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Copy pathaffine_test.go
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203 lines (179 loc) · 4.82 KB
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package curve
import (
"math"
"testing"
"github.com/google/go-cmp/cmp"
"github.com/google/go-cmp/cmp/cmpopts"
)
func assertNear(t *testing.T, p0 Point, p1 Point, epsilon float64) {
t.Helper()
if d := p1.Sub(p0).Hypot(); d > epsilon {
t.Fatalf("got %s, expected %s", p0, p1)
}
}
func TestAffineBasic(t *testing.T) {
const epsilon = 1e-9
p := Pt(3, 4)
assertNear(t, p.Transform(Identity), p, epsilon)
assertNear(t, p.Transform(Scale(2, 2)), Pt(6, 8), epsilon)
assertNear(t, p.Transform(Rotate(0)), p, epsilon)
assertNear(t, p.Transform(Rotate(math.Pi/2)), Pt(-4, 3), epsilon)
assertNear(t, p.Transform(Translate(Vec(5, 6))), Pt(8, 10), epsilon)
assertNear(t, p.Transform(Skew(0, 0)), p, epsilon)
assertNear(t, p.Transform(Skew(2, 4)), Pt(11, 16), epsilon)
}
func TestAffineMul(t *testing.T) {
const epsilon = 1e-9
a1 := Affine{1, 2, 3, 4, 5, 6}
a2 := Affine{0.1, 1.2, 2.3, 3.4, 4.5, 5.6}
px := Pt(1, 0)
py := Pt(0, 1)
pxy := Pt(1, 1)
assertNear(t, px.Transform(a2).Transform(a1), px.Transform(a1.Mul(a2)), epsilon)
assertNear(t, py.Transform(a2).Transform(a1), py.Transform(a1.Mul(a2)), epsilon)
assertNear(t, pxy.Transform(a2).Transform(a1), pxy.Transform(a1.Mul(a2)), epsilon)
}
func TestAffineInvert(t *testing.T) {
const epsilon = 1e-9
a := Affine{0.1, 1.2, 2.3, 3.4, 4.5, 5.6}
aInv := a.Invert()
px := Pt(1, 0)
py := Pt(0, 1)
pxy := Pt(1, 1)
assertNear(t, px.Transform(aInv).Transform(a), px, epsilon)
assertNear(t, py.Transform(aInv).Transform(a), py, epsilon)
assertNear(t, pxy.Transform(aInv).Transform(a), pxy, epsilon)
assertNear(t, px.Transform(a).Transform(aInv), px, epsilon)
assertNear(t, py.Transform(a).Transform(aInv), py, epsilon)
assertNear(t, pxy.Transform(a).Transform(aInv), pxy, epsilon)
}
func TestReflection(t *testing.T) {
affineAssertNear := func(a0, a1 Affine) {
a0a := a0.Coefficients()
a1a := a1.Coefficients()
for i := range 6 {
if d := math.Abs(a0a[i] - a1a[i]); d > 1e-9 {
t.Fatalf("%g > %g", d, 1e-9)
}
}
}
affineAssertNear(Reflect(Point{}, Vec(1, 0)), Affine{1, 0, 0, -1, 0, 0})
affineAssertNear(Reflect(Point{}, Vec(0, 1)), Affine{-1, 0, 0, 1, 0, 0})
affineAssertNear(Reflect(Point{}, Vec(1, 1)), Affine{0, 1, 1, 0, 0, 0})
const epsilon = 1e-9
{
// No translation
point := Pt(0, 0)
vec := Vec(1, 1)
aff := Reflect(point, vec)
assertNear(t, Pt(0, 0).Transform(aff), Pt(0, 0), epsilon)
assertNear(t, Pt(1, 1).Transform(aff), Pt(1, 1), epsilon)
assertNear(t, Pt(1, 2).Transform(aff), Pt(2, 1), epsilon)
}
{
// With translation
point := Pt(1, 0)
vec := Vec(1, 1)
aff := Reflect(point, vec)
assertNear(t, Pt(1, 0).Transform(aff), Pt(1, 0), epsilon)
assertNear(t, Pt(2, 1).Transform(aff), Pt(2, 1), epsilon)
assertNear(t, Pt(2, 2).Transform(aff), Pt(3, 1), epsilon)
}
}
func BenchmarkAffine_svd(b *testing.B) {
aff := Identity.ThenScale(3, 7).ThenRotate(1.23)
for b.Loop() {
aff.svd()
}
}
func BenchmarkAffine_svd0(b *testing.B) {
aff := Identity.ThenScale(3, 7).ThenRotate(1.23)
for b.Loop() {
aff.svd0()
}
}
func BenchmarkAffine_svd1(b *testing.B) {
aff := Identity.ThenScale(3, 7).ThenRotate(1.23)
for b.Loop() {
aff.svd1()
}
}
func TestAffine_svd(t *testing.T) {
tests := []struct {
aff Affine
want Vec2
want2 float64
}{
{
Affine{1, 0, 0, 1, 0, 0},
Vec(1, 1),
0,
},
{
Affine{1, 0, 0, -1, 0, 0},
Vec(1, 1),
0,
},
{
Affine{1, 1, 1, 1, 0, 0},
Vec(2, 0),
1.5707963267948966,
},
{
Affine{0, 0, 1, 0, 0, 0},
Vec(1, 0),
0,
},
{
Scale(4, 8).
ThenRotateAbout(0.733038, Pt(-2, 50)),
Vec(8, 4),
-1.777989284994809,
},
// Correctly handles negative scaling (singular values are necessarily non-negative).
{
Scale(-20, 3),
Vec(20, 3),
0,
},
{
Scale(-20, -3),
Vec(20, 3),
0,
},
{
Scale(20, -3),
Vec(20, 3),
0,
},
}
for _, tt := range tests {
t.Run("", func(t *testing.T) {
got, got2 := tt.aff.svd()
if !cmp.Equal(got, tt.want, cmpopts.EquateApprox(0, 1e-6)) {
t.Errorf("svd() = %v, want %v", got, tt.want)
}
if !cmp.Equal(got2, tt.want2, cmpopts.EquateApprox(0, 1e-6)) {
t.Errorf("svd() = %v, want %v", got2, tt.want2)
}
got = tt.aff.svd0()
if !cmp.Equal(got, tt.want, cmpopts.EquateApprox(0, 1e-6)) {
t.Errorf("svd0() = %v, want %v", got, tt.want)
}
got2 = tt.aff.svd1()
<
3F4B
div>
if !cmp.Equal(got2, tt.want2, cmpopts.EquateApprox(0, 1e-6)) {
t.Errorf("svd() = %v, want %v", got2, tt.want2)
}
})
}
// Given a full-rank transform, the product of its singular values
// should be equal to its absolute determinant.
m := Affine{10, 9, -2.5, 10.0 / 3.0, 0, 0}
s, _ := m.svd()
prod := s.X * s.Y
det := math.Abs(m.Determinant())
if !cmp.Equal(prod, det, cmpopts.EquateApprox(0, 1e-6)) {
t.Errorf("the product of the singular values %v (%v) should be equal to the absolute determinant %v",
s, prod, det)
}
}