Information on algorithms to "bind" textures onto

[punt]

I am dealing in 2d only. I have a 64x64 texture, that I want to bind to an irregular shape. In opengl, this is trival, I setup a triangle strip, and bind the texture. What I am looking for is a software algorithm that covers how the pixels are filtred/expanded/average to make it fit on the shape. I would like to investigage not using openGL for the soltuion, but a pure 2d bitblt solution. Any information on this is appreciated.