7

I found this statement,

The paper presents an automatic approach to reconstruction of 3D objects from point cloud data.

But I feel like this is wrong as I learned with to "should be infinitive". Now I am confused. Can anyone clarify this.

3

You should consider the sentence as:

The paper approaches to (reconstruction of 3D objects) from point cloud data.

Here the preposition "to" is referring to the whole part i.e. "reconstruction of 3D objects".

If the verb form of "reconstruction" i.e. "reconstruct" had been used, it could have been written as:

The paper approaches to reconstruct the 3D objects from point cloud data.

Here the "to" is used for "reconstruct" only.

Note that, it is also possible to rewrite the sentence as:

The paper approaches to (reconstructing the 3D objects) from point cloud data.

EDIT- Sorry, I mistook "approach" as verb here which it isn't. StoneyB pointed out the error, thanks to him! "Approach" is acting as a noun here. So it needs the preposition "to" after it. So, in this particular case, it isnt being used as infinitive. I am changing the examples as per usage of "approach" as a verb.

As for your example, you provided here, like I said in the last paragraph, "to" is acting because the noun needs its complement to be headed with the preposition to.

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4

The word to in OP's example isn't part of an infinitive - it's a preposition (of direction, having the meaning towards). It modifies the noun approach, telling us what the approach is directed at.

But bear in mind reconstruction (of 3D objects) is an abstract noun (it's a process, not a tangible "thing" that you can pick up, locate, or physically approach). So moving to[wards] it is "metaphorical".

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