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kdtree.go
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kdtree.go
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package pointcloud
import (
"math"
"github.com/golang/geo/r3"
"gonum.org/v1/gonum/spatial/kdtree"
)
// PointAndData is a tiny struct to facilitate returning nearest neighbors in a neat way.
type PointAndData struct {
P r3.Vector
D Data
}
// wraps r3.vector to make it compatible with kd trees.
type treeComparableR3Vector struct {
vec r3.Vector
}
func (v treeComparableR3Vector) Compare(c kdtree.Comparable, d kdtree.Dim) float64 {
v2, ok := c.(treeComparableR3Vector)
if !ok {
panic("treeComparableR3Vector Compare got wrong data")
}
switch d {
case 0:
return v.vec.X - v2.vec.X
case 1:
return v.vec.Y - v2.vec.Y
case 2:
return v.vec.Z - v2.vec.Z
default:
panic("illegal dimension fed to treeComparableR3Vector.Compare")
}
}
func (v treeComparableR3Vector) Dims() int {
return 3
}
func (v treeComparableR3Vector) Distance(c kdtree.Comparable) float64 {
v2, ok := c.(treeComparableR3Vector)
if !ok {
panic("treeComparableR3Vector Distance got wrong data")
}
return v.vec.Distance(v2.vec)
}
type kdValues []treeComparableR3Vector
func (vs kdValues) Index(i int) kdtree.Comparable { return vs[i] }
func (vs kdValues) Len() int { return len(vs) }
func (vs kdValues) Slice(start, end int) kdtree.Interface { return vs[start:end] }
func (vs kdValues) Swap(i, j int) {
vs[i], vs[j] = vs[j], vs[i]
}
func (vs kdValues) Pivot(d kdtree.Dim) int {
return kdValuesSlicer{vs: vs}.Pivot()
}
type kdValuesSlicer struct {
vs kdValues
}
func (kdv kdValuesSlicer) Len() int { return len(kdv.vs) }
func (kdv kdValuesSlicer) Less(i, j int) bool {
return kdv.vs[i].vec.Distance(kdv.vs[j].vec) < 0
}
func (kdv kdValuesSlicer) Pivot() int { return kdtree.Partition(kdv, kdtree.MedianOfMedians(kdv)) }
func (kdv kdValuesSlicer) Slice(start, end int) kdtree.SortSlicer {
kdv.vs = kdv.vs[start:end]
return kdv
}
func (kdv kdValuesSlicer) Swap(i, j int) {
kdv.vs[i], kdv.vs[j] = kdv.vs[j], kdv.vs[i]
}
// ----------
// KDTree extends PointCloud and orders the points in 3D space to implement nearest neighbor algos.
type KDTree struct {
tree *kdtree.Tree
points storage
meta MetaData
}
// NewKDTree creates a new KDTree.
func NewKDTree() *KDTree {
return NewKDTreeWithPrealloc(0)
}
// NewKDTreeWithPrealloc creates a new KDTree with preallocated storage.
func NewKDTreeWithPrealloc(size int) *KDTree {
return &KDTree{
tree: kdtree.New(kdValues{}, false),
points: &matrixStorage{points: make([]PointAndData, 0, size), indexMap: make(map[r3.Vector]uint, size)},
meta: NewMetaData(),
}
}
// ToKDTree creates a KDTree from an input PointCloud.
func ToKDTree(pc PointCloud) *KDTree {
kd, ok := pc.(*KDTree)
if ok {
return kd
}
t := NewKDTreeWithPrealloc(pc.Size())
if pc != nil {
pc.Iterate(0, 0, func(p r3.Vector, d Data) bool {
_, pointExists := t.At(p.X, p.Y, p.Z)
err := t.Set(p, d)
if err != nil {
panic(err)
}
err = t.points.Set(p, d)
if err != nil {
panic(err)
}
if !pointExists {
t.meta.Merge(p, d)
}
return true
})
}
return t
}
// MetaData returns the meta data.
func (kd *KDTree) MetaData() MetaData {
return kd.meta
}
// Size returns the size of the pointcloud.
func (kd *KDTree) Size() int {
return kd.points.Size()
}
// Set adds a new point to the PointCloud and tree. Does not rebalance the tree.
func (kd *KDTree) Set(p r3.Vector, d Data) error {
kd.tree.Insert(treeComparableR3Vector{p}, false)
if err := kd.points.Set(p, d); err != nil {
return err
}
kd.meta.Merge(p, d)
return nil
}
// At gets the point at position (x,y,z) from the PointCloud.
// It returns the data of the nearest neighbor and a boolean representing whether there is a point at that position.
func (kd *KDTree) At(x, y, z float64) (Data, bool) {
p, d, _, got := kd.NearestNeighbor(r3.Vector{x, y, z})
if !got {
return nil, false
}
if x == p.X && y == p.Y && z == p.Z {
return d, true
}
return nil, false
}
// NearestNeighbor returns the nearest point and its distance from the input point.
func (kd *KDTree) NearestNeighbor(p r3.Vector) (r3.Vector, Data, float64, bool) {
c, dist := kd.tree.Nearest(&treeComparableR3Vector{p})
if c == nil {
return r3.Vector{}, nil, 0.0, false
}
p2, ok := c.(treeComparableR3Vector)
if !ok {
panic("kdtree.Comparable is not a Point")
}
d, ok := kd.points.At(p2.vec.X, p2.vec.Y, p2.vec.Z)
if !ok {
panic("Mismatch between tree and point storage.")
}
return p2.vec, d, dist, true
}
func keeperToArray(heap kdtree.Heap, points storage, p r3.Vector, includeSelf bool, max int) []*PointAndData {
nearestPoints := make([]*PointAndData, 0, heap.Len())
for i := 0; i < heap.Len(); i++ {
if heap[i].Comparable == nil {
continue
}
pp, ok := heap[i].Comparable.(treeComparableR3Vector)
if !ok {
panic("impossible")
}
if !includeSelf && p.ApproxEqual(pp.vec) {
continue
}
d, ok := points.At(pp.vec.X, pp.vec.Y, pp.vec.Z)
if !ok {
panic("Mismatch between tree and point storage.")
}
nearestPoints = append(nearestPoints, &PointAndData{P: pp.vec, D: d})
if len(nearestPoints) >= max {
break
}
}
return nearestPoints
}
// KNearestNeighbors returns the k nearest points ordered by distance. if includeSelf is true and if the point p
// is in the point cloud, point p will also be returned in the slice as the first element with distance 0.
func (kd *KDTree) KNearestNeighbors(p r3.Vector, k int, includeSelf bool) []*PointAndData {
tempK := k
if !includeSelf {
tempK++
}
keep := kdtree.NewNKeeper(tempK)
kd.tree.NearestSet(keep, &treeComparableR3Vector{p})
return keeperToArray(keep.Heap, kd.points, p, includeSelf, k)
}
// RadiusNearestNeighbors returns the nearest points within a radius r (inclusive) ordered by distance.
// If includeSelf is true and if the point p is in the point cloud, point p will also be returned in the slice
// as the first element with distance 0.
func (kd *KDTree) RadiusNearestNeighbors(p r3.Vector, r float64, includeSelf bool) []*PointAndData {
keep := kdtree.NewDistKeeper(r)
kd.tree.NearestSet(keep, &treeComparableR3Vector{p})
return keeperToArray(keep.Heap, kd.points, p, includeSelf, math.MaxInt)
}
// Iterate iterates over all points in the cloud.
func (kd *KDTree) Iterate(numBatches, myBatch int, fn func(p r3.Vector, d Data) bool) {
kd.tree.Do(func(c kdtree.Comparable, b *kdtree.Bounding, depth int) bool {
p, ok := c.(treeComparableR3Vector)
if !ok {
panic("Comparable is not a Point")
}
d, ok := kd.points.At(p.vec.X, p.vec.Y, p.vec.Z)
if !ok {
panic("Mismatch between tree and point storage.")
}
return !fn(p.vec, d)
})
}