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Reciprocal of Homogenous W?

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I'd like to know if I'm understanding this concept correctly. So W component of a 4d vector is used to... 1) Turn on/off translation in affine transformations. Set w to 1 for points and 0 for vectors. 2) Express the common denominator for x,y and z components. If v is (x/d, y/d, z/d), then this can be expressed to (x, y, z, d). You can put (x, y, z, 1) into some sort of a division matrix, such that (x, y, z, 1) -> (x, y, z, d). This is an easier way to express division during matrix calculation. The actual division is performed during the rasterization process(?). Also this is faster in calculation, because cpu only needs to calculate 1/d once for the vector and then multiply this value to the other three components. 3) In real application, rhw is used for fog calculation, perspective projection and others. Am I understanding it correctly? I'm a little confused with 2), so any explanation or examples will be greatly appreciated. Thanks a lot!

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