spatial/r3: rework test for RotationFromQuat
@@ -189,30 +189,35 @@ func TestOuter(t *testing.T) {
}
func TestRotationFromQuat(t *testing.T) {
- const tol = 1e-11
+ const tol = 1e-14
rnd := rand.New(rand.NewSource(1))
- var backing [9]float64 // reuse memory.
+
for tc := 0; tc < 20; tc++ {
- q := quat.Number{Real: rnd.Float64(), Imag: rnd.Float64(), Jmag: rnd.Float64(), Kmag: rnd.Float64()}
- qabs := quat.Abs(q)
- q = quat.Scale(1/qabs, q)
- m := NewMat(backing[:])
- m.RotationFromQuat(q)
- w, x, y, z := q.Real, q.Imag, q.Jmag, q.Kmag
- x2, y2, z2 := x*x, y*y, z*z
- norm := math.Sqrt(w*w + x2 + y2 + z2)
- _ = norm
- expect := NewMat([]float64{ // From https://en.wikipedia.org/wiki/Rotation_matrix#Quaternion
- 1 - 2*y2 - 2*z2, 2*x*y - 2*z*w, 2*x*z + 2*y*w,
- 2*x*y + 2*z*w, 1 - 2*x2 - 2*z2, 2*y*z - 2*x*w,
- 2*x*z - 2*y*w, 2*y*z + 2*x*w, 1 - 2*x2 - 2*y2,
- })
- if !mat.EqualApprox(m, expect, tol) {
- t.Errorf("Out of tolerance.")
- }
- det := m.Det()
- if math.Abs(det-1) > tol {
- t.Errorf("determinant expected to be 1. got %f", det)
+ // Generate a random unit quaternion.
+ q := quat.Number{Real: rnd.NormFloat64(), Imag: rnd.NormFloat64(), Jmag: rnd.NormFloat64(), Kmag: rnd.NormFloat64()}
+ q = quat.Scale(1/quat.Abs(q), q)
+
+ // Convert it to a rotation matrix R.
+ var r Mat
+ r.RotationFromQuat(q)
+
+ // Check that the matrix has the determinant approximately equal to 1.
+ diff := math.Abs(r.Det() - 1)
+ if diff > tol {
+ t.Errorf("case %d: unexpected determinant of R; got=%f, want=1 (diff=%v)", tc, r.Det(), diff)
+ continue
+ }
+
+ // Generate a random point.
+ v := Vec{X: rnd.NormFloat64(), Y: rnd.NormFloat64(), Z: rnd.NormFloat64()}
+ // Rotate it using the formula q*v*conj(q).
+ want := Rotation(q).Rotate(v)
+ // Rotate it using the rotation matrix R.
+ got := r.MulVec(v)
+ // Check that |got-want| is small.
+ diff = Norm(Sub(got, want))
+ if diff > tol {
+ t.Errorf("case %d: unexpected result; got=%f, want=%f, (diff=%v)", tc, got, want, diff)
}
}
}
