/*
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 r1

import (
	"fmt"
	"math"
)

// Interval represents a closed interval on ℝ.
// Zero-length intervals (where Lo == Hi) represent single points.
// If Lo > Hi then the interval is empty.
type Interval struct {
	Lo, Hi float64
}

// EmptyInterval returns an empty interval.
func EmptyInterval() Interval { return Interval{1, 0} }

// IntervalFromPoint returns an interval representing a single point.
func IntervalFromPoint(p float64) Interval { return Interval{p, p} }

// IsEmpty reports whether the interval is empty.
func (i Interval) IsEmpty() bool { return i.Lo > i.Hi }

// Equal returns true iff the interval contains the same points as oi.
func (i Interval) Equal(oi Interval) bool {
	return i == oi || i.IsEmpty() && oi.IsEmpty()
}

// Center returns the midpoint of the interval.
// It is undefined for empty intervals.
func (i Interval) Center() float64 { return 0.5 * (i.Lo + i.Hi) }

// Length returns the length of the interval.
// The length of an empty interval is negative.
func (i Interval) Length() float64 { return i.Hi - i.Lo }

// Contains returns true iff the interval contains p.
func (i Interval) Contains(p float64) bool { return i.Lo <= p && p <= i.Hi }

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

// InteriorContains returns true iff the the interval strictly contains p.
func (i Interval) InteriorContains(p float64) bool {
	return i.Lo < p && p < i.Hi
}

// InteriorContainsInterval returns true iff the interval strictly contains oi.
func (i Interval) InteriorContainsInterval(oi Interval) bool {
	if oi.IsEmpty() {
		return true
	}
	return i.Lo < oi.Lo && oi.Hi < i.Hi
}

// Intersects returns true iff the interval contains any points in common with oi.
func (i Interval) Intersects(oi Interval) bool {
	if i.Lo <= oi.Lo {
		return oi.Lo <= i.Hi && oi.Lo <= oi.Hi // oi.Lo ∈ i and oi is not empty
	}
	return i.Lo <= oi.Hi && i.Lo <= i.Hi // i.Lo ∈ oi and i is not empty
}

// 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 {
	return oi.Lo < i.Hi && i.Lo < oi.Hi && i.Lo < i.Hi && oi.Lo <= oi.Hi
}

// Intersection returns the interval containing all points common to i and j.
func (i Interval) Intersection(j Interval) Interval {
	// Empty intervals do not need to be special-cased.
	return Interval{
		Lo: math.Max(i.Lo, j.Lo),
		Hi: math.Min(i.Hi, j.Hi),
	}
}

// AddPoint returns the interval expanded so that it contains the given point.
func (i Interval) AddPoint(p float64) Interval {
	if i.IsEmpty() {
		return Interval{p, p}
	}
	if p < i.Lo {
		return Interval{p, i.Hi}
	}
	if p > i.Hi {
		return Interval{i.Lo, p}
	}
	return i
}

// ClampPoint returns the closest point in the interval to the given point "p".
// The interval must be non-empty.
func (i Interval) ClampPoint(p float64) float64 {
	return math.Max(i.Lo, math.Min(i.Hi, p))
}

// 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. Any
// expansion of an empty interval remains empty.
func (i Interval) Expanded(margin float64) Interval {
	if i.IsEmpty() {
		return i
	}
	return Interval{i.Lo - margin, i.Hi + margin}
}

// Union returns the smallest interval that contains this interval and the given interval.
func (i Interval) Union(other Interval) Interval {
	if i.IsEmpty() {
		return other
	}
	if other.IsEmpty() {
		return i
	}
	return Interval{math.Min(i.Lo, other.Lo), math.Max(i.Hi, other.Hi)}
}

func (i Interval) String() string { return fmt.Sprintf("[%.7f, %.7f]", i.Lo, i.Hi) }

// epsilon is a small number that represents a reasonable level of noise between two
// values that can be considered to be equal.
const epsilon = 1e-14

// ApproxEqual reports whether the interval can be transformed into the
// given interval by moving each endpoint a small distance.
// The empty interval is considered to be positioned arbitrarily on the
// real line, so any interval with a small enough length will match
// the empty interval.
func (i Interval) ApproxEqual(other Interval) bool {
	if i.IsEmpty() {
		return other.Length() <= 2*epsilon
	}
	if other.IsEmpty() {
		return i.Length() <= 2*epsilon
	}
	return math.Abs(other.Lo-i.Lo) <= epsilon &&
		math.Abs(other.Hi-i.Hi) <= epsilon
}