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More precisely, How can I determine whether a Solid intersecting with another element. I looked over the Revit API, and had no idea about this.

Any advice will be appreciated!

A: 

have a look into the ray projection API, you can shoot a ray in a certain direction and it will return all the elements it hits and their locations etc.

FindReferencesByDirection method I believe is the method that does that.

RodH257