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spatial/{r2,r3}: add Cos, Unit

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This commit is contained in:
Sebastien Binet
2020-04-08 12:28:23 +02:00
committed by GitHub
parent 962425fcd9
commit 448e2b6d0e
4 changed files with 179 additions and 1 deletions
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14
spatial/r2/vector.go
View File

@@ -54,6 +54,20 @@ func Norm2(p Vec) float64 {
return p.X*p.X + p.Y*p.Y
}
// Unit returns the unit vector colinear to p.
// Unit returns {NaN,NaN} for the zero vector.
func Unit(p Vec) Vec {
if p.X == 0 && p.Y == 0 {
return Vec{X: math.NaN(), Y: math.NaN()}
}
return p.Scale(1 / Norm(p))
}
// Cos returns the cosine of the opening angle between p and q.
func Cos(p, q Vec) float64 {
return p.Dot(q) / (Norm(p) * Norm(q))
}
// Box is a 2D bounding box.
type Box struct {
Min, Max Vec

76
spatial/r2/vector_test.go
View File

@@ -7,6 +7,8 @@ package r2
import (
"math"
"testing"
"gonum.org/v1/gonum/floats"
)
func TestAdd(t *testing.T) {
@@ -181,3 +183,77 @@ func TestNorm2(t *testing.T) {
})
}
}
func TestUnit(t *testing.T) {
for _, test := range []struct {
v, want Vec
}{
{Vec{}, Vec{math.NaN(), math.NaN()}},
{Vec{1, 0}, Vec{1, 0}},
{Vec{0, 1}, Vec{0, 1}},
{Vec{-1, 0}, Vec{-1, 0}},
{Vec{3, 4}, Vec{0.6, 0.8}},
{Vec{3, -4}, Vec{0.6, -0.8}},
{Vec{1, 1}, Vec{1. / math.Sqrt(2), 1. / math.Sqrt(2)}},
{Vec{1, 1e-16}, Vec{1, 1e-16}},
{Vec{1, 1e16}, Vec{1e-16, 1}},
{Vec{1e4, math.MaxFloat32 - 1}, Vec{0, 1}},
} {
t.Run("", func(t *testing.T) {
got := Unit(test.v)
if !vecApproxEqual(got, test.want) {
t.Fatalf(
"Unit(%v) = %v, want %v",
test.v, got, test.want,
)
}
if vecIsNaN(got) {
return
}
if n, want := Norm(got), 1.0; n != want {
t.Fatalf("|%v| = %v, want 1", got, n)
}
})
}
}
func TestCos(t *testing.T) {
for _, test := range []struct {
v1, v2 Vec
want float64
}{
{Vec{1, 1}, Vec{1, 1}, 1},
{Vec{1, 1}, Vec{-1, -1}, -1},
{Vec{1, 0}, Vec{1, 0}, 1},
{Vec{1, 0}, Vec{0, 1}, 0},
{Vec{1, 0}, Vec{-1, 0}, -1},
} {
t.Run("", func(t *testing.T) {
tol := 1e-14
got := Cos(test.v1, test.v2)
if !floats.EqualWithinAbs(got, test.want, tol) {
t.Fatalf("cos(%v, %v)= %v, want %v",
test.v1, test.v2, got, test.want,
)
}
})
}
}
func vecIsNaN(v Vec) bool {
return math.IsNaN(v.X) && math.IsNaN(v.Y)
}
func vecIsNaNAny(v Vec) bool {
return math.IsNaN(v.X) || math.IsNaN(v.Y)
}
func vecApproxEqual(a, b Vec) bool {
const tol = 1e-14
if vecIsNaNAny(a) || vecIsNaNAny(b) {
return vecIsNaN(a) && vecIsNaN(b)
}
return floats.EqualWithinAbs(a.X, b.X, tol) &&
floats.EqualWithinAbs(a.Y, b.Y, tol)
}

14
spatial/r3/vector.go
View File

@@ -61,6 +61,20 @@ func Norm2(p Vec) float64 {
return p.X*p.X + p.Y*p.Y + p.Z*p.Z
}
// Unit returns the unit vector colinear to p.
// Unit returns {NaN,NaN,NaN} for the zero vector.
func Unit(p Vec) Vec {
if p.X == 0 && p.Y == 0 && p.Z == 0 {
return Vec{X: math.NaN(), Y: math.NaN(), Z: math.NaN()}
}
return p.Scale(1 / Norm(p))
}
// Cos returns the cosine of the opening angle between p and q.
func Cos(p, q Vec) float64 {
return p.Dot(q) / (Norm(p) * Norm(q))
}
// Box is a 3D bounding box.
type Box struct {
Min, Max Vec

76
spatial/r3/vector_test.go
View File

@@ -4,7 +4,12 @@
package r3
import "testing"
import (
"math"
"testing"
"gonum.org/v1/gonum/floats"
)
func TestAdd(t *testing.T) {
for _, test := range []struct {
@@ -176,3 +181,72 @@ func TestNorm2(t *testing.T) {
})
}
}
func TestUnit(t *testing.T) {
for _, test := range []struct {
v, want Vec
}{
{Vec{}, Vec{math.NaN(), math.NaN(), math.NaN()}},
{Vec{1, 0, 0}, Vec{1, 0, 0}},
{Vec{0, 1, 0}, Vec{0, 1, 0}},
{Vec{0, 0, 1}, Vec{0, 0, 1}},
{Vec{1, 1, 1}, Vec{1. / math.Sqrt(3), 1. / math.Sqrt(3), 1. / math.Sqrt(3)}},
{Vec{1, 1e-16, 1e-32}, Vec{1, 1e-16, 1e-32}},
} {
t.Run("", func(t *testing.T) {
got := Unit(test.v)
if !vecEqual(got, test.want) {
t.Fatalf(
"Normalize(%v) = %v, want %v",
test.v, got, test.want,
)
}
if test.v == (Vec{}) {
return
}
if n, want := Norm(got), 1.0; n != want {
t.Fatalf("|%v| = %v, want 1", got, n)
}
})
}
}
func TestCos(t *testing.T) {
for _, test := range []struct {
v1, v2 Vec
want float64
}{
{Vec{1, 1, 1}, Vec{1, 1, 1}, 1},
{Vec{1, 1, 1}, Vec{-1, -1, -1}, -1},
{Vec{1, 1, 1}, Vec{1, -1, 1}, 1.0 / 3},
{Vec{1, 0, 0}, Vec{1, 0, 0}, 1},
{Vec{1, 0, 0}, Vec{0, 1, 0}, 0},
{Vec{1, 0, 0}, Vec{0, 1, 1}, 0},
{Vec{1, 0, 0}, Vec{-1, 0, 0}, -1},
} {
t.Run("", func(t *testing.T) {
tol := 1e-14
got := Cos(test.v1, test.v2)
if !floats.EqualWithinAbs(got, test.want, tol) {
t.Fatalf("cos(%v, %v)= %v, want %v",
test.v1, test.v2, got, test.want,
)
}
})
}
}
func vecIsNaN(v Vec) bool {
return math.IsNaN(v.X) && math.IsNaN(v.Y) && math.IsNaN(v.Z)
}
func vecIsNaNAny(v Vec) bool {
return math.IsNaN(v.X) || math.IsNaN(v.Y) || math.IsNaN(v.Z)
}
func vecEqual(a, b Vec) bool {
if vecIsNaNAny(a) || vecIsNaNAny(b) {
return vecIsNaN(a) && vecIsNaN(b)
}
return a == b
}