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Calculating point on polygon's surface

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As in the subject, I am looking for a way to calculate position of a point on the polygon's surface BUT, I have two variables of this point available plus all of the polygons vertices, points x and y coordinates I know I just need to be able calculate its z position so it is matching triangles surface at same point. You must look at the picture from the front to along the z axis, this will be used to write simple zbuffer later on. have a look at attached picture

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