How to map volume data to a slice viewer in a non-linear transformation using custom code?

Operating system:Windows 10
Slicer version: 4.11.0
Expected behavior: How to map volume data to a slice display viewer in a non-linear transformation using custom code?
Actual behavior:

I would like to display a curved slice in Red slice view. This should use a non-linear transformation to do that. Is there any suggestion to do this?
Goal:
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Display the volume upon in a curved style like the volume below by non-linear transform.

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Ultrasound scan conversion can be indeed very efficiently implemented using a grid transform. See for example how it is done in GE Kretz 3D ultrasound reader in SlicerHeart extension.

Note that SlicerHeart extension can import 3D/4D ultrasound data from a wide range of systems. For 2D (and 2D+t) ultrasound scan conversion, you can use SlicerIGT extension and Plus toolkit.

We can give more information about features that could be useful for you if you write a bit about your project. What is your end goal?

Thank you very much lassoan.