GoToSocial/vendor/github.com/golang/geo/r3/vector.go
Tobi Smethurst 98263a7de6
Grand test fixup (#138)
* 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
2021-08-12 21:03:24 +02:00

184 lines
4.5 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 r3
import (
"fmt"
"math"
"github.com/golang/geo/s1"
)
// Vector represents a point in ℝ³.
type Vector struct {
X, Y, Z float64
}
// ApproxEqual reports whether v and ov are equal within a small epsilon.
func (v Vector) ApproxEqual(ov Vector) bool {
const epsilon = 1e-16
return math.Abs(v.X-ov.X) < epsilon && math.Abs(v.Y-ov.Y) < epsilon && math.Abs(v.Z-ov.Z) < epsilon
}
func (v Vector) String() string { return fmt.Sprintf("(%0.24f, %0.24f, %0.24f)", v.X, v.Y, v.Z) }
// Norm returns the vector's norm.
func (v Vector) Norm() float64 { return math.Sqrt(v.Dot(v)) }
// Norm2 returns the square of the norm.
func (v Vector) Norm2() float64 { return v.Dot(v) }
// Normalize returns a unit vector in the same direction as v.
func (v Vector) Normalize() Vector {
n2 := v.Norm2()
if n2 == 0 {
return Vector{0, 0, 0}
}
return v.Mul(1 / math.Sqrt(n2))
}
// IsUnit returns whether this vector is of approximately unit length.
func (v Vector) IsUnit() bool {
const epsilon = 5e-14
return math.Abs(v.Norm2()-1) <= epsilon
}
// Abs returns the vector with nonnegative components.
func (v Vector) Abs() Vector { return Vector{math.Abs(v.X), math.Abs(v.Y), math.Abs(v.Z)} }
// Add returns the standard vector sum of v and ov.
func (v Vector) Add(ov Vector) Vector { return Vector{v.X + ov.X, v.Y + ov.Y, v.Z + ov.Z} }
// Sub returns the standard vector difference of v and ov.
func (v Vector) Sub(ov Vector) Vector { return Vector{v.X - ov.X, v.Y - ov.Y, v.Z - ov.Z} }
// Mul returns the standard scalar product of v and m.
func (v Vector) Mul(m float64) Vector { return Vector{m * v.X, m * v.Y, m * v.Z} }
// Dot returns the standard dot product of v and ov.
func (v Vector) Dot(ov Vector) float64 { return v.X*ov.X + v.Y*ov.Y + v.Z*ov.Z }
// Cross returns the standard cross product of v and ov.
func (v Vector) Cross(ov Vector) Vector {
return Vector{
v.Y*ov.Z - v.Z*ov.Y,
v.Z*ov.X - v.X*ov.Z,
v.X*ov.Y - v.Y*ov.X,
}
}
// Distance returns the Euclidean distance between v and ov.
func (v Vector) Distance(ov Vector) float64 { return v.Sub(ov).Norm() }
// Angle returns the angle between v and ov.
func (v Vector) Angle(ov Vector) s1.Angle {
return s1.Angle(math.Atan2(v.Cross(ov).Norm(), v.Dot(ov))) * s1.Radian
}
// Axis enumerates the 3 axes of ℝ³.
type Axis int
// The three axes of ℝ³.
const (
XAxis Axis = iota
YAxis
ZAxis
)
// Ortho returns a unit vector that is orthogonal to v.
// Ortho(-v) = -Ortho(v) for all v.
func (v Vector) Ortho() Vector {
ov := Vector{0.012, 0.0053, 0.00457}
switch v.LargestComponent() {
case XAxis:
ov.Z = 1
case YAxis:
ov.X = 1
default:
ov.Y = 1
}
return v.Cross(ov).Normalize()
}
// LargestComponent returns the axis that represents the largest component in this vector.
func (v Vector) LargestComponent() Axis {
t := v.Abs()
if t.X > t.Y {
if t.X > t.Z {
return XAxis
}
return ZAxis
}
if t.Y > t.Z {
return YAxis
}
return ZAxis
}
// SmallestComponent returns the axis that represents the smallest component in this vector.
func (v Vector) SmallestComponent() Axis {
t := v.Abs()
if t.X < t.Y {
if t.X < t.Z {
return XAxis
}
return ZAxis
}
if t.Y < t.Z {
return YAxis
}
return ZAxis
}
// Cmp compares v and ov lexicographically and returns:
//
// -1 if v < ov
// 0 if v == ov
// +1 if v > ov
//
// This method is based on C++'s std::lexicographical_compare. Two entities
// are compared element by element with the given operator. The first mismatch
// defines which is less (or greater) than the other. If both have equivalent
// values they are lexicographically equal.
func (v Vector) Cmp(ov Vector) int {
if v.X < ov.X {
return -1
}
if v.X > ov.X {
return 1
}
// First elements were the same, try the next.
if v.Y < ov.Y {
return -1
}
if v.Y > ov.Y {
return 1
}
// Second elements were the same return the final compare.
if v.Z < ov.Z {
return -1
}
if v.Z > ov.Z {
return 1
}
// Both are equal
return 0
}