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Math Help - Definition of relative projection area of the body to a segment of the sphere

  1. #1
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    Post Definition of relative projection area of the body to a segment of the sphere

    Hi folks.
    I'm trying to implement an algorithm that calculates the ratio of the projection area of the geometric body(parallelepiped for ex) to the area of ​​a spherical segment pic here. Inputs are:

    • coordinates of the center and vertices of a cuboid
    • coordinates of the center of the sphere
    • unit vector n (see pic)
    • each spherical segment is known by its two angles (see pic)

    I know how to define an area of a polygon by its spherical coordinates, but there are some special cases, and i don't know what to do with them. Any help is appreciated. Maybe there are some simple and elegant solution to the problem?
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  2. #2
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    Your pic doesn't illustrate the problem very well. You need to explain this better so that it can be formulated mathematically. Let me help. You have a sphere with a light source at the center and a geometric object positioned somewhere inside the sphere. A shadow will appear somewhere on the surface of the spere. You want to calculate the ratio of the surface area of the object to that of its shadow? Have I got this right?
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  3. #3
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    Hmm, no you haven't.

    Ok, lets say that it is a light source. But not usual, because it has axisymmetric discrete distribution of parameters (for each segment... don't know if segment is a proper name of such geometric figure). We are interested only in such parameter as solid angle of each segment.
    Also, according to inputs we can define solid angle of cuboid (origin is centre of the sphere).
    I need the logical AND for these two solid angles.
    Here is explanation pic:
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  4. #4
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    It's very hard to understand what you're asking. Do you have any references to literature discussing similar problems or is this something you came up with?
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