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