mirror of
https://github.com/superseriousbusiness/gotosocial.git
synced 2024-12-05 10:02:47 +00:00
98263a7de6
* start fixing up tests * fix up tests + automate with drone * fiddle with linting * messing about with drone.yml * some more fiddling * hmmm * add cache * add vendor directory * verbose * ci updates * update some little things * update sig
178 lines
5.6 KiB
Go
178 lines
5.6 KiB
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 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))
|
||
}
|