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type_multi_polygon.go
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type_multi_polygon.go
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package geom
import (
"database/sql/driver"
"fmt"
"github.com/peterstace/simplefeatures/rtree"
)
// MultiPolygon is a planar surface geometry that consists of a collection of
// Polygons. The zero value is the empty MultiPolygon (i.e. the collection of
// zero Polygons). It is immutable after creation.
//
// For a MultiPolygon to be valid, the following assertions must hold:
//
// 1. It must be made up of zero or more valid Polygons (any of which may be empty).
//
// 2. The interiors of any two polygons must not intersect.
//
// 3. The boundaries of any two polygons may touch only at a finite number of points.
type MultiPolygon interface {
Geometryer
Area(opts ...AreaOption) float64
Boundary() MultiLineString
Reverse() MultiPolygon
ForceCoordinatesType(newCType CoordinatesType) MultiPolygon
NumPolygons() int
PolygonN(n int) Polygon
Coordinates() [][]Sequence
TransformXY(fn func(XY) XY, opts ...ConstructorOption) (MultiPolygon, error)
ForceCCW() MultiPolygon
ForceCW() MultiPolygon
Dump() []Polygon
forceOrientation(forceCW bool) MultiPolygon
controlPoints() int
}
type multiPolygon struct {
// Invariant: ctype matches the coordinates type of each polygon.
polys []Polygon
ctype CoordinatesType
}
// NewMultiPolygon creates a MultiPolygon from its constituent Polygons. It
// gives an error if any of the MultiPolygon assertions are not maintained. The
// coordinates type of the MultiPolygon is the lowest common coordinates type
// its Polygons.
func NewMultiPolygon(polys []Polygon, opts ...ConstructorOption) (MultiPolygon, error) {
if len(polys) == 0 {
return &multiPolygon{}, nil
}
ctype := DimXYZM
for _, p := range polys {
ctype &= p.CoordinatesType()
}
polys = append([]Polygon(nil), polys...)
for i := range polys {
polys[i] = polys[i].ForceCoordinatesType(ctype)
}
ctorOpts := newOptionSet(opts)
if err := validateMultiPolygon(polys, ctorOpts); err != nil {
if ctorOpts.omitInvalid {
return &multiPolygon{}, nil
}
return &multiPolygon{}, err
}
return &multiPolygon{polys, ctype}, nil
}
func validateMultiPolygon(polys []Polygon, opts ctorOptionSet) error {
if opts.skipValidations {
return nil
}
polyBoundaries := make([]indexedLines, len(polys))
polyBoundaryPopulated := make([]bool, len(polys))
// Construct RTree of Polygons.
boxes := make([]rtree.Box, len(polys))
items := make([]rtree.BulkItem, 0, len(polys))
for i, p := range polys {
if box, ok := p.Envelope().box(); ok {
boxes[i] = box
item := rtree.BulkItem{Box: boxes[i], RecordID: i}
items = append(items, item)
}
}
tree := rtree.BulkLoad(items)
for i := range polys {
if polys[i].IsEmpty() {
continue
}
if err := tree.RangeSearch(boxes[i], func(j int) error {
// Only consider each pair of polygons once.
if i <= j {
return nil
}
for _, k := range [...]int{i, j} {
if !polyBoundaryPopulated[k] {
polyBoundaries[k] = newIndexedLines(polys[k].Boundary().asLines())
polyBoundaryPopulated[k] = true
}
}
interMP, interMLS := intersectionOfIndexedLines(
polyBoundaries[i],
polyBoundaries[j],
)
if !interMLS.IsEmpty() {
return validationError{"multipolygon child polygon " +
"boundaries intersect at multiple points"}
}
// Fast case: If both the point and line parts of the intersection
// are empty, then the only thing we have to worry about is one
// polygon being nested entirely within the other. But since the
// boundaries don't intersect in any way, we just have to check a
// single point.
if interMP.IsEmpty() {
// We already know the polygons are NOT empty, so it's safe to
// directly access index 0.
ptI := polys[i].ExteriorRing().Coordinates().GetXY(0)
ptJ := polys[j].ExteriorRing().Coordinates().GetXY(0)
if relatePointToPolygon(ptI, polyBoundaries[j]) != exterior ||
relatePointToPolygon(ptJ, polyBoundaries[i]) != exterior {
return validationError{"multipolygon has nested child polygons"}
}
return nil
}
// Slow case: The boundaries intersect at a point (or many points).
// But we still need to ensure that the interiors don't intersect.
for _, pair := range [...]struct{ pb1, pb2 indexedLines }{
{polyBoundaries[i], polyBoundaries[j]},
{polyBoundaries[j], polyBoundaries[i]},
} {
if err := validatePolyNotInsidePoly(pair.pb1, pair.pb2); err != nil {
return err
}
}
return nil
}); err != nil {
return err
}
}
return nil
}
func validatePolyNotInsidePoly(p1, p2 indexedLines) error {
// For each point where the boundaries of the two polygons intersect, we
// take points clockwise and counterclockwise along the boundaries and see
// if they are inside the opposing polygon. If they are, then the interiors
// intersect.
for j := range p2.lines {
// Find intersection points.
var pts []XY
p1.tree.RangeSearch(p2.lines[j].box(), func(i int) error {
inter := p1.lines[i].intersectLine(p2.lines[j])
if inter.empty {
return nil
}
if inter.ptA != inter.ptB {
panic(fmt.Sprintf("already established that boundaries only "+
"intersect at points, but got: %v", inter))
}
pts = append(pts, inter.ptA)
return nil
})
if len(pts) == 0 {
continue
}
// Construct midpoints between intersection points and endpoints.
pts = append(pts, p2.lines[j].a, p2.lines[j].b)
pts = sortAndUniquifyXYs(pts)
// Check if midpoints are inside the other polygon.
for k := 0; k+1 < len(pts); k++ {
midpoint := pts[k].Add(pts[k+1]).Scale(0.5)
if relatePointToPolygon(midpoint, p1) == interior {
return validationError{fmt.Sprintf("multipolygon child polygon "+
"interiors intersect at %v", midpoint)}
}
}
}
return nil
}
func (m multiPolygon) reverse() Geometryer {
return m.Reverse()
}
func (m multiPolygon) Length() float64 {
return 0
}
func (m multiPolygon) Dimension() int {
return 2
}
// Type returns the GeometryType for a MultiPolygon
func (m multiPolygon) Type() GeometryType {
return TypeMultiPolygon
}
// AsGeometry converts this MultiPolygon into a Geometry.
func (m multiPolygon) AsGeometry() Geometry {
return Geometry{&m}
}
// NumPolygons gives the number of Polygon elements in the MultiPolygon.
func (m multiPolygon) NumPolygons() int {
return len(m.polys)
}
// PolygonN gives the nth (zero based) Polygon element.
func (m multiPolygon) PolygonN(n int) Polygon {
return m.polys[n]
}
// AsText returns the WKT (Well Known Text) representation of this geometry.
func (m multiPolygon) AsText() string {
return string(m.AppendWKT(nil))
}
// AppendWKT appends the WKT (Well Known Text) representation of this geometry
// to the input byte slice.
func (m multiPolygon) AppendWKT(dst []byte) []byte {
dst = appendWKTHeader(dst, "MULTIPOLYGON", m.ctype)
if len(m.polys) == 0 {
return appendWKTEmpty(dst)
}
dst = append(dst, '(')
for i, poly := range m.polys {
if i > 0 {
dst = append(dst, ',')
}
dst = poly.appendWKTBody(dst)
}
return append(dst, ')')
}
// IsSimple returns true if this geometry contains no anomalous geometry
// points, such as self intersection or self tangency. Because MultiPolygons
// are always simple, this method always returns true.
func (m multiPolygon) IsSimple() bool {
return true
}
// IsEmpty return true if and only if this MultiPolygon doesn't contain any
// Polygons, or only contains empty Polygons.
func (m multiPolygon) IsEmpty() bool {
for _, p := range m.polys {
if !p.IsEmpty() {
return false
}
}
return true
}
// Envelope returns the Envelope that most tightly surrounds the geometry.
func (m multiPolygon) Envelope() Envelope {
var env Envelope
for _, poly := range m.polys {
env = env.ExpandToIncludeEnvelope(poly.Envelope())
}
return env
}
// Boundary returns the spatial boundary of this MultiPolygon. This is the
// MultiLineString containing the boundaries of the MultiPolygon's elements.
func (m multiPolygon) Boundary() MultiLineString {
var n int
for _, p := range m.polys {
n += len(p.getRings())
}
bounds := make([]LineString, 0, n)
for _, p := range m.polys {
for _, r := range p.getRings() {
bounds = append(bounds, r.Force2D())
}
}
return NewMultiLineString(bounds)
}
// Value implements the database/sql/driver.Valuer interface by returning the
// WKB (Well Known Binary) representation of this Geometry.
func (m multiPolygon) Value() (driver.Value, error) {
return m.AsBinary(), nil
}
// Scan implements the database/sql.Scanner interface by parsing the src value
// as WKB (Well Known Binary).
//
// If the WKB doesn't represent a MultiPolygon geometry, then an error is returned.
//
// It constructs the resultant geometry with no ConstructionOptions. If
// ConstructionOptions are needed, then the value should be scanned into a byte
// slice and then UnmarshalWKB called manually (passing in the
// ConstructionOptions as desired).
func (m *multiPolygon) Scan(src interface{}) error {
return scanAsType(src, m, TypeMultiPolygon)
}
// AsBinary returns the WKB (Well Known Text) representation of the geometry.
func (m multiPolygon) AsBinary() []byte {
return m.AppendWKB(nil)
}
// AppendWKB appends the WKB (Well Known Text) representation of the geometry
// to the input slice.
func (m multiPolygon) AppendWKB(dst []byte) []byte {
marsh := newWKBMarshaller(dst)
marsh.writeByteOrder()
marsh.writeGeomType(TypeMultiPolygon, m.ctype)
n := m.NumPolygons()
marsh.writeCount(n)
for i := 0; i < n; i++ {
poly := m.PolygonN(i)
marsh.buf = poly.AppendWKB(marsh.buf)
}
return marsh.buf
}
// ConvexHull returns the geometry representing the smallest convex geometry
// that contains this geometry.
func (m multiPolygon) ConvexHull() Geometry {
return convexHull(m.AsGeometry())
}
// MarshalJSON implements the encoding/json.Marshaller interface by encoding
// this geometry as a GeoJSON geometry object.
func (m multiPolygon) MarshalJSON() ([]byte, error) {
var dst []byte
dst = append(dst, `{"type":"MultiPolygon","coordinates":`...)
dst = appendGeoJSONSequenceMatrix(dst, m.Coordinates())
dst = append(dst, '}')
return dst, nil
}
// Coordinates returns the coordinates of each constituent Polygon of the
// MultiPolygon.
func (m multiPolygon) Coordinates() [][]Sequence {
numPolys := m.NumPolygons()
coords := make([][]Sequence, numPolys)
for i := 0; i < numPolys; i++ {
coords[i] = m.PolygonN(i).Coordinates()
}
return coords
}
// TransformXY transforms this MultiPolygon into another MultiPolygon according to fn.
func (m multiPolygon) TransformXY(fn func(XY) XY, opts ...ConstructorOption) (MultiPolygon, error) {
polys := make([]Polygon, m.NumPolygons())
for i := range polys {
transformed, err := m.PolygonN(i).TransformXY(fn, opts...)
if err != nil {
return &multiPolygon{}, wrapTransformed(err)
}
polys[i] = transformed
}
mp, err := NewMultiPolygon(polys, opts...)
return mp.ForceCoordinatesType(m.ctype), wrapTransformed(err)
}
// Area in the case of a MultiPolygon is the sum of the areas of its polygons.
func (m multiPolygon) Area(opts ...AreaOption) float64 {
var area float64
n := m.NumPolygons()
for i := 0; i < n; i++ {
area += m.PolygonN(i).Area(opts...)
}
return area
}
// Centroid returns the multi polygon's centroid point. It returns the empty
// Point if the multi polygon is empty.
func (m multiPolygon) Centroid() Point {
if m.IsEmpty() {
return NewEmptyPoint(DimXY)
}
areas := make([]float64, m.NumPolygons())
var totalArea float64
for i := 0; i < m.NumPolygons(); i++ {
area := m.PolygonN(i).Area()
areas[i] = area
totalArea += area
}
var weightedCentroid XY
for i := 0; i < m.NumPolygons(); i++ {
centroid, ok := m.PolygonN(i).Centroid().XY()
if ok {
weightedCentroid = weightedCentroid.Add(centroid.Scale(areas[i] / totalArea))
}
}
return weightedCentroid.asUncheckedPoint()
}
// Reverse in the case of MultiPolygon outputs the component polygons in their original order,
// each individually reversed.
func (m multiPolygon) Reverse() MultiPolygon {
polys := make([]Polygon, len(m.polys))
// Form the reversed slice.
for i := 0; i < len(m.polys); i++ {
polys[i] = m.polys[i].Reverse()
}
return &multiPolygon{polys, m.ctype}
}
// CoordinatesType returns the CoordinatesType used to represent points making
// up the geometry.
func (m multiPolygon) CoordinatesType() CoordinatesType {
return m.ctype
}
// ForceCoordinatesType returns a new MultiPolygon with a different CoordinatesType. If a
// dimension is added, then new values are populated with 0.
func (m multiPolygon) ForceCoordinatesType(newCType CoordinatesType) MultiPolygon {
flat := make([]Polygon, len(m.polys))
for i := range m.polys {
flat[i] = m.polys[i].ForceCoordinatesType(newCType)
}
return &multiPolygon{flat, newCType}
}
// Force2D returns a copy of the MultiPolygon with Z and M values removed.
func (m multiPolygon) Force2D() MultiPolygon {
return m.ForceCoordinatesType(DimXY)
}
// PointOnSurface returns a Point on the interior of the MultiPolygon.
func (m multiPolygon) PointOnSurface() Point {
var (
bestWidth float64
)
bestPoint := NewEmptyPoint(DimXY)
for i := 0; i < m.NumPolygons(); i++ {
poly := m.PolygonN(i)
point, bisectorWidth := pointOnAreaSurface(poly)
if point.IsEmpty() {
continue
}
if bisectorWidth > bestWidth {
bestWidth = bisectorWidth
bestPoint = point
}
}
return bestPoint
}
// ForceCW returns the equivalent MultiPolygon that has its exterior rings in a
// clockwise orientation and any inner rings in a counter-clockwise
// orientation.
func (m multiPolygon) ForceCW() MultiPolygon {
return m.forceOrientation(true)
}
// ForceCCW returns the equivalent MultiPolygon that has its exterior rings in
// a counter-clockwise orientation and any inner rings in a clockwise
// orientation.
func (m multiPolygon) ForceCCW() MultiPolygon {
return m.forceOrientation(false)
}
func (m multiPolygon) forceOrientation(forceCW bool) MultiPolygon {
polys := make([]Polygon, len(m.polys))
for i, poly := range m.polys {
polys[i] = poly.forceOrientation(forceCW)
}
return &multiPolygon{polys, m.ctype}
}
func (m multiPolygon) controlPoints() int {
var sum int
for _, p := range m.polys {
sum += p.controlPoints()
}
return sum
}
// Dump returns the MultiPolygon represented as a Polygon slice.
func (m multiPolygon) Dump() []Polygon {
ps := make([]Polygon, len(m.polys))
copy(ps, m.polys)
return ps
}
// DumpCoordinates returns the points making up the rings in a MultiPolygon as
// a Sequence.
func (m multiPolygon) DumpCoordinates() Sequence {
var n int
for _, p := range m.polys {
for _, r := range p.getRings() {
n += r.Coordinates().Length()
}
}
ctype := m.CoordinatesType()
coords := make([]float64, 0, n*ctype.Dimension())
for _, p := range m.polys {
for _, r := range p.getRings() {
coords = r.Coordinates().appendAllPoints(coords)
}
}
seq := NewSequence(coords, ctype)
seq.assertNoUnusedCapacity()
return seq
}
// Summary returns a text summary of the MultiPolygon following a similar format to https://postgis.net/docs/ST_Summary.html.
func (m multiPolygon) Summary() string {
numPoints := m.DumpCoordinates().Length()
var polygonSuffix string
numPolygons := m.NumPolygons()
if numPolygons != 1 {
polygonSuffix = "s"
}
var numRings int
for _, polygon := range m.polys {
numRings += polygon.NumRings()
}
var ringSuffix string
if numRings != 1 {
ringSuffix = "s"
}
return fmt.Sprintf("%s[%s] with %d polygon%s consisting of %d total ring%s and %d total points",
m.Type(), m.CoordinatesType(), numPolygons, polygonSuffix, numRings, ringSuffix, numPoints)
}
// String returns the string representation of the MultiPolygon.
func (m multiPolygon) String() string {
return m.Summary()
}