gtsocial-umbx

interval.go (5746B)

---

 // 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 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) }
 
 const (
 	// 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.
 	// This is the C++ DBL_EPSILON equivalent.
 	dblEpsilon = 2.220446049250313e-16
 )
 
 // 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
 }
 
 // DirectedHausdorffDistance returns the Hausdorff distance to the given interval. For two
 // intervals x and y, this distance is defined as
 //     h(x, y) = max_{p in x} min_{q in y} d(p, q).
 func (i Interval) DirectedHausdorffDistance(other Interval) float64 {
 	if i.IsEmpty() {
 		return 0
 	}
 	if other.IsEmpty() {
 		return math.Inf(1)
 	}
 	return math.Max(0, math.Max(i.Hi-other.Hi, other.Lo-i.Lo))
 }