staticmap/vendor/github.com/golang/geo/s1/interval.go

/*
Copyright 2014 Google Inc. All rights reserved.

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/

package s1

import (
	"math"
	"strconv"
)

// Interval represents a closed interval on a unit circle.
// Zero-length intervals (where Lo == Hi) represent single points.
// If Lo > Hi then the interval is "inverted".
// The point at (-1, 0) on the unit circle has two valid representations,
// [π,π] and [-π,-π]. We normalize the latter to the former in IntervalFromEndpoints.
// There are two special intervals that take advantage of that:
//   - the full interval, [-π,π], and
//   - the empty interval, [π,-π].
// Treat the exported fields as read-only.
type Interval struct {
	Lo, Hi float64
}

// IntervalFromEndpoints constructs a new interval from endpoints.
// Both arguments must be in the range [-π,π]. This function allows inverted intervals
// to be created.
func IntervalFromEndpoints(lo, hi float64) Interval {
	i := Interval{lo, hi}
	if lo == -math.Pi && hi != math.Pi {
		i.Lo = math.Pi
	}
	if hi == -math.Pi && lo != math.Pi {
		i.Hi = math.Pi
	}
	return i
}

// IntervalFromPointPair returns the minimal interval containing the two given points.
// Both arguments must be in [-π,π].
func IntervalFromPointPair(a, b float64) Interval {
	if a == -math.Pi {
		a = math.Pi
	}
	if b == -math.Pi {
		b = math.Pi
	}
	if positiveDistance(a, b) <= math.Pi {
		return Interval{a, b}
	}
	return Interval{b, a}
}

// EmptyInterval returns an empty interval.
func EmptyInterval() Interval { return Interval{math.Pi, -math.Pi} }

// FullInterval returns a full interval.
func FullInterval() Interval { return Interval{-math.Pi, math.Pi} }

// IsValid reports whether the interval is valid.
func (i Interval) IsValid() bool {
	return (math.Abs(i.Lo) <= math.Pi && math.Abs(i.Hi) <= math.Pi &&
		!(i.Lo == -math.Pi && i.Hi != math.Pi) &&
		!(i.Hi == -math.Pi && i.Lo != math.Pi))
}

// IsFull reports whether the interval is full.
func (i Interval) IsFull() bool { return i.Lo == -math.Pi && i.Hi == math.Pi }

// IsEmpty reports whether the interval is empty.
func (i Interval) IsEmpty() bool { return i.Lo == math.Pi && i.Hi == -math.Pi }

// IsInverted reports whether the interval is inverted; that is, whether Lo > Hi.
func (i Interval) IsInverted() bool { return i.Lo > i.Hi }

// Invert returns the interval with endpoints swapped.
func (i Interval) Invert() Interval {
	return Interval{i.Hi, i.Lo}
}

// Center returns the midpoint of the interval.
// It is undefined for full and empty intervals.
func (i Interval) Center() float64 {
	c := 0.5 * (i.Lo + i.Hi)
	if !i.IsInverted() {
		return c
	}
	if c <= 0 {
		return c + math.Pi
	}
	return c - math.Pi
}

// Length returns the length of the interval.
// The length of an empty interval is negative.
func (i Interval) Length() float64 {
	l := i.Hi - i.Lo
	if l >= 0 {
		return l
	}
	l += 2 * math.Pi
	if l > 0 {
		return l
	}
	return -1
}

// Assumes p ∈ (-π,π].
func (i Interval) fastContains(p float64) bool {
	if i.IsInverted() {
		return (p >= i.Lo || p <= i.Hi) && !i.IsEmpty()
	}
	return p >= i.Lo && p <= i.Hi
}

// Contains returns true iff the interval contains p.
// Assumes p ∈ [-π,π].
func (i Interval) Contains(p float64) bool {
	if p == -math.Pi {
		p = math.Pi
	}
	return i.fastContains(p)
}

// ContainsInterval returns true iff the interval contains oi.
func (i Interval) ContainsInterval(oi Interval) bool {
	if i.IsInverted() {
		if oi.IsInverted() {
			return oi.Lo >= i.Lo && oi.Hi <= i.Hi
		}
		return (oi.Lo >= i.Lo || oi.Hi <= i.Hi) && !i.IsEmpty()
	}
	if oi.IsInverted() {
		return i.IsFull() || oi.IsEmpty()
	}
	return oi.Lo >= i.Lo && oi.Hi <= i.Hi
}

// InteriorContains returns true iff the interior of the interval contains p.
// Assumes p ∈ [-π,π].
func (i Interval) InteriorContains(p float64) bool {
	if p == -math.Pi {
		p = math.Pi
	}
	if i.IsInverted() {
		return p > i.Lo || p < i.Hi
	}
	return (p > i.Lo && p < i.Hi) || i.IsFull()
}

// InteriorContainsInterval returns true iff the interior of the interval contains oi.
func (i Interval) InteriorContainsInterval(oi Interval) bool {
	if i.IsInverted() {
		if oi.IsInverted() {
			return (oi.Lo > i.Lo && oi.Hi < i.Hi) || oi.IsEmpty()
		}
		return oi.Lo > i.Lo || oi.Hi < i.Hi
	}
	if oi.IsInverted() {
		return i.IsFull() || oi.IsEmpty()
	}
	return (oi.Lo > i.Lo && oi.Hi < i.Hi) || i.IsFull()
}

// Intersects returns true iff the interval contains any points in common with oi.
func (i Interval) Intersects(oi Interval) bool {
	if i.IsEmpty() || oi.IsEmpty() {
		return false
	}
	if i.IsInverted() {
		return oi.IsInverted() || oi.Lo <= i.Hi || oi.Hi >= i.Lo
	}
	if oi.IsInverted() {
		return oi.Lo <= i.Hi || oi.Hi >= i.Lo
	}
	return oi.Lo <= i.Hi && oi.Hi >= i.Lo
}

// InteriorIntersects returns true iff the interior of the interval contains any points in common with oi, including the latter's boundary.
func (i Interval) InteriorIntersects(oi Interval) bool {
	if i.IsEmpty() || oi.IsEmpty() || i.Lo == i.Hi {
		return false
	}
	if i.IsInverted() {
		return oi.IsInverted() || oi.Lo < i.Hi || oi.Hi > i.Lo
	}
	if oi.IsInverted() {
		return oi.Lo < i.Hi || oi.Hi > i.Lo
	}
	return (oi.Lo < i.Hi && oi.Hi > i.Lo) || i.IsFull()
}

// Compute distance from a to b in [0,2π], in a numerically stable way.
func positiveDistance(a, b float64) float64 {
	d := b - a
	if d >= 0 {
		return d
	}
	return (b + math.Pi) - (a - math.Pi)
}

// Union returns the smallest interval that contains both the interval and oi.
func (i Interval) Union(oi Interval) Interval {
	if oi.IsEmpty() {
		return i
	}
	if i.fastContains(oi.Lo) {
		if i.fastContains(oi.Hi) {
			// Either oi ⊂ i, or i ∪ oi is the full interval.
			if i.ContainsInterval(oi) {
				return i
			}
			return FullInterval()
		}
		return Interval{i.Lo, oi.Hi}
	}
	if i.fastContains(oi.Hi) {
		return Interval{oi.Lo, i.Hi}
	}

	// Neither endpoint of oi is in i. Either i ⊂ oi, or i and oi are disjoint.
	if i.IsEmpty() || oi.fastContains(i.Lo) {
		return oi
	}

	// This is the only hard case where we need to find the closest pair of endpoints.
	if positiveDistance(oi.Hi, i.Lo) < positiveDistance(i.Hi, oi.Lo) {
		return Interval{oi.Lo, i.Hi}
	}
	return Interval{i.Lo, oi.Hi}
}

// Intersection returns the smallest interval that contains the intersection of the interval and oi.
func (i Interval) Intersection(oi Interval) Interval {
	if oi.IsEmpty() {
		return EmptyInterval()
	}
	if i.fastContains(oi.Lo) {
		if i.fastContains(oi.Hi) {
			// Either oi ⊂ i, or i and oi intersect twice. Neither are empty.
			// In the first case we want to return i (which is shorter than oi).
			// In the second case one of them is inverted, and the smallest interval
			// that covers the two disjoint pieces is the shorter of i and oi.
			// We thus want to pick the shorter of i and oi in both cases.
			if oi.Length() < i.Length() {
				return oi
			}
			return i
		}
		return Interval{oi.Lo, i.Hi}
	}
	if i.fastContains(oi.Hi) {
		return Interval{i.Lo, oi.Hi}
	}

	// Neither endpoint of oi is in i. Either i ⊂ oi, or i and oi are disjoint.
	if oi.fastContains(i.Lo) {
		return i
	}
	return EmptyInterval()
}

// AddPoint returns the interval expanded by the minimum amount necessary such
// that it contains the given point "p" (an angle in the range [-Pi, Pi]).
func (i Interval) AddPoint(p float64) Interval {
	if math.Abs(p) > math.Pi {
		return i
	}
	if p == -math.Pi {
		p = math.Pi
	}
	if i.fastContains(p) {
		return i
	}
	if i.IsEmpty() {
		return Interval{p, p}
	}
	if positiveDistance(p, i.Lo) < positiveDistance(i.Hi, p) {
		return Interval{p, i.Hi}
	}
	return Interval{i.Lo, p}
}

// Define the maximum rounding error for arithmetic operations. Depending on the
// platform the mantissa precision may be different than others, so we choose to
// use specific values to be consistent across all.
// The values come from the C++ implementation.
var (
	// epsilon is a small number that represents a reasonable level of noise between two
	// values that can be considered to be equal.
	epsilon = 1e-15
	// dblEpsilon is a smaller number for values that require more precision.
	dblEpsilon = 2.220446049e-16
)

// Expanded returns an interval that has been expanded on each side by margin.
// If margin is negative, then the function shrinks the interval on
// each side by margin instead. The resulting interval may be empty or
// full. Any expansion (positive or negative) of a full interval remains
// full, and any expansion of an empty interval remains empty.
func (i Interval) Expanded(margin float64) Interval {
	if margin >= 0 {
		if i.IsEmpty() {
			return i
		}
		// Check whether this interval will be full after expansion, allowing
		// for a rounding error when computing each endpoint.
		if i.Length()+2*margin+2*dblEpsilon >= 2*math.Pi {
			return FullInterval()
		}
	} else {
		if i.IsFull() {
			return i
		}
		// Check whether this interval will be empty after expansion, allowing
		// for a rounding error when computing each endpoint.
		if i.Length()+2*margin-2*dblEpsilon <= 0 {
			return EmptyInterval()
		}
	}
	result := IntervalFromEndpoints(
		math.Remainder(i.Lo-margin, 2*math.Pi),
		math.Remainder(i.Hi+margin, 2*math.Pi),
	)
	if result.Lo <= -math.Pi {
		result.Lo = math.Pi
	}
	return result
}

func (i Interval) String() string {
	// like "[%.7f, %.7f]"
	return "[" + strconv.FormatFloat(i.Lo, 'f', 7, 64) + ", " + strconv.FormatFloat(i.Hi, 'f', 7, 64) + "]"
}

// BUG(dsymonds): The major differences from the C++ version are:
//   - no validity checking on construction, etc. (not a bug?)
//   - a few operations