tl,dr: I want to talk with a female coworker for clarify certain situation going on.

This post is kind of large in content, but I need to express the whole situation.

About me:

I'm male, 27's, obese (not morbid) and with a grim-serious face expression. Since I recall, I'm introvert (and not much has changed so far). In my previous work positions there was no really romantic or friendship interests with anyone. If someone looked at me in the street, they mostly tended to avoid eye-contact, so as I.

After quit my last job, I read (as I called) a self-help (motivational) book where it basically says about smile, be happy and be grateful with God and life. Due to this new approach, I not only tend to smile more, but be more open to salutate, ask about how day is going and basically, go to work with a smile - an honest, not faked smile. This job is good in the economic sense and I literally prayed for it because I was unemployed for two months and I was getting worried about my next moves.

Backstory:

Now I'm working in a company 6 months ago. During lunch time, I did noticed a female coworker who works in another floor in another department in the same building.

At first, it was eye contact (usually because I just tend to look towards where there is movement) and I never think it was a problem - the company's culture tends to its workers to be professional and "friendlier" - I can't recall the exact words, but it's in these lines, hence, my new "mood" was in line with the company culture and frankly, this is a big company which I didn't knew poeple behaves in this way (frendlier, for say it in a word).

Only during lunch times (when our lunch schedules might cross, which is not often) and when I passed in front of her departament's floor, I tend to look if she's there and watch if I keep eye-contact with her while I'm walking for entering of leaving the building - (entering to go to my desk or leaving for either have a walk alone after lunch or go home).

I (think) that she keeps the eye-contact with me but in a more subtle way; however, when she ends her lunch and leaves and despite my efforts to not look at her for avoid making her awkward, sometimes we have a short eye contact or not at all.

But after a few days, I noticed that she avoids eye contact with me and I think this is due to that, a few days "while I was walking to my desk", I looked and smiled at her - which I didn't previously - but I recall telling myself: "I should smile to her - due that when we have eye contact it was no smiles involved", it was an eye contact in a serious way, but not rude or threateing, it was like, if we're checking the one to another.

The halloween day, her department was dressed in costumes while some other floors didn't or few other personnel made the same thing. That day, I was eating my lunch and when I check she was leaving, I looked and smile at her - in my way, it was for demonstrate I'm a good person and I just want to smile at her -, but when she keeped walking, not only she avoided eye contact but take a step back and hide back of another female coworker of her that was in front of our range vision. I didn't keep looking at her and continue my lunch.

When I leave the building for have a walk alone after lunch, I was thinking in a way for approach to her and say to her that I'm sorry I make her uncomfortable.

Situation:

Due to I perceive (by her reactions) as a bad manners from me, I have the need of not only apologize but also for express with honesty my thoughs to her, but, the problems are:

• I don't know her name or her coworkers's - we work in different departments.
• I really don't know if this is the right step to make.

After read some related posts here on IPS and think for days about this matter, I would like to know your thoughs/answers about how I should be handle/approach this situation.