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rotation and (selection selection of edges of a model)

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Hi, Currently , I'm doing an application that actually acts as a "cut" tool for 3D meshs.Well had some problems with it now which I am clueless on how to solve it sinces its my first application. I have loaded a model from an object file onto the canvas. den on the same canvas i use the mouse drag event to draw lines to define the cutting point. lets say I want to cut a ball into half and I draw the line in the middle, How do I detect that the vectices of the ball that is under the line. secondlly, if I rotate / translate the ball, would all the the vertices information change??

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