add para to parent scaling

[j042]

Overview

Integrations for bsplines weren't correct - it was missing parametric space to "parent" (or integration) element scaling. Added corresponding test

Addressed issues

• consider parametric space to parent element mapping

Checklists

• [ ] Documentations are up-to-date.
• [ ] Added example(s)
• [ ] Added test(s)

Summary by CodeRabbit

• New Features

  • Enhanced integration method for parametric functions, improving accuracy for splines with knot vectors.
  • Introduced a new method for physical function integration (currently not implemented).

• Bug Fixes

  • Updated integration calculations to better account for spline geometry.

• Tests

  • Added comprehensive tests for volume integration across 1D, 2D, and 3D splines, ensuring consistency after operations like degree elevation and knot insertion.
  • Included tests for complex geometries and validation of error handling for unsupported operations.

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Walkthrough

The changes involve modifications to the parametric_function method in the splinepy/helpme/integrate.py file, where the integral calculation now includes an additional multiplication factor based on the control point bounds of the Bezier element. The tests/helpme/test_integrate.py file has been updated to refine the volume function's input handling and to include assertions for B-spline integration, enhancing test coverage. Additionally, the examples/iga/galerkin_laplace_problem.py file has been adjusted to scale the Jacobian determinant by the element size.

Changes

File	Change Summary
splinepy/helpme/integrate.py	Updated parametric_function to include a multiplication factor for integration based on control point bounds.
tests/helpme/test_integrate.py	Refined volume function's input handling and added assertions for B-spline integration checks alongside Bezier spline tests.
examples/iga/galerkin_laplace_problem.py	Introduced scaling to the determinant of the Jacobian matrix in map_positions, clarifying the scaling by element size.

Poem

🐇 In the world of splines, where curves intertwine,
A factor added makes integration divine.
With tests for B-splines, our coverage expands,
Ensuring our volumes meet all demands.
Hooray for the changes, let’s dance and cheer,
For every new feature brings splendor near! ✨

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[j042]

I think this is also missing in iga-galerkin example

[clemens-fricke]

@markriegler did you check this out? This might be relevant for your integration PR #447 as well.

[markriegler]

@markriegler did you check this out? This might be relevant for your integration PR #447 as well.

I just realized that I did the same parent to para scaling in my PR #447 , but in another unnecessarily more complicated way.

[clemens-fricke]

Closed, commits were cherry-picked to #447.