fix: replace deprecated 2-D np.cross with explicit determinant

[abhijithneilabraham]

• Self-reviewed the code
• Updated documentation, follow Google-style
  (https://google.github.io/styleguide/pyguide.html#383-functions-and-methods)
• Added docs entry for autogeneration (if new functions/classes)
• Added/updated tests
• All tests pass locally

Description

np.cross(a, b) on 2-D vectors is deprecated in NumPy 2.0 and prints a
DeprecationWarning on every call. Two supervision call sites hit it:

• get_polygon_center in src/supervision/geometry/utils.py fires once per
  polygon.
• cross_product in src/supervision/detection/utils/internal.py fires three
  times per LineZone.trigger call.

Under pytest -W error::DeprecationWarning the current suite errors during
collection at tests/detection/test_polygon_zone_annotator.py.

For 2-D inputs np.cross(a, b) equals a[..., 0] * b[..., 1] - a[..., 1] *
b[..., 0] bit-exact. This PR swaps both call sites for the inline expression.

Type of Change

• 🐛 Bug fix (non-breaking change which fixes an issue)

Motivation and Context

Fixes the DeprecationWarning fired on every sv.LineZone.trigger and
sv.get_polygon_center call on NumPy 2.x. pyproject.toml allows numpy>=1.21.2
with no upper bound. When NumPy removes the 2-D np.cross code path, the
affected APIs will hard-crash instead of just warning.

Closes #2384

Changes Made

• Replace np.cross(polygon, shift_polygon) in get_polygon_center with the
  explicit 2-D determinant.
• Replace np.cross(vector_at_zero, anchors - vector_start) in cross_product
  with the explicit 2-D determinant.

Testing

• I have tested this code locally
• I have added unit tests that prove my fix is effective or that my
  feature works
• All new and existing tests pass

Existing suite: 2288 passed, 1 skipped, no regressions. The suite now also
passes under pytest -W error::DeprecationWarning, which errored during
collection before this PR. Happy to add a regression test asserting no
DeprecationWarning on the two paths if that's the preferred direction.

Additional Notes

No public API changes or dependencies. Diff is 7 insertions, 2 deletions
across the two files.

[CLAassistant]

All committers have signed the CLA.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 84%. Comparing base (99049d8) to head (564ab63).

Additional details and impacted files

@@           Coverage Diff           @@
##           develop   #2386   +/-   ##
=======================================
  Coverage       84%     84%           
=======================================
  Files           70      70           
  Lines        10003   10004    +1     
=======================================
+ Hits          8435    8436    +1     
  Misses        1568    1568           

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[Copilot]

Pull request overview

This PR removes reliance on NumPy’s deprecated 2-D np.cross(a, b) behavior by replacing it with an explicit 2-D determinant expression, eliminating DeprecationWarning spam on NumPy 2.x and preventing a future hard failure when that path is removed upstream (Issue #2384).

Changes:

• Replace np.cross(polygon, shift_polygon) in get_polygon_center with the explicit 2-D determinant.
• Replace np.cross(vector_at_zero, anchors - vector_start) in cross_product with the explicit 2-D determinant (and factor out diff).

Review Scores (n/5):

• Code quality: 5/5
• Testing: 3/5
• Documentation: 4/5

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 2 comments.

File	Description
src/supervision/geometry/utils.py	Replaces the 2-D np.cross centroid signed-area computation with an explicit determinant to avoid NumPy 2.x deprecation warnings.
src/supervision/detection/utils/internal.py	Replaces the 2-D np.cross in cross_product with an explicit determinant (hot path for LineZone.trigger).