mirror of https://github.com/tidwall/tile38.git
878 lines
21 KiB
Go
878 lines
21 KiB
Go
package collection
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import (
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"math"
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"runtime"
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"github.com/tidwall/btree"
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"github.com/tidwall/geoindex"
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"github.com/tidwall/geojson"
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"github.com/tidwall/geojson/geo"
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"github.com/tidwall/geojson/geometry"
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"github.com/tidwall/rbang"
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"github.com/tidwall/tile38/internal/deadline"
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"github.com/tidwall/tinybtree"
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)
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// yieldStep forces the iterator to yield goroutine every 255 steps.
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const yieldStep = 255
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// Cursor allows for quickly paging through Scan, Within, Intersects, and Nearby
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type Cursor interface {
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Offset() uint64
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Step(count uint64)
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}
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type itemT struct {
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id string
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obj geojson.Object
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}
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func (item *itemT) Less(other btree.Item, ctx interface{}) bool {
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value1 := item.obj.String()
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value2 := other.(*itemT).obj.String()
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if value1 < value2 {
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return true
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}
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if value1 > value2 {
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return false
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}
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// the values match so we'll compare IDs, which are always unique.
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return item.id < other.(*itemT).id
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}
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// Collection represents a collection of geojson objects.
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type Collection struct {
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items tinybtree.BTree // items sorted by keys
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index *geoindex.Index // items geospatially indexed
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values *btree.BTree // items sorted by value+key
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fieldMap map[string]int
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fieldArr []string
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fieldValues map[string][]float64
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weight int
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points int
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objects int // geometry count
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nobjects int // non-geometry count
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}
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var counter uint64
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// New creates an empty collection
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func New() *Collection {
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col := &Collection{
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index: geoindex.Wrap(&rbang.RTree{}),
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values: btree.New(32, nil),
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fieldMap: make(map[string]int),
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fieldArr: make([]string, 0),
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}
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return col
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}
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func (c *Collection) setFieldValues(id string, values []float64) {
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if c.fieldValues == nil {
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c.fieldValues = make(map[string][]float64)
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}
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c.fieldValues[id] = values
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}
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func (c *Collection) getFieldValues(id string) (values []float64) {
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return c.fieldValues[id]
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}
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func (c *Collection) deleteFieldValues(id string) {
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if c.fieldValues != nil {
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delete(c.fieldValues, id)
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}
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}
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// Count returns the number of objects in collection.
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func (c *Collection) Count() int {
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return c.objects + c.nobjects
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}
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// StringCount returns the number of string values.
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func (c *Collection) StringCount() int {
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return c.nobjects
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}
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// PointCount returns the number of points (lat/lon coordinates) in collection.
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func (c *Collection) PointCount() int {
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return c.points
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}
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// TotalWeight calculates the in-memory cost of the collection in bytes.
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func (c *Collection) TotalWeight() int {
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return c.weight
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}
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// Bounds returns the bounds of all the items in the collection.
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func (c *Collection) Bounds() (minX, minY, maxX, maxY float64) {
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min, max := c.index.Bounds()
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if len(min) >= 2 && len(max) >= 2 {
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return min[0], min[1], max[0], max[1]
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}
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return
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}
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func objIsSpatial(obj geojson.Object) bool {
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_, ok := obj.(geojson.Spatial)
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return ok
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}
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func (c *Collection) objWeight(item *itemT) int {
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var weight int
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if objIsSpatial(item.obj) {
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weight = item.obj.NumPoints() * 16
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} else {
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weight = len(item.obj.String())
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}
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return weight + len(c.getFieldValues(item.id))*8 + len(item.id)
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}
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func (c *Collection) indexDelete(item *itemT) {
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if !item.obj.Empty() {
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rect := item.obj.Rect()
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c.index.Delete(
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[2]float64{rect.Min.X, rect.Min.Y},
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[2]float64{rect.Max.X, rect.Max.Y},
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item)
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}
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}
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func (c *Collection) indexInsert(item *itemT) {
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if !item.obj.Empty() {
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rect := item.obj.Rect()
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c.index.Insert(
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[2]float64{rect.Min.X, rect.Min.Y},
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[2]float64{rect.Max.X, rect.Max.Y},
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item)
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}
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}
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// Set adds or replaces an object in the collection and returns the fields
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// array. If an item with the same id is already in the collection then the
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// new item will adopt the old item's fields.
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// The fields argument is optional.
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// The return values are the old object, the old fields, and the new fields
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func (c *Collection) Set(
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id string, obj geojson.Object, fields []string, values []float64,
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) (
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oldObject geojson.Object, oldFields []float64, newFields []float64,
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) {
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newItem := &itemT{id: id, obj: obj}
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// add the new item to main btree and remove the old one if needed
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oldItem, ok := c.items.Set(id, newItem)
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if ok {
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oldItem := oldItem.(*itemT)
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// the old item was removed, now let's remove it from the rtree/btree.
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if objIsSpatial(oldItem.obj) {
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c.indexDelete(oldItem)
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c.objects--
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} else {
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c.values.Delete(oldItem)
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c.nobjects--
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}
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// decrement the point count
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c.points -= oldItem.obj.NumPoints()
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// decrement the weights
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c.weight -= c.objWeight(oldItem)
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// references
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oldObject = oldItem.obj
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oldFields = c.getFieldValues(id)
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newFields = oldFields
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}
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// insert the new item into the rtree or strings tree.
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if objIsSpatial(newItem.obj) {
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c.indexInsert(newItem)
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c.objects++
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} else {
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c.values.ReplaceOrInsert(newItem)
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c.nobjects++
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}
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// increment the point count
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c.points += newItem.obj.NumPoints()
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// add the new weights
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c.weight += c.objWeight(newItem)
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if fields == nil {
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if len(values) > 0 {
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// directly set the field values, update weight
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c.weight -= len(newFields) * 8
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newFields = values
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c.setFieldValues(id, newFields)
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c.weight += len(newFields) * 8
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}
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} else {
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// map field name to value
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for i, field := range fields {
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c.setField(newItem, field, values[i])
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}
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newFields = c.getFieldValues(id)
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}
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return oldObject, oldFields, newFields
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}
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// Delete removes an object and returns it.
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// If the object does not exist then the 'ok' return value will be false.
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func (c *Collection) Delete(id string) (
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obj geojson.Object, fields []float64, ok bool,
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) {
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oldItemV, ok := c.items.Delete(id)
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if !ok {
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return nil, nil, false
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}
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oldItem := oldItemV.(*itemT)
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if objIsSpatial(oldItem.obj) {
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if !oldItem.obj.Empty() {
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c.indexDelete(oldItem)
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}
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c.objects--
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} else {
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c.values.Delete(oldItem)
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c.nobjects--
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}
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c.weight -= c.objWeight(oldItem)
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c.points -= oldItem.obj.NumPoints()
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fields = c.getFieldValues(id)
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c.deleteFieldValues(id)
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return oldItem.obj, fields, true
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}
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// Get returns an object.
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// If the object does not exist then the 'ok' return value will be false.
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func (c *Collection) Get(id string) (
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obj geojson.Object, fields []float64, ok bool,
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) {
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itemV, ok := c.items.Get(id)
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if !ok {
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return nil, nil, false
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}
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item := itemV.(*itemT)
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return item.obj, c.getFieldValues(id), true
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}
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// SetField set a field value for an object and returns that object.
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// If the object does not exist then the 'ok' return value will be false.
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func (c *Collection) SetField(id, field string, value float64) (
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obj geojson.Object, fields []float64, updated bool, ok bool,
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) {
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itemV, ok := c.items.Get(id)
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if !ok {
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return nil, nil, false, false
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}
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item := itemV.(*itemT)
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updated = c.setField(item, field, value)
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return item.obj, c.getFieldValues(id), updated, true
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}
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// SetFields is similar to SetField, just setting multiple fields at once
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func (c *Collection) SetFields(
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id string, inFields []string, inValues []float64,
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) (obj geojson.Object, fields []float64, updatedCount int, ok bool) {
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itemV, ok := c.items.Get(id)
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if !ok {
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return nil, nil, 0, false
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}
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item := itemV.(*itemT)
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for idx, field := range inFields {
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if c.setField(item, field, inValues[idx]) {
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updatedCount++
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}
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}
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return item.obj, c.getFieldValues(id), updatedCount, true
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}
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func (c *Collection) setField(item *itemT, field string, value float64) (
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updated bool,
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) {
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idx, ok := c.fieldMap[field]
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if !ok {
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idx = len(c.fieldMap)
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c.fieldMap[field] = idx
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c.addToFieldArr(field)
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}
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fields := c.getFieldValues(item.id)
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c.weight -= len(fields) * 8
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for idx >= len(fields) {
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fields = append(fields, 0)
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}
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c.weight += len(fields) * 8
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ovalue := fields[idx]
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fields[idx] = value
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c.setFieldValues(item.id, fields)
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return ovalue != value
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}
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// FieldMap return a maps of the field names.
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func (c *Collection) FieldMap() map[string]int {
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return c.fieldMap
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}
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// FieldArr return an array representation of the field names.
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func (c *Collection) FieldArr() []string {
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return c.fieldArr
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}
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// bsearch searches array for value.
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func bsearch(arr []string, val string) (index int, found bool) {
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i, j := 0, len(arr)
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for i < j {
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h := i + (j-i)/2
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if val >= arr[h] {
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i = h + 1
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} else {
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j = h
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}
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}
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if i > 0 && arr[i-1] >= val {
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return i - 1, true
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}
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return i, false
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}
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func (c *Collection) addToFieldArr(field string) {
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if index, found := bsearch(c.fieldArr, field); !found {
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c.fieldArr = append(c.fieldArr, "")
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copy(c.fieldArr[index+1:], c.fieldArr[index:len(c.fieldArr)-1])
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c.fieldArr[index] = field
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}
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}
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// Scan iterates though the collection ids.
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func (c *Collection) Scan(
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desc bool,
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cursor Cursor,
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deadline *deadline.Deadline,
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iterator func(id string, obj geojson.Object, fields []float64) bool,
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) bool {
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var keepon = true
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var count uint64
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var offset uint64
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if cursor != nil {
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offset = cursor.Offset()
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cursor.Step(offset)
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}
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iter := func(key string, value interface{}) bool {
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count++
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if count <= offset {
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return true
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}
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nextStep(count, cursor, deadline)
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iitm := value.(*itemT)
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keepon = iterator(iitm.id, iitm.obj, c.getFieldValues(iitm.id))
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return keepon
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}
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if desc {
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c.items.Reverse(iter)
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} else {
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c.items.Scan(iter)
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}
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return keepon
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}
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// ScanRange iterates though the collection starting with specified id.
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func (c *Collection) ScanRange(
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start, end string,
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desc bool,
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cursor Cursor,
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deadline *deadline.Deadline,
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iterator func(id string, obj geojson.Object, fields []float64) bool,
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) bool {
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var keepon = true
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var count uint64
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var offset uint64
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if cursor != nil {
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offset = cursor.Offset()
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cursor.Step(offset)
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}
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iter := func(key string, value interface{}) bool {
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count++
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if count <= offset {
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return true
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}
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nextStep(count, cursor, deadline)
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if !desc {
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if key >= end {
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return false
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}
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} else {
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if key <= end {
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return false
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}
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}
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iitm := value.(*itemT)
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keepon = iterator(iitm.id, iitm.obj, c.getFieldValues(iitm.id))
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return keepon
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}
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if desc {
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c.items.Descend(start, iter)
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} else {
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c.items.Ascend(start, iter)
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}
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return keepon
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}
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// SearchValues iterates though the collection values.
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func (c *Collection) SearchValues(
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desc bool,
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cursor Cursor,
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deadline *deadline.Deadline,
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iterator func(id string, obj geojson.Object, fields []float64) bool,
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) bool {
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var keepon = true
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var count uint64
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var offset uint64
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if cursor != nil {
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offset = cursor.Offset()
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cursor.Step(offset)
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}
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iter := func(item btree.Item) bool {
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count++
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if count <= offset {
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return true
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}
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nextStep(count, cursor, deadline)
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iitm := item.(*itemT)
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keepon = iterator(iitm.id, iitm.obj, c.getFieldValues(iitm.id))
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return keepon
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}
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if desc {
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c.values.Descend(iter)
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} else {
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c.values.Ascend(iter)
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}
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return keepon
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}
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// SearchValuesRange iterates though the collection values.
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func (c *Collection) SearchValuesRange(start, end string, desc bool,
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cursor Cursor,
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deadline *deadline.Deadline,
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iterator func(id string, obj geojson.Object, fields []float64) bool,
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) bool {
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var keepon = true
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var count uint64
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var offset uint64
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if cursor != nil {
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offset = cursor.Offset()
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cursor.Step(offset)
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}
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iter := func(item btree.Item) bool {
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count++
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if count <= offset {
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return true
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}
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nextStep(count, cursor, deadline)
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iitm := item.(*itemT)
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keepon = iterator(iitm.id, iitm.obj, c.getFieldValues(iitm.id))
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return keepon
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}
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if desc {
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c.values.DescendRange(&itemT{obj: String(start)},
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&itemT{obj: String(end)}, iter)
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} else {
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c.values.AscendRange(&itemT{obj: String(start)},
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&itemT{obj: String(end)}, iter)
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}
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return keepon
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}
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// ScanGreaterOrEqual iterates though the collection starting with specified id.
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func (c *Collection) ScanGreaterOrEqual(id string, desc bool,
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cursor Cursor,
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deadline *deadline.Deadline,
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iterator func(id string, obj geojson.Object, fields []float64) bool,
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) bool {
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var keepon = true
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var count uint64
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var offset uint64
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if cursor != nil {
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offset = cursor.Offset()
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cursor.Step(offset)
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}
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iter := func(key string, value interface{}) bool {
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count++
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if count <= offset {
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return true
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}
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nextStep(count, cursor, deadline)
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iitm := value.(*itemT)
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keepon = iterator(iitm.id, iitm.obj, c.getFieldValues(iitm.id))
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return keepon
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}
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if desc {
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c.items.Descend(id, iter)
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} else {
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c.items.Ascend(id, iter)
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}
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return keepon
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}
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func (c *Collection) geoSearch(
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rect geometry.Rect,
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iter func(id string, obj geojson.Object, fields []float64) bool,
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) bool {
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alive := true
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c.index.Search(
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[2]float64{rect.Min.X, rect.Min.Y},
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[2]float64{rect.Max.X, rect.Max.Y},
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func(_, _ [2]float64, itemv interface{}) bool {
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item := itemv.(*itemT)
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alive = iter(item.id, item.obj, c.getFieldValues(item.id))
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return alive
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},
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)
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return alive
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}
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func (c *Collection) geoSparse(
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obj geojson.Object, sparse uint8,
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iter func(id string, obj geojson.Object, fields []float64) (match, ok bool),
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) bool {
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matches := make(map[string]bool)
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alive := true
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c.geoSparseInner(obj.Rect(), sparse,
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func(id string, o geojson.Object, fields []float64) (
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match, ok bool,
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) {
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ok = true
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if !matches[id] {
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match, ok = iter(id, o, fields)
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if match {
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matches[id] = true
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}
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}
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return match, ok
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},
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)
|
||
return alive
|
||
}
|
||
func (c *Collection) geoSparseInner(
|
||
rect geometry.Rect, sparse uint8,
|
||
iter func(id string, obj geojson.Object, fields []float64) (match, ok bool),
|
||
) bool {
|
||
if sparse > 0 {
|
||
w := rect.Max.X - rect.Min.X
|
||
h := rect.Max.Y - rect.Min.Y
|
||
quads := [4]geometry.Rect{
|
||
geometry.Rect{
|
||
Min: geometry.Point{X: rect.Min.X, Y: rect.Min.Y + h/2},
|
||
Max: geometry.Point{X: rect.Min.X + w/2, Y: rect.Max.Y},
|
||
},
|
||
geometry.Rect{
|
||
Min: geometry.Point{X: rect.Min.X + w/2, Y: rect.Min.Y + h/2},
|
||
Max: geometry.Point{X: rect.Max.X, Y: rect.Max.Y},
|
||
},
|
||
geometry.Rect{
|
||
Min: geometry.Point{X: rect.Min.X, Y: rect.Min.Y},
|
||
Max: geometry.Point{X: rect.Min.X + w/2, Y: rect.Min.Y + h/2},
|
||
},
|
||
geometry.Rect{
|
||
Min: geometry.Point{X: rect.Min.X + w/2, Y: rect.Min.Y},
|
||
Max: geometry.Point{X: rect.Max.X, Y: rect.Min.Y + h/2},
|
||
},
|
||
}
|
||
for _, quad := range quads {
|
||
if !c.geoSparseInner(quad, sparse-1, iter) {
|
||
return false
|
||
}
|
||
}
|
||
return true
|
||
}
|
||
alive := true
|
||
c.geoSearch(rect,
|
||
func(id string, obj geojson.Object, fields []float64) bool {
|
||
match, ok := iter(id, obj, fields)
|
||
if !ok {
|
||
alive = false
|
||
return false
|
||
}
|
||
return !match
|
||
},
|
||
)
|
||
return alive
|
||
}
|
||
|
||
// Within returns all object that are fully contained within an object or
|
||
// bounding box. Set obj to nil in order to use the bounding box.
|
||
func (c *Collection) Within(
|
||
obj geojson.Object,
|
||
sparse uint8,
|
||
cursor Cursor,
|
||
deadline *deadline.Deadline,
|
||
iter func(id string, obj geojson.Object, fields []float64) bool,
|
||
) bool {
|
||
var count uint64
|
||
var offset uint64
|
||
if cursor != nil {
|
||
offset = cursor.Offset()
|
||
cursor.Step(offset)
|
||
}
|
||
if sparse > 0 {
|
||
return c.geoSparse(obj, sparse,
|
||
func(id string, o geojson.Object, fields []float64) (
|
||
match, ok bool,
|
||
) {
|
||
count++
|
||
if count <= offset {
|
||
return false, true
|
||
}
|
||
nextStep(count, cursor, deadline)
|
||
if match = o.Within(obj); match {
|
||
ok = iter(id, o, fields)
|
||
}
|
||
return match, ok
|
||
},
|
||
)
|
||
}
|
||
return c.geoSearch(obj.Rect(),
|
||
func(id string, o geojson.Object, fields []float64) bool {
|
||
count++
|
||
if count <= offset {
|
||
return true
|
||
}
|
||
nextStep(count, cursor, deadline)
|
||
if o.Within(obj) {
|
||
return iter(id, o, fields)
|
||
}
|
||
return true
|
||
},
|
||
)
|
||
}
|
||
|
||
// Intersects returns all object that are intersect an object or bounding box.
|
||
// Set obj to nil in order to use the bounding box.
|
||
func (c *Collection) Intersects(
|
||
obj geojson.Object,
|
||
sparse uint8,
|
||
cursor Cursor,
|
||
deadline *deadline.Deadline,
|
||
iter func(id string, obj geojson.Object, fields []float64) bool,
|
||
) bool {
|
||
var count uint64
|
||
var offset uint64
|
||
if cursor != nil {
|
||
offset = cursor.Offset()
|
||
cursor.Step(offset)
|
||
}
|
||
if sparse > 0 {
|
||
return c.geoSparse(obj, sparse,
|
||
func(id string, o geojson.Object, fields []float64) (
|
||
match, ok bool,
|
||
) {
|
||
count++
|
||
if count <= offset {
|
||
return false, true
|
||
}
|
||
nextStep(count, cursor, deadline)
|
||
if match = o.Intersects(obj); match {
|
||
ok = iter(id, o, fields)
|
||
}
|
||
return match, ok
|
||
},
|
||
)
|
||
}
|
||
return c.geoSearch(obj.Rect(),
|
||
func(id string, o geojson.Object, fields []float64) bool {
|
||
count++
|
||
if count <= offset {
|
||
return true
|
||
}
|
||
nextStep(count, cursor, deadline)
|
||
if o.Intersects(obj) {
|
||
return iter(id, o, fields)
|
||
}
|
||
return true
|
||
},
|
||
)
|
||
}
|
||
|
||
// Nearby returns the nearest neighbors
|
||
func (c *Collection) Nearby(
|
||
target geojson.Object,
|
||
cursor Cursor,
|
||
deadline *deadline.Deadline,
|
||
iter func(id string, obj geojson.Object, fields []float64, dist float64) bool,
|
||
) bool {
|
||
// First look to see if there's at least one candidate in the circle's
|
||
// outer rectangle. This is a fast-fail operation.
|
||
if circle, ok := target.(*geojson.Circle); ok {
|
||
meters := circle.Meters()
|
||
if meters > 0 {
|
||
center := circle.Center()
|
||
minLat, minLon, maxLat, maxLon :=
|
||
geo.RectFromCenter(center.Y, center.X, meters)
|
||
var exists bool
|
||
c.index.Search(
|
||
[2]float64{minLon, minLat},
|
||
[2]float64{maxLon, maxLat},
|
||
func(_, _ [2]float64, itemv interface{}) bool {
|
||
exists = true
|
||
return false
|
||
},
|
||
)
|
||
if !exists {
|
||
// no candidates
|
||
return true
|
||
}
|
||
}
|
||
}
|
||
// do the kNN operation
|
||
alive := true
|
||
center := target.Center()
|
||
var count uint64
|
||
var offset uint64
|
||
if cursor != nil {
|
||
offset = cursor.Offset()
|
||
cursor.Step(offset)
|
||
}
|
||
c.index.Nearby(
|
||
geodeticDistAlgo([2]float64{center.X, center.Y}),
|
||
func(_, _ [2]float64, itemv interface{}, dist float64) bool {
|
||
count++
|
||
if count <= offset {
|
||
return true
|
||
}
|
||
nextStep(count, cursor, deadline)
|
||
item := itemv.(*itemT)
|
||
alive = iter(item.id, item.obj, c.getFieldValues(item.id), dist)
|
||
return alive
|
||
},
|
||
)
|
||
return alive
|
||
}
|
||
|
||
func nextStep(step uint64, cursor Cursor, deadline *deadline.Deadline) {
|
||
if step&yieldStep == yieldStep {
|
||
runtime.Gosched()
|
||
deadline.Check()
|
||
}
|
||
if cursor != nil {
|
||
cursor.Step(1)
|
||
}
|
||
}
|
||
|
||
func geodeticDistAlgo(center [2]float64) func(
|
||
min, max [2]float64, data interface{}, item bool,
|
||
add func(min, max [2]float64, data interface{}, item bool, dist float64),
|
||
) {
|
||
const earthRadius = 6371e3
|
||
return func(
|
||
min, max [2]float64, data interface{}, item bool,
|
||
add func(min, max [2]float64, data interface{}, item bool, dist float64),
|
||
) {
|
||
add(min, max, data, item, earthRadius*pointRectDistGeodeticDeg(
|
||
center[1], center[0],
|
||
min[1], min[0],
|
||
max[1], max[0],
|
||
))
|
||
}
|
||
}
|
||
|
||
func pointRectDistGeodeticDeg(pLat, pLng, minLat, minLng, maxLat, maxLng float64) float64 {
|
||
result := pointRectDistGeodeticRad(
|
||
pLat*math.Pi/180, pLng*math.Pi/180,
|
||
minLat*math.Pi/180, minLng*math.Pi/180,
|
||
maxLat*math.Pi/180, maxLng*math.Pi/180,
|
||
)
|
||
return result
|
||
}
|
||
|
||
func pointRectDistGeodeticRad(φq, λq, φl, λl, φh, λh float64) float64 {
|
||
// Algorithm from:
|
||
// Schubert, E., Zimek, A., & Kriegel, H.-P. (2013).
|
||
// Geodetic Distance Queries on R-Trees for Indexing Geographic Data.
|
||
// Lecture Notes in Computer Science, 146–164.
|
||
// doi:10.1007/978-3-642-40235-7_9
|
||
const (
|
||
twoΠ = 2 * math.Pi
|
||
halfΠ = math.Pi / 2
|
||
)
|
||
|
||
// distance on the unit sphere computed using Haversine formula
|
||
distRad := func(φa, λa, φb, λb float64) float64 {
|
||
if φa == φb && λa == λb {
|
||
return 0
|
||
}
|
||
|
||
Δφ := φa - φb
|
||
Δλ := λa - λb
|
||
sinΔφ := math.Sin(Δφ / 2)
|
||
sinΔλ := math.Sin(Δλ / 2)
|
||
cosφa := math.Cos(φa)
|
||
cosφb := math.Cos(φb)
|
||
|
||
return 2 * math.Asin(math.Sqrt(sinΔφ*sinΔφ+sinΔλ*sinΔλ*cosφa*cosφb))
|
||
}
|
||
|
||
// Simple case, point or invalid rect
|
||
if φl >= φh && λl >= λh {
|
||
return distRad(φl, λl, φq, λq)
|
||
}
|
||
|
||
if λl <= λq && λq <= λh { // q is north or south of r
|
||
if φl <= φq && φq <= φh { // Inside
|
||
return 0
|
||
}
|
||
|
||
if φq < φl { // South
|
||
return φl - φq
|
||
}
|
||
|
||
return φq - φh // North
|
||
}
|
||
|
||
// determine if q is closer to the east or west edge of r to select edge for
|
||
// tests below
|
||
Δλe := λl - λq
|
||
Δλw := λq - λh
|
||
if Δλe < 0 {
|
||
Δλe += twoΠ
|
||
}
|
||
if Δλw < 0 {
|
||
Δλw += twoΠ
|
||
}
|
||
var Δλ float64 // distance to closest edge
|
||
var λedge float64 // longitude of closest edge
|
||
if Δλe <= Δλw {
|
||
Δλ = Δλe
|
||
λedge = λl
|
||
} else {
|
||
Δλ = Δλw
|
||
λedge = λh
|
||
}
|
||
|
||
sinΔλ, cosΔλ := math.Sincos(Δλ)
|
||
tanφq := math.Tan(φq)
|
||
|
||
if Δλ >= halfΠ {
|
||
// If Δλ > 90 degrees (1/2 pi in radians) we're in one of the corners
|
||
// (NW/SW or NE/SE depending on the edge selected). Compare against the
|
||
// center line to decide which case we fall into
|
||
φmid := (φh + φl) / 2
|
||
if tanφq >= math.Tan(φmid)*cosΔλ {
|
||
return distRad(φq, λq, φh, λedge) // North corner
|
||
}
|
||
return distRad(φq, λq, φl, λedge) // South corner
|
||
}
|
||
|
||
if tanφq >= math.Tan(φh)*cosΔλ {
|
||
return distRad(φq, λq, φh, λedge) // North corner
|
||
}
|
||
|
||
if tanφq <= math.Tan(φl)*cosΔλ {
|
||
return distRad(φq, λq, φl, λedge) // South corner
|
||
}
|
||
|
||
// We're to the East or West of the rect, compute distance using cross-track
|
||
// Note that this is a simplification of the cross track distance formula
|
||
// valid since the track in question is a meridian.
|
||
return math.Asin(math.Cos(φq) * sinΔλ)
|
||
}
|