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Math Help - calculating penumbra frustum from polygon light source

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    calculating penumbra frustum from polygon light source

    hi, I'm having trouble working out how to construct the outer-most planes of a frustum (penumbra) formed by two arbitrary polygons in 3-space, if you consider the first polygon (A) to be a light source and the second polygon (B) to be an occluder then I am looking to find the volume formed from the penumbra of the occluder as a set of planes defining a frustum. The only way I can see to do this is by constructing each 3d line formed from the two polygons i.e:

    for all points in A
    for all points in B
    line(a, b)

    this would give me a set of 3d lines but how do I find the outer-most convex set that defines the penumbra frustum? or is there another way.
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  2. #2
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    Quote Originally Posted by staticVoid2 View Post
    hi, I'm having trouble working out how to construct the outer-most planes of a frustum (penumbra) formed by two arbitrary polygons in 3-space, if you consider the first polygon (A) to be a light source and the second polygon (B) to be an occluder then I am looking to find the volume formed from the penumbra of the occluder as a set of planes defining a frustum. The only way I can see to do this is by constructing each 3d line formed from the two polygons i.e:

    for all points in A
    for all points in B
    line(a, b)

    this would give me a set of 3d lines but how do I find the outer-most convex set that defines the penumbra frustum? or is there another way.
    In my opinion this question can't be answered in general. You must know:

    1. the shape of the light source (L)
    2. the shape and the width of the opening of the occluder (W)
    3. the orientation of A and B. I've assumed that they are parallel but according to your question that isn't necessary
    4. the distance between L and W (d)
    5. the distance of the light from the plane of the shadow (D)

    I've attached a rough sketch of the (simplified) situation.
    Attached Thumbnails Attached Thumbnails calculating penumbra frustum from polygon light source-halbschatten1.gif  
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