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First release.

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Tessa Nordgren 2015-03-25 09:53:31 -07:00
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GNU LESSER GENERAL PUBLIC LICENSE
Version 3, 29 June 2007
Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
Everyone is permitted to copy and distribute verbatim copies
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# ntree - an n-dimensional tree structure in Go.
This library is an abstraction of the design behind
[Quadtrees](https://en.wikipedia.org/wiki/Quadtree) and
[Octrees](https://en.wikipedia.org/wiki/Octree), useful data structures in 2d
and 3d graphics. Those cases are n=2 and n=3 specific cases for this library,
which should handle any case up to 63 dimensions.
Note that each additional dimension added makes the tree structure exponentially
slower, so cases over about 16 dimensions are not recommended.
## Install
This library is fully installable via go get:
go get -u -v github.com/nergdron/ntree
## Tests and Benchmarks
There are useful unit tests and benchmarks included. Run them with the
standard go test command:
go test -bench=.*
You can also verify thread safety by running the same tests with more
active CPUs:
go test -bench=.* -cpu 4
You should find that Add() becomes slightly slower per op with more concurrency
due to lock contention, but Search() becomes linearly faster due to parallelism.
## License
NTree is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
kdtree is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with kdtree. If not, see
[http://www.gnu.org/licenses/](http://www.gnu.org/licenses/).

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ntree.go Normal file
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// NTrees are an N-dimensional subdividing spacial representation.
// Common dimension-specific types are the 2-dimensional (quadtree) and
// 3-dimensional (octree) variants. This library supports an arbitrary number of
// dimensions, implemented in the same manner as those specific cases.
package ntree
import (
"errors"
"strconv"
"sync"
"github.com/cznic/mathutil"
)
// Maximum number of dimensions handled by this lib. Currently restricted by
// number of usable bits in Go's int type.
const MaxN = 63
// NTree is a bounding box in N-dimensional space, along with optional data
// and children.
type NTree struct {
// The bounding n-dimensional box for this ntree. It should always
// be true that origin[i] += bounds[i] contains p.coords[i].
center, bounds []float64
// Optional piece of data to associate with this node. Location may be
// imprecise on leaf nodes.
p *Point
// Slice for child storage, should be 2^n if initialized.
children []*NTree
// Used to coordinate write operations, concurrency.
mutex sync.RWMutex
// keep track of child point counts under each node, useful for
// histograms, density predictions, etc.
count uint64
}
// New creates an ntree root node, using N dimensional slices for
// the center coordinates and relative bounds of the tree space.
// Bounds slice values must be positive, as they define
// a range of center[i] +- bounds[i] for each dimension.
//
// Returns an error if center and bounds don't have the same cardinality,
// or a bounds dimension is <= 0.
func New(center, bounds []float64) (nt *NTree, err error) {
if len(center) > MaxN {
return nil, errors.New("64 bit ints limit this library to <= 63 dimensions")
}
if len(center) != len(bounds) {
return nil, errors.New("center and bounds have mismatched lengths")
}
if len(center) == 0 {
return nil, errors.New("Can't have 0-dimensional ntree")
}
for i := range bounds {
if bounds[i] <= 0 {
return nil, errors.New("Dimension " + strconv.FormatInt(int64(i), 10) +
" has bounding size <= 0.")
}
}
nt = new(NTree)
nt.center = center
nt.bounds = bounds
return nt, nil
}
// N returns the number of dimensions (N) for this NTree.
func (nt *NTree) N() int {
return len(nt.center)
}
// Center returns the center coordinates for this NTree node.
func (nt *NTree) Center() []float64 {
nt.mutex.RLock()
defer nt.mutex.RUnlock()
return nt.center
}
// Bounds returns the positive bounding dimensions from center for this NTree
// node. This node covers the entire space of Center() +- Bounds().
func (nt *NTree) Bounds() []float64 {
nt.mutex.RLock()
defer nt.mutex.RUnlock()
return nt.bounds
}
// BoundPoints returns the min and max points for this NTree node.
// This is a shortcut instead of doing the Center() +- Bounds() math manually.
func (nt *NTree) BoundPoints() (min, max []float64) {
nt.mutex.RLock()
defer nt.mutex.RUnlock()
min = make([]float64, len(nt.center))
max = make([]float64, len(nt.center))
for i := range nt.center {
min[i] = nt.center[i] - nt.bounds[i]
max[i] = nt.center[i] + nt.bounds[i]
}
return min, max
}
// Point returns the optional data chunk associated with this NTree nodes.
// This will return null if there's no Point on this node, which should happen
// on any non-leaf node.
func (nt *NTree) Point() *Point {
nt.mutex.RLock()
defer nt.mutex.RUnlock()
return nt.p
}
// Count returns this node's estimate of how many Points lie within it.
func (nt *NTree) Count() uint64 {
nt.mutex.RLock()
defer nt.mutex.RUnlock()
return nt.count
}
// Contains checks if point p is within the bounds of the ntree.
// Returns an error if len(p) != nt.N().
func (nt *NTree) Contains(p *Point) (bool, error) {
nt.mutex.RLock()
defer nt.mutex.RUnlock()
if p == nil {
return false, errors.New("Point is nil")
}
if len(p.Coords) != nt.N() {
return false, errors.New("Point is " + strconv.FormatUint(uint64(len(p.Coords)), 10) +
" dimensional, NTree is " + strconv.FormatUint(uint64(nt.N()), 10))
}
// fmt.Println(p)
for i := range p.Coords {
if (nt.center[i]-nt.bounds[i]) > p.Coords[i] || (nt.center[i]+nt.bounds[i]) < p.Coords[i] {
return false, nil
}
}
return true, nil
}
// Bitwise operations on array indices are used to keep track of what subset of
// space each child occupies, as described here:
// http://www.brandonpelfrey.com/blog/coding-a-simple-octree/
func hasBit(n int, pos uint) bool {
val := n & (1 << pos)
return (val > 0)
}
func setBit(n int, pos uint) int {
n |= (1 << pos)
return n
}
// Add inserts a new Point into the NTree. Returns an error on any failure,
// or nil.
func (nt *NTree) Add(p *Point) error {
in, err := nt.Contains(p)
if err != nil {
return err
}
if !in {
return errors.New("Point doesn't fall within bounds of NTree.")
}
nt.mutex.Lock()
if nt.p == nil && nt.children == nil {
defer nt.mutex.Unlock()
// simplest case, add to current node
nt.p = p
nt.count++
return nil
}
if nt.children != nil {
defer nt.mutex.Unlock()
// recurse into children by generating child bounding bitmask
var target int
for j := range nt.center {
if p.Coords[j] > nt.center[j] {
target = setBit(target, uint(j))
}
}
err = nt.children[target].Add(p)
if err == nil {
nt.count++
}
return err
}
if nt.p != nil && nt.children == nil {
// create children, re-add current node's Point data, then add Point p.
size := mathutil.ModPowUint64(2, uint64(nt.N()), mathutil.MaxInt)
nt.children = make([]*NTree, size)
// create new child nodes with correct bounds
for i := range nt.children {
// determine child dimensions
center := make([]float64, nt.N())
bounds := make([]float64, nt.N())
for j := range center {
// use bitmask of child index to determine dimension range for child.
// positive bit means positive range, otherwise negative range.
if hasBit(i, uint(j)) {
bounds[j] = nt.bounds[j] / 2.0
center[j] = nt.center[j] + bounds[j]
} else {
bounds[j] = nt.bounds[j] / 2.0
center[j] = nt.center[j] - bounds[j]
}
}
if nt.children[i], err = New(center, bounds); err != nil {
return err
}
}
// remove current Point data and re-add so it cascades into child nodes.
// need to bounce the mutex for this, prossible race condition?
curP := nt.p
nt.p = nil
nt.count--
nt.mutex.Unlock()
if err = nt.Add(curP); err != nil {
return err
}
// now add new Point
return nt.Add(p)
}
return nil
}

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package ntree
import (
"math/rand"
"runtime"
"sync"
"testing"
"time"
)
var wg sync.WaitGroup
func init() {
// Use different values every test to try and catch edge cases.
rand.Seed(time.Now().Unix())
}
func TestInit(t *testing.T) {
// test all available dimensional combinations
for n := 1; n <= MaxN; n++ {
t.Log("Testing", n, "dimension(s).")
center := make([]float64, n)
bounds := make([]float64, n)
for i := range center {
center[i] = 0
bounds[i] = 1
}
nt, err := New(center, bounds)
if err != nil {
t.Fatal(err)
}
if nt.N() != n {
t.Fatal(n, "dimensional tree returned n=", nt.N())
}
}
}
func TestAdd(t *testing.T) {
count := 500
max := runtime.GOMAXPROCS(-1)
// > 16 dimensions quickly becomes impractical for memory and processing reasons.
for n := 1; n <= 16; n++ {
t.Log("Testing", n, "dimension(s).")
center := make([]float64, n)
bounds := make([]float64, n)
p1 := make([]float64, n)
for i := range center {
center[i] = 0.0
bounds[i] = 1.0
p1[i] = -1.0
}
nt, err := New(center, bounds)
if err != nil {
t.Fatal(err, n)
}
wg.Add(max)
for i := 0; i < max; i++ {
go func() {
for j := 0; j < count/max; j++ {
p := new(Point)
p.Coords = make([]float64, n)
for j := range p.Coords {
p.Coords[j] = (rand.Float64() * 2.0) - 1.0
}
if err = nt.Add(p); err != nil {
t.Error(err, n, i)
}
}
wg.Done()
}()
}
count = (count / max) * max
wg.Wait()
points, err := nt.Search(p1, bounds)
if err != nil {
t.Fatal(err)
}
if len(points) != count {
t.Fatal("Search returned", len(points), "points instead of", count)
}
if nt.Count() != uint64(count) {
t.Error("Tree estimated incorrect, sees", nt.Count(), "points instead of", count)
}
}
}
func benchAdd(b *testing.B, n int) {
b.StopTimer()
max := runtime.GOMAXPROCS(-1)
center := make([]float64, n)
bounds := make([]float64, n)
for i := range center {
center[i] = 0
bounds[i] = 1
}
nt, err := New(center, bounds)
if err != nil {
b.Fatal(err)
}
wg.Add(max)
b.StartTimer()
for i := 0; i < max; i++ {
go func() {
for j := 0; j < b.N/max; j++ {
p := new(Point)
p.Coords = make([]float64, n)
for j := range p.Coords {
p.Coords[j] = (rand.Float64() * 2.0) - 1.0
}
if err = nt.Add(p); err != nil {
b.Error(err)
}
}
wg.Done()
}()
}
wg.Wait()
}
func benchSearch(b *testing.B, n int) {
b.StopTimer()
max := runtime.GOMAXPROCS(-1)
center := make([]float64, n)
bounds := make([]float64, n)
for i := range center {
center[i] = 0
bounds[i] = 1
}
nt, err := New(center, bounds)
if err != nil {
b.Fatal(err)
}
// 10k points gives a reasonable search space.
for i := 0; i < 10000; i++ {
p := new(Point)
p.Coords = make([]float64, n)
for j := range p.Coords {
p.Coords[j] = (rand.Float64() * 2.0) - 1.0
}
if err = nt.Add(p); err != nil {
b.Fatal(err)
}
}
var swap float64
var count uint64
wg.Add(max)
b.StartTimer()
for i := 0; i < max; i++ {
go func() {
p1 := make([]float64, n)
p2 := make([]float64, n)
for j := 0; j < (b.N / max); j++ {
// generate random search area
for j := range p1 {
p1[j] = (rand.Float64() * 2.0) - 1.0
p2[j] = (rand.Float64() * 2.0) - 1.0
if p1[j] > p2[j] {
swap = p1[j]
p1[j] = p2[j]
p2[j] = swap
}
}
// find points within it!
points, err := nt.Search(p1, p2)
if err != nil {
b.Fatal(err)
}
count += uint64(len(points))
}
wg.Done()
}()
}
wg.Wait()
if count == 0 && b.N > 100 {
b.Log("Failed to find any points after", b.N, "searches.")
}
}
func BenchmarkQuadtreeAdd(b *testing.B) {
benchAdd(b, 2)
}
func BenchmarkQuadtreeSearch(b *testing.B) {
benchSearch(b, 2)
}
func BenchmarkOctreeAdd(b *testing.B) {
benchAdd(b, 3)
}
func BenchmarkOcttreeSearch(b *testing.B) {
benchSearch(b, 3)
}

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package ntree
// Point information to be stored in an NTree leaf node.
type Point struct {
Coords []float64
// Arbitrary data attached to this Point.
Data *interface{}
}

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package ntree
import "errors"
// Iter runs function f on every node in the tree.
func (nt *NTree) Iter(f func(n *NTree)) {
nt.mutex.Lock()
defer nt.mutex.Unlock()
f(nt)
if nt.children != nil {
for i := range nt.children {
f(nt.children[i])
}
}
}
// Search finds all Points falling within the bounding box between p1 and p2.
// Note that it is assumed for every dimension i, p1[i] <= p2[i].
// This is an inclusive search, so Points whose coordinates are equal to
// the supplied bounds in a given dimension will match.
//
// Returns nil, error if the length of p1, p2 don't match
// nt.N().
func (nt *NTree) Search(p1, p2 []float64) (points []*Point, err error) {
nt.mutex.RLock()
defer nt.mutex.RUnlock()
if len(p1) != len(p2) || len(p2) != nt.N() {
return nil, errors.New("Bounding points have different dimensions than tree.")
}
if nt.children == nil && nt.p != nil {
// check local Point for leaf node
for i := range nt.p.Coords {
if nt.p.Coords[i] < p1[i] || nt.p.Coords[i] > p2[i] {
return nil, nil
}
}
return []*Point{nt.p}, nil
}
if nt.children != nil {
// check children for matching bounds, and collect matching points from them.
points = make([]*Point, 0)
for _, child := range nt.children {
for i := range p1 {
s1 := child.center[i] - child.bounds[i]
s2 := child.center[i] + child.bounds[i]
// skip this child if outside this dimension's bounds
if (s1 < p1[i] && s2 < p1[i]) || (s1 > p2[i] && s2 > p2[i]) {
continue
}
}
p, err := child.Search(p1, p2)
if err != nil {
return nil, err
}
points = append(points, p...)
}
}
return points, nil
}