Warping an image without using imwarp

Yeah, so my assignment is to make warping function so that I can apply some transform matrix to an image. I cannot use any image functions except imread and imwrite, so I really have to go with essential stuff. I can guess that if I can make warp function then I would be able to make rotating function based on this as well.

I even tried to open imwarp or other functions, but just realised that I cannot understand any single line of those complicated functions made by some genius ppl :(

I thought I was almost close to make, but just things went wrong... and realised that I have to add feature to choose "near-neighbour" or "bilinear" to fill the blank pixels... plz help this poor bachelor student who just cannot sleep at all suffering from this stuff :(