Skip to content

Preserve ellipse size when constructing from polynomial coefficients #290

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
xixihaha-ha wants to merge 1 commit into
base: master
Choose a base branch
from
Open

Preserve ellipse size when constructing from polynomial coefficients #290

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
9 changes: 5 additions & 4 deletions spatialmath/geom2d.py
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -765,10 +765,8 @@ def Polynomial(cls, e: ArrayLike, p: Optional[ArrayLike2] = None) -> Self:

x^2 + \epsilon_1 y^2 + \epsilon_2 xy + \epsilon_3 x + \epsilon_4 y + \epsilon_5 = 0

In this latter case, position, orientation and aspect ratio of the
ellipse will be correct, but the overall scale of the ellipse is not
determined. To correct this, we can pass in a single point ``p`` that
we know lies on the perimeter of the ellipse.
Both forms determine the position, orientation and size of the ellipse.
An optional perimeter point ``p`` can be used to override the size.

Example:

Expand Down Expand Up @@ -802,6 +800,9 @@ def Polynomial(cls, e: ArrayLike, p: Optional[ArrayLike2] = None) -> Self:
p = smb.getvector(p, 2) - centre
s = p @ E @ p
E /= s
else:
# Complete the square: (x-centre).T E (x-centre) = s.
E /= centre @ E @ centre - e[5]

return cls(E=E, centre=centre)

Expand Down
36 changes: 36 additions & 0 deletions tests/test_geom2d.py
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -142,6 +142,42 @@ def test_intersect_segment(self):


class EllipseTest(unittest.TestCase):
def test_polynomial_circle_size(self):
for coefficients, centre in (
([1, 1, 0, 0, 0, -4], (0, 0)),
([1, 1, 0, -6, -8, 21], (3, 4)),
):
with self.subTest(centre=centre):
circle = Ellipse.Polynomial(coefficients)
nt.assert_allclose(circle.centre, centre)
nt.assert_allclose(circle.radii, [2, 2])
self.assertAlmostEqual(circle.area, 4 * np.pi)

def test_polynomial_scale(self):
for theta, centre, scale, implicit in (
(0, (0, 0), 1, False),
(0, (0, 0), 4, False),
(0, (3, 4), 1, False),
(0.4, (3, -2), 3, False),
(0.4, (3, -2), 1, True),
):
with self.subTest(
theta=theta, centre=centre, scale=scale, implicit=implicit
):
expected = Ellipse(radii=(2, 3), theta=theta, centre=centre)
E = expected.E
c = np.array(centre)
linear = -2 * E @ c
coefficients = (
scale * np.r_[E[0, 0], E[1, 1], 2 * E[0, 1], linear, c @ E @ c - 1]
)
if implicit:
coefficients = (coefficients / coefficients[0])[1:]
actual = Ellipse.Polynomial(coefficients)
nt.assert_allclose(actual.centre, c, atol=1e-12)
nt.assert_allclose(actual.E, expected.E, atol=1e-12)
self.assertAlmostEqual(actual.area, expected.area)

def test_constructor(self):
E = np.array([[1, 1], [1, 3]])
e = Ellipse(E=E)
Expand Down