]);
const step = this.isExteriorRing() ? 1 : -1;
const iStart = this.isExteriorRing() ? 0 : points.length - 1;
const iEnd = this.isExteriorRing() ? points.length : -1;
const orderedPoints = [];
for (let i = iStart; i != iEnd; i += step) orderedPoints.push([points[i].x, points[i].y]);
return orderedPoints;
}
isExteriorRing() {
if (this._isExteriorRing === undefined) {
const enclosing = this.enclosingRing();
this._isExteriorRing = enclosing ? !enclosing.isExteriorRing() : true;
}
return this._isExteriorRing;
}
enclosingRing() {
if (this._enclosingRing === undefined) {
this._enclosingRing = this._calcEnclosingRing();
}
return this._enclosingRing;
}
/* Returns the ring that encloses this one, if any */
_calcEnclosingRing() {
// start with the ealier sweep line event so that the prevSeg
// chain doesn't lead us inside of a loop of ours
let leftMostEvt = this.events[0];
for (let i = 1, iMax = this.events.length; i < iMax; i++) {
const evt = this.events[i];
if (SweepEvent.compare(leftMostEvt, evt) > 0) leftMostEvt = evt;
}
let prevSeg = leftMostEvt.segment.prevInResult();
let prevPrevSeg = prevSeg ? prevSeg.prevInResult() : null;
while (true) {
// no segment found, thus no ring can enclose us
if (!prevSeg) return null;
// no segments below prev segment found, thus the ring of the prev
// segment must loop back around and enclose us
if (!prevPrevSeg) return prevSeg.ringOut;
// if the two segments are of different rings, the ring of the prev
// segment must either loop around us or the ring of the prev prev
// seg, which would make us and the ring of the prev peers
if (prevPrevSeg.ringOut !== prevSeg.ringOut) {
if (prevPrevSeg.ringOut.enclosingRing() !== prevSeg.ringOut) {
return prevSeg.ringOut;
} else return prevSeg.ringOut.enclosingRing();
}
// two segments are from the same ring, so this was a penisula
// of that ring. iterate downward, keep searching
prevSeg = prevPrevSeg.prevInResult();
prevPrevSeg = prevSeg ? prevSeg.prevInResult() : null;
}
}
}
class PolyOut {
constructor(exteriorRing) {
this.exteriorRing = exteriorRing;
exteriorRing.poly = this;
this.interiorRings = [];
}
addInterior(ring) {
this.interiorRings.push(ring);
ring.poly = this;
}
getGeom() {
const geom = [this.exteriorRing.getGeom()];
// exterior ring was all (within rounding error of angle calc) colinear points
if (geom[0] === null) return null;
for (let i = 0, iMax = this.interiorRings.length; i < iMax; i++) {
const ringGeom = this.interiorRings[i].getGeom();
// interior ring was all (within rounding error of angle calc) colinear points
if (ringGeom === null) continue;
geom.push(ringGeom);
}
return geom;
}
}
class MultiPolyOut {
constructor(rings) {
this.rings = rings;
this.polys = this._composePolys(rings);
}
getGeom() {
const geom = [];
for (let i = 0, iMax = this.polys.length; i < iMax; i++) {
const polyGeom = this.polys[i].getGeom();
// exterior ring was all (within rounding error of angle calc) colinear points
if (polyGeom === null) continue;
geom.push(polyGeom);
}
return geom;
}
_composePolys(rings) {
const polys = [];
for (let i = 0, iMax = rings.length; i < iMax; i++) {
const ring = rings[i];
if (ring.poly) continue;
if (ring.isExteriorRing()) polys.push(new PolyOut(ring));else {
const enclosingRing = ring.enclosingRing();
if (!enclosingRing.poly) polys.push(new PolyOut(enclosingRing));
enclosingRing.poly.addInterior(ring);
}
}
return polys;
}
}
/**
* NOTE: We must be careful not to change any segments while
* they are in the SplayTree. AFAIK, there's no way to tell
* the tree to rebalance itself - thus before splitting
* a segment that's in the tree, we remove it from the tree,
* do the split, then re-insert it. (Even though splitting a
* segment *shouldn't* change its correct position in the
* sweep line tree, the reality is because of rounding errors,
* it sometimes does.)
*/
class SweepLine {
constructor(queue) {
let comparator = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : Segment.compare;
this.queue = queue;
this.tree = new SplayTree(comparator);
this.segments = [];
}
process(event) {
const segment = event.segment;
const newEvents = [];
// if we've already been consumed by another segment,
// clean up our body parts and get out
if (event.consumedBy) {
if (event.isLeft) this.queue.remove(event.otherSE);else this.tree.remove(segment);
return newEvents;
}
const node = event.isLeft ? this.tree.add(segment) : this.tree.find(segment);
if (!node) throw new Error(`Unable to find segment #${segment.id} ` + `[${segment.leftSE.point.x}, ${segment.leftSE.point.y}] -> ` + `[${segment.rightSE.point.x}, ${segment.rightSE.point.y}] ` + "in SweepLine tree.");
let prevNode = node;
let nextNode = node;
let prevSeg = undefined;
let nextSeg = undefined;
// skip consumed segments still in tree
while (prevSeg === undefined) {
prevNode = this.tree.prev(prevNode);
if (prevNode === null) prevSeg = null;else if (prevNode.key.consumedBy === undefined) prevSeg = prevNode.key;
}
// skip consumed segments still in tree
while (nextSeg === undefined) {
nextNode = this.tree.next(nextNode);
if (nextNode === null) nextSeg = null;else if (nextNode.key.consumedBy === undefined) nextSeg = nextNode.key;
}
if (event.isLeft) {
// Check for intersections against the previous segment in the sweep line
let prevMySplitter = null;
if (prevSeg) {
const prevInter = prevSeg.getIntersection(segment);
if (prevInter !== null) {
if (!segment.isAnEndpoint(prevInter)) prevMySplitter = prevInter;
if (!prevSeg.isAnEndpoint(prevInter)) {
const newEventsFromSplit = this._splitSafely(prevSeg, prevInter);
for (let i = 0, iMax = newEventsFromSplit.length; i < iMax; i++) {
newEvents.push(newEventsFromSplit[i]);
}
}
}
}
// Check for intersections against the next segment in the sweep line
let nextMySplitter = null;
if (nextSeg) {
const nextInter = nextSeg.getIntersection(segment);
if (nextInter !== null) {
if (!segment.isAnEndpoint(nextInter)) nextMySplitter = nextInter;
if (!nextSeg.isAnEndpoint(nextInter)) {
const newEventsFromSplit = this._splitSafely(nextSeg, nextInter);
for (let i = 0, iMax = newEventsFromSplit.length; i < iMax; i++) {
newEvents.push(newEventsFromSplit[i]);
}
}
}
}
// For simplicity, even if we find more than one intersection we only
// spilt on the 'earliest' (sweep-line style) of the intersections.
// The other intersection will be handled in a future process().
if (prevMySplitter !== null || nextMySplitter !== null) {
let mySplitter = null;
if (prevMySplitter === null) mySplitter = nextMySplitter;else if (nextMySplitter === null) mySplitter = prevMySplitter;else {
const cmpSplitters = SweepEvent.comparePoints(prevMySplitter, nextMySplitter);
mySplitter = cmpSplitters <= 0 ? prevMySplitter : nextMySplitter;
}
// Rounding errors can cause changes in ordering,
// so remove afected segments and right sweep events before splitting
this.queue.remove(segment.rightSE);
newEvents.push(segment.rightSE);
const newEventsFromSplit = segment.split(mySplitter);
for (let i = 0, iMax = newEventsFromSplit.length; i < iMax; i++) {
newEvents.push(newEventsFromSplit[i]);
}
}
if (newEvents.length > 0) {
// We found some intersections, so re-do the current event to
// make sure sweep line ordering is totally consistent for later
// use with the segment 'prev' pointers
this.tree.remove(segment);
newEvents.push(event);
} else {
// done with left event
this.segments.push(segment);
segment.prev = prevSeg;
}
} else {
// event.isRight
// since we're about to be removed from the sweep line, check for
// intersections between our previous and next segments
if (prevSeg && nextSeg) {
const inter = prevSeg.getIntersection(nextSeg);
if (inter !== null) {
if (!prevSeg.isAnEndpoint(inter)) {
const newEventsFromSplit = this._splitSafely(prevSeg, inter);
for (let i = 0, iMax = newEventsFromSplit.length; i < iMax; i++) {
newEvents.push(newEventsFromSplit[i]);
}
}
if (!nextSeg.isAnEndpoint(inter)) {
const newEventsFromSplit = this._splitSafely(nextSeg, inter);
for (let i = 0, iMax = newEventsFromSplit.length; i < iMax; i++) {
newEvents.push(newEventsFromSplit[i]);
}
}
}
}
this.tree.remove(segment);
}
return newEvents;
}
/* Safely split a segment that is currently in the datastructures
* IE - a segment other than the one that is currently being processed. */
_splitSafely(seg, pt) {
// Rounding errors can cause changes in ordering,
// so remove afected segments and right sweep events before splitting
// removeNode() doesn't work, so have re-find the seg
// https://github.com/w8r/splay-tree/pull/5
this.tree.remove(seg);
const rightSE = seg.rightSE;
this.queue.remove(rightSE);
const newEvents = seg.split(pt);
newEvents.push(rightSE);
// splitting can trigger consumption
if (seg.consumedBy === undefined) this.tree.add(seg);
return newEvents;
}
}
// Limits on iterative processes to prevent infinite loops - usually caused by floating-point math round-off errors.
const POLYGON_CLIPPING_MAX_QUEUE_SIZE = typeof process !== "undefined" && process.env.POLYGON_CLIPPING_MAX_QUEUE_SIZE || 1000000;
const POLYGON_CLIPPING_MAX_SWEEPLINE_SEGMENTS = typeof process !== "undefined" && process.env.POLYGON_CLIPPING_MAX_SWEEPLINE_SEGMENTS || 1000000;
class Operation {
run(type, geom, moreGeoms) {
operation.type = type;
rounder.