mirror of
https://github.com/superseriousbusiness/gotosocial.git
synced 2024-12-05 01:52:46 +00:00
94e87610c4
* add back exif-terminator and use only for jpeg,png,webp * fix arguments passed to terminateExif() * pull in latest exif-terminator * fix test * update processed img --------- Co-authored-by: tobi <tobi.smethurst@protonmail.com>
251 lines
8.8 KiB
Go
251 lines
8.8 KiB
Go
// Copyright 2015 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"
|
|
)
|
|
|
|
// ChordAngle represents the angle subtended by a chord (i.e., the straight
|
|
// line segment connecting two points on the sphere). Its representation
|
|
// makes it very efficient for computing and comparing distances, but unlike
|
|
// Angle it is only capable of representing angles between 0 and π radians.
|
|
// Generally, ChordAngle should only be used in loops where many angles need
|
|
// to be calculated and compared. Otherwise it is simpler to use Angle.
|
|
//
|
|
// ChordAngle loses some accuracy as the angle approaches π radians.
|
|
// Specifically, the representation of (π - x) radians has an error of about
|
|
// (1e-15 / x), with a maximum error of about 2e-8 radians (about 13cm on the
|
|
// Earth's surface). For comparison, for angles up to π/2 radians (10000km)
|
|
// the worst-case representation error is about 2e-16 radians (1 nanonmeter),
|
|
// which is about the same as Angle.
|
|
//
|
|
// ChordAngles are represented by the squared chord length, which can
|
|
// range from 0 to 4. Positive infinity represents an infinite squared length.
|
|
type ChordAngle float64
|
|
|
|
const (
|
|
// NegativeChordAngle represents a chord angle smaller than the zero angle.
|
|
// The only valid operations on a NegativeChordAngle are comparisons,
|
|
// Angle conversions, and Successor/Predecessor.
|
|
NegativeChordAngle = ChordAngle(-1)
|
|
|
|
// RightChordAngle represents a chord angle of 90 degrees (a "right angle").
|
|
RightChordAngle = ChordAngle(2)
|
|
|
|
// StraightChordAngle represents a chord angle of 180 degrees (a "straight angle").
|
|
// This is the maximum finite chord angle.
|
|
StraightChordAngle = ChordAngle(4)
|
|
|
|
// maxLength2 is the square of the maximum length allowed in a ChordAngle.
|
|
maxLength2 = 4.0
|
|
)
|
|
|
|
// ChordAngleFromAngle returns a ChordAngle from the given Angle.
|
|
func ChordAngleFromAngle(a Angle) ChordAngle {
|
|
if a < 0 {
|
|
return NegativeChordAngle
|
|
}
|
|
if a.isInf() {
|
|
return InfChordAngle()
|
|
}
|
|
l := 2 * math.Sin(0.5*math.Min(math.Pi, a.Radians()))
|
|
return ChordAngle(l * l)
|
|
}
|
|
|
|
// ChordAngleFromSquaredLength returns a ChordAngle from the squared chord length.
|
|
// Note that the argument is automatically clamped to a maximum of 4 to
|
|
// handle possible roundoff errors. The argument must be non-negative.
|
|
func ChordAngleFromSquaredLength(length2 float64) ChordAngle {
|
|
if length2 > maxLength2 {
|
|
return StraightChordAngle
|
|
}
|
|
return ChordAngle(length2)
|
|
}
|
|
|
|
// Expanded returns a new ChordAngle that has been adjusted by the given error
|
|
// bound (which can be positive or negative). Error should be the value
|
|
// returned by either MaxPointError or MaxAngleError. For example:
|
|
// a := ChordAngleFromPoints(x, y)
|
|
// a1 := a.Expanded(a.MaxPointError())
|
|
func (c ChordAngle) Expanded(e float64) ChordAngle {
|
|
// If the angle is special, don't change it. Otherwise clamp it to the valid range.
|
|
if c.isSpecial() {
|
|
return c
|
|
}
|
|
return ChordAngle(math.Max(0.0, math.Min(maxLength2, float64(c)+e)))
|
|
}
|
|
|
|
// Angle converts this ChordAngle to an Angle.
|
|
func (c ChordAngle) Angle() Angle {
|
|
if c < 0 {
|
|
return -1 * Radian
|
|
}
|
|
if c.isInf() {
|
|
return InfAngle()
|
|
}
|
|
return Angle(2 * math.Asin(0.5*math.Sqrt(float64(c))))
|
|
}
|
|
|
|
// InfChordAngle returns a chord angle larger than any finite chord angle.
|
|
// The only valid operations on an InfChordAngle are comparisons, Angle
|
|
// conversions, and Successor/Predecessor.
|
|
func InfChordAngle() ChordAngle {
|
|
return ChordAngle(math.Inf(1))
|
|
}
|
|
|
|
// isInf reports whether this ChordAngle is infinite.
|
|
func (c ChordAngle) isInf() bool {
|
|
return math.IsInf(float64(c), 1)
|
|
}
|
|
|
|
// isSpecial reports whether this ChordAngle is one of the special cases.
|
|
func (c ChordAngle) isSpecial() bool {
|
|
return c < 0 || c.isInf()
|
|
}
|
|
|
|
// isValid reports whether this ChordAngle is valid or not.
|
|
func (c ChordAngle) isValid() bool {
|
|
return (c >= 0 && c <= maxLength2) || c.isSpecial()
|
|
}
|
|
|
|
// Successor returns the smallest representable ChordAngle larger than this one.
|
|
// This can be used to convert a "<" comparison to a "<=" comparison.
|
|
//
|
|
// Note the following special cases:
|
|
// NegativeChordAngle.Successor == 0
|
|
// StraightChordAngle.Successor == InfChordAngle
|
|
// InfChordAngle.Successor == InfChordAngle
|
|
func (c ChordAngle) Successor() ChordAngle {
|
|
if c >= maxLength2 {
|
|
return InfChordAngle()
|
|
}
|
|
if c < 0 {
|
|
return 0
|
|
}
|
|
return ChordAngle(math.Nextafter(float64(c), 10.0))
|
|
}
|
|
|
|
// Predecessor returns the largest representable ChordAngle less than this one.
|
|
//
|
|
// Note the following special cases:
|
|
// InfChordAngle.Predecessor == StraightChordAngle
|
|
// ChordAngle(0).Predecessor == NegativeChordAngle
|
|
// NegativeChordAngle.Predecessor == NegativeChordAngle
|
|
func (c ChordAngle) Predecessor() ChordAngle {
|
|
if c <= 0 {
|
|
return NegativeChordAngle
|
|
}
|
|
if c > maxLength2 {
|
|
return StraightChordAngle
|
|
}
|
|
|
|
return ChordAngle(math.Nextafter(float64(c), -10.0))
|
|
}
|
|
|
|
// MaxPointError returns the maximum error size for a ChordAngle constructed
|
|
// from 2 Points x and y, assuming that x and y are normalized to within the
|
|
// bounds guaranteed by s2.Point.Normalize. The error is defined with respect to
|
|
// the true distance after the points are projected to lie exactly on the sphere.
|
|
func (c ChordAngle) MaxPointError() float64 {
|
|
// There is a relative error of (2.5*dblEpsilon) when computing the squared
|
|
// distance, plus a relative error of 2 * dblEpsilon, plus an absolute error
|
|
// of (16 * dblEpsilon**2) because the lengths of the input points may differ
|
|
// from 1 by up to (2*dblEpsilon) each. (This is the maximum error in Normalize).
|
|
return 4.5*dblEpsilon*float64(c) + 16*dblEpsilon*dblEpsilon
|
|
}
|
|
|
|
// MaxAngleError returns the maximum error for a ChordAngle constructed
|
|
// as an Angle distance.
|
|
func (c ChordAngle) MaxAngleError() float64 {
|
|
return dblEpsilon * float64(c)
|
|
}
|
|
|
|
// Add adds the other ChordAngle to this one and returns the resulting value.
|
|
// This method assumes the ChordAngles are not special.
|
|
func (c ChordAngle) Add(other ChordAngle) ChordAngle {
|
|
// Note that this method (and Sub) is much more efficient than converting
|
|
// the ChordAngle to an Angle and adding those and converting back. It
|
|
// requires only one square root plus a few additions and multiplications.
|
|
|
|
// Optimization for the common case where b is an error tolerance
|
|
// parameter that happens to be set to zero.
|
|
if other == 0 {
|
|
return c
|
|
}
|
|
|
|
// Clamp the angle sum to at most 180 degrees.
|
|
if c+other >= maxLength2 {
|
|
return StraightChordAngle
|
|
}
|
|
|
|
// Let a and b be the (non-squared) chord lengths, and let c = a+b.
|
|
// Let A, B, and C be the corresponding half-angles (a = 2*sin(A), etc).
|
|
// Then the formula below can be derived from c = 2 * sin(A+B) and the
|
|
// relationships sin(A+B) = sin(A)*cos(B) + sin(B)*cos(A)
|
|
// cos(X) = sqrt(1 - sin^2(X))
|
|
x := float64(c * (1 - 0.25*other))
|
|
y := float64(other * (1 - 0.25*c))
|
|
return ChordAngle(math.Min(maxLength2, x+y+2*math.Sqrt(x*y)))
|
|
}
|
|
|
|
// Sub subtracts the other ChordAngle from this one and returns the resulting
|
|
// value. This method assumes the ChordAngles are not special.
|
|
func (c ChordAngle) Sub(other ChordAngle) ChordAngle {
|
|
if other == 0 {
|
|
return c
|
|
}
|
|
if c <= other {
|
|
return 0
|
|
}
|
|
x := float64(c * (1 - 0.25*other))
|
|
y := float64(other * (1 - 0.25*c))
|
|
return ChordAngle(math.Max(0.0, x+y-2*math.Sqrt(x*y)))
|
|
}
|
|
|
|
// Sin returns the sine of this chord angle. This method is more efficient
|
|
// than converting to Angle and performing the computation.
|
|
func (c ChordAngle) Sin() float64 {
|
|
return math.Sqrt(c.Sin2())
|
|
}
|
|
|
|
// Sin2 returns the square of the sine of this chord angle.
|
|
// It is more efficient than Sin.
|
|
func (c ChordAngle) Sin2() float64 {
|
|
// Let a be the (non-squared) chord length, and let A be the corresponding
|
|
// half-angle (a = 2*sin(A)). The formula below can be derived from:
|
|
// sin(2*A) = 2 * sin(A) * cos(A)
|
|
// cos^2(A) = 1 - sin^2(A)
|
|
// This is much faster than converting to an angle and computing its sine.
|
|
return float64(c * (1 - 0.25*c))
|
|
}
|
|
|
|
// Cos returns the cosine of this chord angle. This method is more efficient
|
|
// than converting to Angle and performing the computation.
|
|
func (c ChordAngle) Cos() float64 {
|
|
// cos(2*A) = cos^2(A) - sin^2(A) = 1 - 2*sin^2(A)
|
|
return float64(1 - 0.5*c)
|
|
}
|
|
|
|
// Tan returns the tangent of this chord angle.
|
|
func (c ChordAngle) Tan() float64 {
|
|
return c.Sin() / c.Cos()
|
|
}
|
|
|
|
// TODO(roberts): Differences from C++:
|
|
// Helpers to/from E5/E6/E7
|
|
// Helpers to/from degrees and radians directly.
|
|
// FastUpperBoundFrom(angle Angle)
|