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getPointInsideOutline,
isInsidePolygon,
isSamePoint2D
} from './geometry'
import {
getIntersections,
getNodeList,
getEdgeList,
getOutlineList
} from './splitMergePolygons'
// Determines whether a given polygon is self-intersecting
//is counterClockwise
export function isCounterClockwise(A, B, C) {
return (C.y - A.y) * (B.x - A.x) > (B.y - A.y) * (C.x - A.x)
}
// Determines whether line segment AB intersects line segment CD
export function doLineSegmentsIntersect(A, B, C, D) {
return (
isCounterClockwise(A, C, D) != isCounterClockwise(B, C, D) &&
isCounterClockwise(A, B, C) != isCounterClockwise(A, B, D)
)
}
export function isSelfIntersecting(outline, isClosePolygon = true) {
let isSelfIntersecting = false
const length = outline.length
//check if two nodes are in same position
for (let k = 0; k < length; k++) {
let A = outline[k]
let B = outline[(k + 1) % length]
if (isSamePoint2D(A, B)) return true
}
if (length < 4) return false
let closeOffset = isClosePolygon ? 0 : 1
//let AB and CD be two edges we are testing for intersection
for (let k = 0; k < length - closeOffset; k++) {
let A = outline[k]
let B = outline[(k + 1) % length]
let offset = k == 0 ? 0 : 1
for (let j = k + 2; j < length - 1 + offset - closeOffset; j++) {
let C = outline[j]
let D = outline[(j + 1) % length]
if (doLineSegmentsIntersect(A, B, C, D)) {
isSelfIntersecting = true
break
}
}
if (isSelfIntersecting) {
break
}
}
return isSelfIntersecting
}
export function logicOperationOnPolygons(
outline1,
outline2,
mode = 'intersect'
) {
const fig1 = outline1.map((p) => {
return { x: p.x, y: p.y, z: p.z }
})
fig1.push(fig1[0])
const fig2 = outline2.map((p) => {
return { x: p.x, y: p.y, z: p.z }
})
//nodeList:
let dirtyNodeList = []
fig1.forEach((p) => {
dirtyNodeList.push(p)
})
fig2.forEach((p) => {
dirtyNodeList.push(p)
})
//edgeList (just in term of indexes)
const edges = fig2.map((p, index) => {
return { outline: [p, fig2[(index + 1) % fig2.length]] }
})
let intersections = getIntersections({ outline: fig1 }, edges)
//2. gather all nodes+intersection in a list[[x,y],[x,y]]
const nodeList = getNodeList(intersections, edges, { outline: fig1 })
//3. generate all edges not cut, those cut and those from construction polyline
const edgeList = getEdgeList(
nodeList,
intersections,
edges,
{ outline: fig1 },
1
)
//4. run planar-face-discovery to get all cycles and rebuild our polygons
try {
const outlineList = getOutlineList(nodeList, edgeList)
return filterPolygons(outlineList, fig1, fig2, mode)
} catch (err) {
console.error('error with getOutlineList', nodeList, edgeList, err)
return []
}
}
function filterPolygons(polygons, fig1, fig2, mode) {
var filtered = []
var c1, c2
var point
var bigPolygons = removeSmallPolygons(polygons, 0.0001)
for (var i = 0; i < bigPolygons.length; i++) {
point = getPointInsideOutline(
bigPolygons[i],
bigPolygons.filter((p, index) => index != i)
)
c1 = isInsidePolygon(point, fig1)
c2 = isInsidePolygon(point, fig2)
if (
(mode === 'intersect' && c1 && c2) || //intersection
(mode === 'cut1' && c1 && !c2) || //fig1 - fig2
(mode === 'cut2' && !c1 && c2) || //fig2 - fig2
(mode === 'sum' && (c1 || c2))
) {
//fig1 + fig2
//remove undefined point:
bigPolygons[i] = bigPolygons[i].filter((p) => !!p)
filtered.push(bigPolygons[i])
}
}
return filtered
}
export function intersectOutlines(outline1, outline2) {
const fig1 = outline1.map((p) => {
return { x: p.x, y: p.y, z: p.z }
})
const fig2 = outline2.map((p) => {
return { x: p.x, y: p.y, z: p.z }
})
return logicOperationOnPolygons(fig1, fig2, 'intersect')
}
function alignPolygon(polygon, points) {
for (let i = 0; i < polygon.length; i++) {
for (let j = 0; j < points.length; j++) {
if (distance(polygon[i], points[j]) < 0.0001) polygon[i] = points[j]
}
}
return polygon
}
function distance(p1, p2) {
var dx = Math.abs(p1.x - p2.x)
var dy = Math.abs(p1.y - p2.y)
return Math.sqrt(dx * dx + dy * dy)
}
//check polygons for correctness
function checkPolygons(fig1, fig2) {
var figs = [fig1, fig2]
for (var i = 0; i < figs.length; i++) {
if (figs[i].length < 3) {
console.error('Polygon ' + (i + 1) + ' is invalid!')
return false
}
}
return true
}
//create array of edges of all polygons
function edgify(fig1, fig2) {
//create primary array from all edges
var primEdges = getEdges(fig1).concat(getEdges(fig2))
var secEdges = []
//check every edge
for (var i = 0; i < primEdges.length; i++) {
var points = []
//for intersection with every edge except itself
for (var j = 0; j < primEdges.length; j++) {
if (i != j) {
var interPoints = findEdgeIntersection(primEdges[i], primEdges[j])
addNewPoints(interPoints, points)
}
}
//add start and end points to intersection points
let startPoint = primEdges[i][0]
startPoint.t = 0
let endPoint = primEdges[i][1]
endPoint.t = 1
addNewPoints([startPoint, endPoint], points)
//sort all points by position on edge
points = sortPoints(points)
//break edge to parts
for (var k = 0; k < points.length - 1; k++) {
var edge = [
{ x: points[k].x, y: points[k].y },
{ x: points[k + 1].x, y: points[k + 1].y }
]
// check for existanse in sec.array
if (!edgeExists(edge, secEdges)) {
//push if not exists
secEdges.push(edge)
}
}
}
return secEdges
}
function addNewPoints(newPoints, points) {
if (newPoints.length > 0) {
//check for uniqueness
for (var k = 0; k < newPoints.length; k++) {
if (!pointExists(newPoints[k], points)) {
points.push(newPoints[k])
}
}
}
}
function sortPoints(points) {
var p = points
p.sort((a, b) => {
if (a.t > b.t) return 1
if (a.t < b.t) return -1
})
return p
}
function getEdges(fig) {
var edges = []
var len = fig.length
for (var i = 0; i < len; i++) {
edges.push([
{ x: fig[i % len].x, y: fig[i % len].y },
{ x: fig[(i + 1) % len].x, y: fig[(i + 1) % len].y }
])
}
return edges
}
function findEdgeIntersection(edge1, edge2) {
var x1 = edge1[0].x
var x2 = edge1[1].x
var x3 = edge2[0].x
var x4 = edge2[1].x
var y1 = edge1[0].y
var y2 = edge1[1].y
var y3 = edge2[0].y
var y4 = edge2[1].y
var nom1 = (x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3)
var nom2 = (x2 - x1) * (y1 - y3) - (y2 - y1) * (x1 - x3)
var denom = (y4 - y3) * (x2 - x1) - (x4 - x3) * (y2 - y1)
var t1 = nom1 / denom
var t2 = nom2 / denom
var interPoints = []
//1. lines are parallel or edges don't intersect
if ((denom === 0 && nom1 !== 0) || t1 <= 0 || t1 >= 1 || t2 < 0 || t2 > 1) {
return interPoints
}
//2. lines are collinear
else if (nom1 === 0 && denom === 0) {
//check if endpoints of edge2 lies on edge1
for (var i = 0; i < 2; i++) {
var classify = classifyPoint(edge2[i], edge1)
//find position of this endpoints relatively to edge1
if (classify.loc == 'ORIGIN' || classify.loc == 'DESTINATION') {
interPoints.push({ x: edge2[i].x, y: edge2[i].y, t: classify.t })
} else if (classify.loc == 'BETWEEN') {
x = +(x1 + classify.t * (x2 - x1)).toFixed(9)
y = +(y1 + classify.t * (y2 - y1)).toFixed(9)
interPoints.push({ x: x, y: y, t: classify.t })
}
}
return interPoints
}
//3. edges intersect
else {
for (var i = 0; i < 2; i++) {
var classify = classifyPoint(edge2[i], edge1)
if (classify.loc == 'ORIGIN' || classify.loc == 'DESTINATION') {
interPoints.push({ x: edge2[i].x, y: edge2[i].y, t: classify.t })
}
}
if (interPoints.length > 0) {
return interPoints
}
var x = +(x1 + t1 * (x2 - x1)).toFixed(9)
var y = +(y1 + t1 * (y2 - y1)).toFixed(9)
interPoints.push({ x: x, y: y, t: t1 })
return interPoints
}
}
function classifyPoint(p, edge) {
var ax = edge[1].x - edge[0].x
var ay = edge[1].y - edge[0].y
var bx = p.x - edge[0].x
var by = p.y - edge[0].y
var sa = ax * by - bx * ay
if (p.x === edge[0].x && p.y === edge[0].y) {
return { loc: 'ORIGIN', t: 0 }
}
if (p.x === edge[1].x && p.y === edge[1].y) {
return { loc: 'DESTINATION', t: 1 }
}
var theta =
(polarAngle([edge[1], edge[0]]) -
polarAngle([
{ x: edge[1].x, y: edge[1].y },
{ x: p.x, y: p.y }
])) %
360
if (theta < 0) {
theta = theta + 360
}
if (sa < -0.0000001) {
return { loc: 'LEFT', theta: theta }
}
if (sa > 0.0000001) {
return { loc: 'RIGHT', theta: theta }
}
if (ax * bx < 0 || ay * by < 0) {
return { loc: 'BEHIND', theta: theta }
}
if (Math.sqrt(ax * ax + ay * ay) < Math.sqrt(bx * bx + by * by)) {
return { loc: 'BEYOND', theta: theta }
}
var t
if (ax !== 0) {
t = bx / ax
} else {
t = by / ay
}
return { loc: 'BETWEEN', t: t }
}
function polarAngle(edge) {
var dx = edge[1].x - edge[0].x
var dy = edge[1].y - edge[0].y
if (dx === 0 && dy === 0) {
//console.error("Edge has zero length.");
return false
}
if (dx === 0) {
return dy > 0 ? 90 : 270
}
if (dy === 0) {
return dx > 0 ? 0 : 180
}
var theta = (Math.atan(dy / dx) * 360) / (2 * Math.PI)
if (dx > 0) {
return dy >= 0 ? theta : theta + 360
} else {
return theta + 180
}
}
function pointExists(p, points) {
if (points.length === 0) {
return false
}
for (var i = 0; i < points.length; i++) {
if (p.x === points[i].x && p.y === points[i].y) {
return true
}
}
return false
}
function edgeExists(e, edges) {
if (edges.length === 0) {
return false
}
for (var i = 0; i < edges.length; i++) {
if (equalEdges(e, edges[i])) return true
}
return false
}
function equalEdges(edge1, edge2) {
if (
(edge1[0].x === edge2[0].x &&
edge1[0].y === edge2[0].y &&
edge1[1].x === edge2[1].x &&
edge1[1].y === edge2[1].y) ||
(edge1[0].x === edge2[1].x &&
edge1[0].y === edge2[1].y &&
edge1[1].x === edge2[0].x &&
edge1[1].y === edge2[0].y)
) {
return true
} else {
return false
}
}
function polygonate(edges) {
var polygons = []
var polygon = []
var len = edges.length
var midpoints = getMidpoints(edges)
//start from every edge and create non-selfintersecting polygons
for (var i = 0; i < len - 2; i++) {
var org = { x: edges[i][0].x, y: edges[i][0].y }
var dest = { x: edges[i][1].x, y: edges[i][1].y }
var currentEdge = i
var point
var p
var direction
var stop
//while we havn't come to the starting edge again
for (direction = 0; direction < 2; direction++) {
polygon = []
stop = false
while (polygon.length === 0 || !stop) {
//add point to polygon
polygon.push({ x: org.x, y: org.y })
point = undefined
//look for edge connected with end of current edge
for (var j = 0; j < len; j++) {
p = undefined
//except itself
if (!equalEdges(edges[j], edges[currentEdge])) {
//if some edge is connected to current edge in one endpoint
if (edges[j][0].x === dest.x && edges[j][0].y === dest.y) {
p = edges[j][1]
}
if (edges[j][1].x === dest.x && edges[j][1].y === dest.y) {
p = edges[j][0]
}
//compare it with last found connected edge for minimum angle between itself and current edge
if (p) {
var classify = classifyPoint(p, [org, dest])
//if this edge has smaller theta then last found edge update data of next edge of polygon
if (
!point ||
(classify.theta < point.theta && direction === 0) ||
(classify.theta > point.theta && direction === 1)
) {
point = { x: p.x, y: p.y, theta: classify.theta, edge: j }
}
}
}
}
//change current edge to next edge
org.x = dest.x
org.y = dest.y
dest.x = point.x
dest.y = point.y
currentEdge = point.edge
//if we reach start edge
if (equalEdges([org, dest], edges[i])) {
stop = true
//check polygon for correctness
/*for (var k = 0; k < allPoints.length; k++) {
//if some point is inside polygon it is incorrect
if ((!pointExists(allPoints[k], polygon)) && (findPointInsidePolygon(allPoints[k], polygon))) {
polygon = false;
}
}*/
for (let k = 0; k < midpoints.length; k++) {
//if some midpoint is inside polygon (edge inside polygon) it is incorrect
if (findPointInsidePolygon(midpoints[k], polygon)) {
polygon = false
}
}
}
}
//add created polygon if it is correct and was not found before
if (polygon && !polygonExists(polygon, polygons)) {
polygons.push(polygon)
}
}
}
return polygons
}
function polygonExists(polygon, polygons) {
//if array is empty element doesn't exist in it
if (polygons.length === 0) return false
//check every polygon in array
for (var i = 0; i < polygons.length; i++) {
//if lengths are not same go to next element
if (polygon.length !== polygons[i].length) continue
//if length are same need to check
else {
//if all the points are same
for (var j = 0; j < polygon.length; j++) {
//if point is not found break forloop and go to next element
if (!pointExists(polygon[j], polygons[i])) break
//if point found
else {
//and it is last point in polygon we found polygon in array!
if (j === polygon.length - 1) return true
}
}
}
}
return false
}
function filterPolygonsOld(polygons, fig1, fig2, mode) {
var filtered = []
var c1, c2
var point
var bigPolygons = removeSmallPolygons(polygons, 0.0001)
for (var i = 0; i < bigPolygons.length; i++) {
point = getPointInsidePolygon(bigPolygons[i])
c1 = findPointInsidePolygon(point, fig1)
c2 = findPointInsidePolygon(point, fig2)
if (
(mode === 'intersect' && c1 && c2) || //intersection
(mode === 'cut1' && c1 && !c2) || //fig1 - fig2
(mode === 'cut2' && !c1 && c2) || //fig2 - fig2
(mode === 'sum' && (c1 || c2))
) {
//fig1 + fig2
filtered.push(bigPolygons[i])
}
}
return filtered
}
function removeSmallPolygons(polygons, minSize) {
var big = []
for (var i = 0; i < polygons.length; i++) {
if (polygonArea(polygons[i]) >= minSize) {
big.push(polygons[i])
}
}
return big
}
function polygonArea(p) {
var len = p.length
var s = 0
for (var i = 0; i < len; i++) {
s += Math.abs(
p[i % len].x * p[(i + 1) % len].y - p[i % len].y * p[(i + 1) % len].x
)
}
return s / 2
}
function getPointInsidePolygon(polygon) {
var point
var size = getSize(polygon)
var edges = getEdges(polygon)
var y = size.y.min + (size.y.max - size.y.min) / Math.PI
var dy = (size.y.max - size.y.min) / 13
var line = []
var points
var interPoints = []
var pointsOK = false
while (!pointsOK) {
line = [
{ x: size.x.min - 1, y: y },
{ x: size.x.max + 1, y: y }
]
//find intersections with all polygon edges
for (var i = 0; i < edges.length; i++) {
points = findEdgeIntersection(line, edges[i])
//if edge doesn't lie inside line
if (points && points.length === 1) {
interPoints.push(points[0])
}
}
interPoints = sortPoints(interPoints)
//find two correct interpoints
for (var i = 0; i < interPoints.length - 1; i++) {
if (interPoints[i].t !== interPoints[i + 1].t) {
//enable exit from loop and calculate point coordinates
pointsOK = true
point = { x: (interPoints[i].x + interPoints[i + 1].x) / 2, y: y }
}
}
//all points are incorrect, need to change line parameters
y = y + dy
if ((y > size.y.max || y < size.y.min) && pointsOK === false) {
pointsOK = true
point = undefined
}
}
return point
}
function getSize(polygon) {
var size = {
x: {
min: polygon[0].x,
max: polygon[0].x
},
y: {
min: polygon[0].y,
max: polygon[0].y
}
}
for (var i = 1; i < polygon.length; i++) {
if (polygon[i].x < size.x.min) size.x.min = polygon[i].x
if (polygon[i].x > size.x.max) size.x.max = polygon[i].x
if (polygon[i].y < size.y.min) size.y.min = polygon[i].y
if (polygon[i].y > size.y.max) size.y.max = polygon[i].y
}
return size
}
function findPointInsidePolygon(point, polygon) {
var cross = 0
var edges = getEdges(polygon)
var classify
var org, dest
for (var i = 0; i < edges.length; i++) {
[org, dest] = edges[i]
classify = classifyPoint(point, [org, dest])
if (
(classify.loc === 'RIGHT' && org.y < point.y && dest.y >= point.y) ||
(classify.loc === 'LEFT' && org.y >= point.y && dest.y < point.y)
) {
cross++
}
if (classify.loc === 'BETWEEN') return false
}
if (cross % 2) {
return true
} else {
return false
}
}
function getMidpoints(edges) {
var midpoints = []
var x, y
for (var i = 0; i < edges.length; i++) {
x = (edges[i][0].x + edges[i][1].x) / 2
y = (edges[i][0].y + edges[i][1].y) / 2
let classify = classifyPoint({ x: x, y: y }, edges[i])
if (classify.loc != 'BETWEEN') {
//console.error('Midpoint calculation error in intersect algo',edges)
}
midpoints.push({ x: x, y: y })
}
return midpoints
}
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