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Converting selection between sub-object levels is limited, cumbersome and unintuitive. The Select By... window the fault of this.
The Select By... can only convert from selected segments/splines to knots, but not from selected knots to segments/splines. And the workflow feels excessive, like if you are in knot mode and want to select by segments, you switch to segment and make your selection, then switch back to knot, open the tool and click Segment to get your desired selection.
It should be possible to convert sub-selections in spline objects the same way you conveniently convert sub-selections in Editable Poly, by making the selection in the level you want to convert from and hold CTRL while clicking on the sub-level you wish to convert to.
There is no technical limitation why it shouldn't be possible to convert from selected knots to segments/splines, as you can think of it as converting selected vertices to connected edges. If the knot is selected, convert that selection to connected segments.
Addition:
In Editable Poly there are shortcuts that convert sub-selections you can assign to hotkeys and menus. Splines should have similar context-sensitive shortcuts for quick selection conversion.
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