Connect Raspberry Pi to Projector or TV

When we have a meeting in a meeting room, we need to connect our laptop to a projector to show our desktop. But sometimes, several persons need to show their desktop, they need to change their laptop. This is complex and waste some time.
Currently, we have some mobile project, they are can be run in android/ios system. Before publish the project, we need to demo it to our team members or other guys. It is hard to demo them( in a phone) in the projector.

What I want to do is: 
1. Write a video player in Raspberry Pi
2. Connect the Raspberry Pi to the Projector or TV
3. Write a desktop capture in a pc/mobile phone, and send the data to the Raspberry Pi
4. Who want to show their desktop in a pc/mobile phone, run the program to connect Raspberry Pi and it will show it in the Projector/TV

Step 1: Port FFmpeg/SDL to Raspberry Pi

How to write a video player in Raspberry Pi?
1. Port FFmepg/SDL to it.
 2. Write a server program to accept the pc/mobile phone to connect it
3. Call ffmpeg to play the network data.

Comments

[grimpirate]

A Raspberry Pi can share files on a network. So if it's sole purpose is to play video files then all you need do is access the shared file directory and play the videos from there. Your various laptop users would create the video however they please on their laptops, upload it to the shared file directory and then someone would just point the Raspberry Pi to the proper file. omxplayer already exists for playing video on the RasPi.

[ciak]

try debian all you ned is in the repositories