1// Copyright ©2019 The Gonum Authors. All rights reserved.
2// Use of this source code is governed by a BSD-style
3// license that can be found in the LICENSE file.
4
5package kdtree
6
7import "math"
8
9var (
10	_ Interface  = Points(nil)
11	_ Comparable = Point(nil)
12)
13
14// Point represents a point in a k-d space that satisfies the Comparable interface.
15type Point []float64
16
17// Compare returns the signed distance of p from the plane passing through c and
18// perpendicular to the dimension d. The concrete type of c must be Point.
19func (p Point) Compare(c Comparable, d Dim) float64 { q := c.(Point); return p[d] - q[d] }
20
21// Dims returns the number of dimensions described by the receiver.
22func (p Point) Dims() int { return len(p) }
23
24// Distance returns the squared Euclidean distance between c and the receiver. The
25// concrete type of c must be Point.
26func (p Point) Distance(c Comparable) float64 {
27	q := c.(Point)
28	var sum float64
29	for dim, c := range p {
30		d := c - q[dim]
31		sum += d * d
32	}
33	return sum
34}
35
36// Extend returns a bounding box that has been extended to include the receiver.
37func (p Point) Extend(b *Bounding) *Bounding {
38	if b == nil {
39		b = &Bounding{append(Point(nil), p...), append(Point(nil), p...)}
40	}
41	min := b.Min.(Point)
42	max := b.Max.(Point)
43	for d, v := range p {
44		min[d] = math.Min(min[d], v)
45		max[d] = math.Max(max[d], v)
46	}
47	*b = Bounding{Min: min, Max: max}
48	return b
49}
50
51// Points is a collection of point values that satisfies the Interface.
52type Points []Point
53
54func (p Points) Bounds() *Bounding {
55	if p.Len() == 0 {
56		return nil
57	}
58	min := append(Point(nil), p[0]...)
59	max := append(Point(nil), p[0]...)
60	for _, e := range p[1:] {
61		for d, v := range e {
62			min[d] = math.Min(min[d], v)
63			max[d] = math.Max(max[d], v)
64		}
65	}
66	return &Bounding{Min: min, Max: max}
67}
68func (p Points) Index(i int) Comparable         { return p[i] }
69func (p Points) Len() int                       { return len(p) }
70func (p Points) Pivot(d Dim) int                { return Plane{Points: p, Dim: d}.Pivot() }
71func (p Points) Slice(start, end int) Interface { return p[start:end] }
72
73// Plane is a wrapping type that allows a Points type be pivoted on a dimension.
74// The Pivot method of Plane uses MedianOfRandoms sampling at most 100 elements
75// to find a pivot element.
76type Plane struct {
77	Dim
78	Points
79}
80
81// randoms is the maximum number of random values to sample for calculation of
82// median of random elements.
83const randoms = 100
84
85func (p Plane) Less(i, j int) bool              { return p.Points[i][p.Dim] < p.Points[j][p.Dim] }
86func (p Plane) Pivot() int                      { return Partition(p, MedianOfRandoms(p, randoms)) }
87func (p Plane) Slice(start, end int) SortSlicer { p.Points = p.Points[start:end]; return p }
88func (p Plane) Swap(i, j int)                   { p.Points[i], p.Points[j] = p.Points[j], p.Points[i] }
89