Convert 4:3 to 16:9 Pal

I had some video footage at 4:3 aspect which I wanted to scale and crop to fit a 16:9 wide-screen PAL format. My first attempt was to scale the video to 720×540 (maintaining the 4:3 aspect ratio) and then crop to 720×405 (a 16:9 ratio)

mplayer -vf scale=720:540,crop=720:405 movie.mpg

However PAL has a resolution of 720×576 so I then had to scale the video again

mplayer -vf scale=720:540,crop=720:405,scale=720:576 -aspect 16/9 movie.mpg

What I wanted was to do this in a more simple manner. I realised that I mearly need to scale it to be larger in the first operation, But how much larger? Well since I wanted to crop the same proportion of the image I simply needed to calculate the aspect of the cropped proportion. Which was 540/405 or 4/3 So I actually want my video to be 4/3 taller than its final height. So we want the movie to be 576 × 4/3 = 768

mplayer -vf scale=720:768,crop=720:576 -aspect 16/9 movie.mpg

Scale Diagram

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