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polygon.go
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polygon.go
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// Copyright ©2016-2023 by Richard A. Wilkes. All rights reserved.
//
// This Source Code Form is subject to the terms of the Mozilla Public
// License, version 2.0. If a copy of the MPL was not distributed with
// this file, You can obtain one at http://mozilla.org/MPL/2.0/.
//
// This Source Code Form is "Incompatible With Secondary Licenses", as
// defined by the Mozilla Public License, version 2.0.
package poly
import (
"strings"
"github.com/richardwilkes/toolbox/xmath/geom"
"golang.org/x/exp/constraints"
)
const (
clipping = iota
subject
)
type clipOp int
const (
subtractOp clipOp = iota
intersectOp
xorOp
unionOp
)
// Polygon holds one or more contour lines. The polygon may contain holes and may be self-intersecting.
type Polygon[T constraints.Float] []Contour[T]
// Clone returns a duplicate of this polygon.
func (p Polygon[T]) Clone() Polygon[T] {
if len(p) == 0 {
return nil
}
clone := Polygon[T](make([]Contour[T], len(p)))
for i := range p {
clone[i] = p[i].Clone()
}
return clone
}
// String implements fmt.Stringer.
func (p Polygon[T]) String() string {
var buffer strings.Builder
buffer.WriteByte('{')
for i, c := range p {
if i != 0 {
buffer.WriteByte(',')
}
buffer.WriteString(c.String())
}
buffer.WriteByte('}')
return buffer.String()
}
// Bounds returns the bounding rectangle of this polygon.
func (p Polygon[T]) Bounds() geom.Rect[T] {
if len(p) == 0 {
return geom.Rect[T]{}
}
b := p[0].Bounds()
for _, c := range p[1:] {
b = b.Union(c.Bounds())
}
return b
}
// Contains returns true if the point is contained by this polygon.
func (p Polygon[T]) Contains(pt geom.Point[T]) bool {
for i := range p {
if p[i].Contains(pt) {
return true
}
}
return false
}
// ContainsEvenOdd returns true if the point is contained by the polygon using the even-odd rule.
// https://en.wikipedia.org/wiki/Even-odd_rule
func (p Polygon[T]) ContainsEvenOdd(pt geom.Point[T]) bool {
var count int
for i := range p {
if p[i].Contains(pt) {
count++
}
}
return count%2 == 1
}
// Transform returns the result of transforming this Polygon by the Matrix.
func (p Polygon[T]) Transform(m geom.Matrix[T]) Polygon[T] {
clone := p.Clone()
for _, c := range clone {
for i := range c {
c[i] = m.TransformPoint(c[i])
}
}
return clone
}
// Union returns a new Polygon holding the union of both Polygons.
func (p Polygon[T]) Union(other Polygon[T]) Polygon[T] {
return p.construct(unionOp, other)
}
// Intersect returns a new Polygon holding the intersection of both Polygons.
func (p Polygon[T]) Intersect(other Polygon[T]) Polygon[T] {
return p.construct(intersectOp, other)
}
// Sub returns a new Polygon holding the result of removing the other Polygon from this Polygon.
func (p Polygon[T]) Sub(other Polygon[T]) Polygon[T] {
return p.construct(subtractOp, other)
}
// Xor returns a new Polygon holding the result of xor'ing this Polygon with the other Polygon.
func (p Polygon[T]) Xor(other Polygon[T]) Polygon[T] {
return p.construct(xorOp, other)
}
func (p Polygon[T]) construct(op clipOp, other Polygon[T]) Polygon[T] {
var result Polygon[T]
// Short-circuit the work if we can trivially determine the result is an empty polygon.
if (len(p) == 0 && len(other) == 0) ||
(len(p) == 0 && (op == intersectOp || op == subtractOp)) ||
(len(other) == 0 && op == intersectOp) {
return result
}
// Build the local minima table and the scan beam table
sbTree := &scanBeamTree[T]{}
subjNonContributing, clipNonContributing := p.identifyNonContributingContours(op, other)
lmt := buildLocalMinimaTable(nil, sbTree, p, subjNonContributing, subject, op)
if lmt = buildLocalMinimaTable(lmt, sbTree, other, clipNonContributing, clipping, op); lmt == nil {
return result
}
sbt := sbTree.buildScanBeamTable()
// Process each scan beam
var aet *edgeNode[T]
var outPoly *polygonNode[T]
localMin := lmt
i := 0
for i < len(sbt) {
// Set yb and yt to the bottom and top of the scanbeam
var yt, dy T
var bPt geom.Point[T]
bPt.Y = sbt[i]
i++
if i < len(sbt) {
yt = sbt[i]
dy = yt - bPt.Y
}
// If LMT node corresponding to bPt.Y exists
if localMin != nil && localMin.y == bPt.Y {
// Add edges starting at this local minimum to the AET
for edge := localMin.firstBound; edge != nil; edge = edge.nextBound {
aet = edge.addEdgeToActiveEdgeTable(aet, nil)
}
localMin = localMin.next
}
if aet == nil {
continue
}
aet.bundleFields(bPt)
bPt, outPoly = aet.process(op, bPt, outPoly)
aet = aet.deleteTerminatingEdges(bPt, yt)
if i < len(sbt) {
// Process each node in the intersection table
for inter := aet.buildIntersections(dy); inter != nil; inter = inter.next {
outPoly = inter.process(op, bPt, outPoly)
aet = aet.swapIntersectingEdgeBundles(inter)
}
aet = aet.prepareForNextScanBeam(yt)
}
}
// Generate the resulting polygon
if outPoly != nil {
return outPoly.generate()
}
return Polygon[T]{}
}
func (p Polygon[T]) identifyNonContributingContours(op clipOp, clip Polygon[T]) (subjNC, clipNC []bool) {
subjNC = make([]bool, len(p))
clipNC = make([]bool, len(clip))
if (op == intersectOp || op == subtractOp) && len(p) > 0 && len(clip) > 0 {
// Check all subject contour bounding boxes against clip boxes
overlaps := make([]bool, len(p)*len(clip))
boxes := make([]geom.Rect[T], len(clip))
for i, c := range clip {
boxes[i] = c.Bounds()
}
for si := range p {
box := p[si].Bounds()
for ci := range clip {
overlaps[ci*len(p)+si] = box.Intersects(boxes[ci])
}
}
// For each clip contour, search for any subject contour overlaps
for ci := range clip {
clipNC[ci] = true
for si := range p {
if overlaps[ci*len(p)+si] {
clipNC[ci] = false
break
}
}
}
if op == intersectOp {
// For each subject contour, search for any clip contour overlaps
for si := range p {
subjNC[si] = true
for ci := range clip {
if overlaps[ci*len(p)+si] {
subjNC[si] = false
break
}
}
}
}
}
return
}