Does the three.js library come out of the box with method to detect non watertight mesh and method to close holes?
No. No¹.
¹ The closest I can think of is mergeVertices from the Three.js addon BufferGeometryUtils. It can be used to cover-up small gaps. Also, there is another add-on ConvexGeometry, which will transform a geometry into a convex polyhedron, which is guaranteed to be watertight … but you won’t want it.
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