121 lines
3.6 KiB
Go
121 lines
3.6 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 s1
|
|
|
|
import (
|
|
"math"
|
|
"strconv"
|
|
)
|
|
|
|
// Angle represents a 1D angle. The internal representation is a double precision
|
|
// value in radians, so conversion to and from radians is exact.
|
|
// Conversions between E5, E6, E7, and Degrees are not always
|
|
// exact. For example, Degrees(3.1) is different from E6(3100000) or E7(31000000).
|
|
//
|
|
// The following conversions between degrees and radians are exact:
|
|
//
|
|
// Degree*180 == Radian*math.Pi
|
|
// Degree*(180/n) == Radian*(math.Pi/n) for n == 0..8
|
|
//
|
|
// These identities hold when the arguments are scaled up or down by any power
|
|
// of 2. Some similar identities are also true, for example,
|
|
//
|
|
// Degree*60 == Radian*(math.Pi/3)
|
|
//
|
|
// But be aware that this type of identity does not hold in general. For example,
|
|
//
|
|
// Degree*3 != Radian*(math.Pi/60)
|
|
//
|
|
// Similarly, the conversion to radians means that (Angle(x)*Degree).Degrees()
|
|
// does not always equal x. For example,
|
|
//
|
|
// (Angle(45*n)*Degree).Degrees() == 45*n for n == 0..8
|
|
//
|
|
// but
|
|
//
|
|
// (60*Degree).Degrees() != 60
|
|
//
|
|
// When testing for equality, you should allow for numerical errors (ApproxEqual)
|
|
// or convert to discrete E5/E6/E7 values first.
|
|
type Angle float64
|
|
|
|
// Angle units.
|
|
const (
|
|
Radian Angle = 1
|
|
Degree = (math.Pi / 180) * Radian
|
|
|
|
E5 = 1e-5 * Degree
|
|
E6 = 1e-6 * Degree
|
|
E7 = 1e-7 * Degree
|
|
)
|
|
|
|
// Radians returns the angle in radians.
|
|
func (a Angle) Radians() float64 { return float64(a) }
|
|
|
|
// Degrees returns the angle in degrees.
|
|
func (a Angle) Degrees() float64 { return float64(a / Degree) }
|
|
|
|
// round returns the value rounded to nearest as an int32.
|
|
// This does not match C++ exactly for the case of x.5.
|
|
func round(val float64) int32 {
|
|
if val < 0 {
|
|
return int32(val - 0.5)
|
|
}
|
|
return int32(val + 0.5)
|
|
}
|
|
|
|
// InfAngle returns an angle larger than any finite angle.
|
|
func InfAngle() Angle {
|
|
return Angle(math.Inf(1))
|
|
}
|
|
|
|
// isInf reports whether this Angle is infinite.
|
|
func (a Angle) isInf() bool {
|
|
return math.IsInf(float64(a), 0)
|
|
}
|
|
|
|
// E5 returns the angle in hundred thousandths of degrees.
|
|
func (a Angle) E5() int32 { return round(a.Degrees() * 1e5) }
|
|
|
|
// E6 returns the angle in millionths of degrees.
|
|
func (a Angle) E6() int32 { return round(a.Degrees() * 1e6) }
|
|
|
|
// E7 returns the angle in ten millionths of degrees.
|
|
func (a Angle) E7() int32 { return round(a.Degrees() * 1e7) }
|
|
|
|
// Abs returns the absolute value of the angle.
|
|
func (a Angle) Abs() Angle { return Angle(math.Abs(float64(a))) }
|
|
|
|
// Normalized returns an equivalent angle in (-π, π].
|
|
func (a Angle) Normalized() Angle {
|
|
rad := math.Remainder(float64(a), 2*math.Pi)
|
|
if rad <= -math.Pi {
|
|
rad = math.Pi
|
|
}
|
|
return Angle(rad)
|
|
}
|
|
|
|
func (a Angle) String() string {
|
|
return strconv.FormatFloat(a.Degrees(), 'f', 7, 64) // like "%.7f"
|
|
}
|
|
|
|
// ApproxEqual reports whether the two angles are the same up to a small tolerance.
|
|
func (a Angle) ApproxEqual(other Angle) bool {
|
|
return math.Abs(float64(a)-float64(other)) <= epsilon
|
|
}
|
|
|
|
// BUG(dsymonds): The major differences from the C++ version are:
|
|
// - no unsigned E5/E6/E7 methods
|