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Thread: Equi-Spacong on a Sphere.

  1. #1 Equi-Spacong on a Sphere. 
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    I need to place say 100 seperate Devices, as equi-spaced as possible on the Surface of a Sphere.

    I am a little confused as to how to Calculate their distance apart - in either straight-line measurements, or in measurements along the surface of the Sphere.

    What I really need is a Formula for Calculating the Distance - given a known Radius.

    This is the case for 100 Devices.

    And, a Fomula for calculating the number of Devices spaced a fixed distance apart, on the surface of a known Sphere.

    This latter case involves putting several Devices, which are to be 8 Units apart - on the surface of a Sphere of Radius 150 Units.
    I originally calculated this on the basis of a circle of Radius 150 Units - then a number of circles, which would be 8 Units apart at their furthest.
    However - I now realise that I am seriously in error - because although they will e equally spaced around each circle - they will get closer together in the other direction, the nearer they get to the point of intersection of the circles.
    I realise that Iam using TOO MANY Devices - a lot of these being spaced much less than 8 Units apart in one of their distances.

    I will not go into why I need to do these Calculations - but it is important.
    However, it is way outside my understanding of Mathematics.
    I was Educated to Degree Level - but 3-D Geometry of this kind never came into our Syllabus.

    If I wasn't so stupid - I might know what I was doing
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  3. #2  
    Genius Duck Moderator Dywyddyr's Avatar
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    Distributing points on the sphere | School of Mathematics and Statistics

    Building a nuke?

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  4. #3  
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    Well - No.

    For 100 Devices equally spaced - Additional Gravity Generators on Mars.
    These will be placed deep underground - to create additional Surface Gravity, bringing it up to 1 G on the surface.

    For Devices equally spaced at 8 Units apart.
    Long Distance Detectors for Ships travelling using FTL Drives.
    These will have Detection Range of 10 Light Years - so best to be 8 Light Years apart.
    On a Sphere of 150 Light Years Radius - 300 Light Years Diameter.

    As these APPLICATIONS are strictly Sci Fi - in my Sci Fi Game / Sci Fi Universe - set in the 2130's. I did not really want to go into the Details of the Applications.

    However, even if it is Sci Fi - I TRY to keep most things agreeing with Real, Known Science.
    Of course it includes some Sciences or Technologies which are NOT Real now, and of course Unknown now.
    That is how come it is Sci Fi - and also set in the Future.

    However - I really dould do with some Real Help in the "world" of Real Science - such as with this Geometry Problem ( I think it is probably Geometry ).
    __________________________________________________ _______________________

    Thanks for the two Articles - However, this still leaves me a bit baffled.

    The first Example looks the most useful - however, I am not a Computer Programmer ( at least I have not done any Programming since 2003 at the most recent ).
    And I do not have access to a Programmable Computer which uses any Programming Language with which I am that familiar.
    The "second method", using a Regular Placement seems the most useful and appropriate -
    However, I am not sure how to put this into useable form for an Exel Spreadsheet Calculation.

    Notes -

    I do not need to know the actual Locations for the Points.

    For Case 1 - I just need to know how to Calculate how far apart they are, if there are 100 on a sphere of stated Radius.
    Ideally - A Useable Formula.

    For Case 2 - I just need to know how to Calculate how many Points there are, for a given distnace.
    on a Sphere of stated Radius.
    Ideally - A Useable Formula.

    The Second Article is waaay too Theoretical for me - and does not seem to offer any Useable Solutions for my Problems.
    Last edited by Karakris; May 12th, 2013 at 10:46 AM.
    If I wasn't so stupid - I might know what I was doing
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