mathematical formulation of a series of polygonal manipulation in 3d computer graphics?

hello, i want to build a small program that do 3d shape modeling using programming, i do not buy maya/3dmax/softimage/blender etc because to save money and practice programming, for i am still not very well familiar with 3d graphics, could anybody teach me math foundation of process such as tapor,circularize,warp,twist,extrude,bevel, so forth

thanks

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