There is a couple of ways to find 3d curve intersection base on the input geometry (Geom to TopoDS_Shape).
Have a look at the documentation "occt_modeling_algos.pdf" for more details.
Also in 3D extrema algorithms are use to find intersection, look at GeomAPI_ExtremaCurveCurve and BRepExtrema_ExtCC.
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Where is the 3d curve intersection algorithm？
Where is the 3d curve intersection algorithm？ The OCCT version is 7.5.0
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