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Math Help - axonometric projection transformations

  1. #1
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    Jan 2009
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    axonometric projection transformations

    High School and College were so long ago and I can't for the life of me figure this out (plus it doesn't help I was a music major):

    Given a 3D point in space (x, y, z) and an angle of projection ϴ I want to convert to screen coordinates (x', y'). I can do this successfully going from space to screen via the following transformations:

    x' = (x - y) * cos ϴ;
    y' = (x + y) * sin ϴ - z;

    I cannot however figure out the transformations for going from screen back to space assuming space.z = 0 after the transformation. Any help is much appreciated.

    And if you are still interested in this kind of thing after this one is solved, I have a bunch more.

    Thank you.
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  2. #2
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    Jan 2009
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    Ok I figured out one of them for a 2:1 isometric ratio.

    space to screen:
    x' = x - y
    y' = (x + y) / 2 - z

    screen to space (assuming z = 0):
    x = x' / 2 + y' + z'
    y = y' - x' / 2 + z'
    z = z'
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