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Math Help - Midpoint on the elliptical arc

  1. #1
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    Midpoint on the elliptical arc

    Hi,
    I want to find the midpoint on the elliptical arc

    I know the following
    1 Start point of elliptical arc
    2 End point of elliptical arc
    3 Center Angle of elliptical arc or Sweep Angle
    4 Center point of elliptical arc
    5 Major radius of elliptical arc
    6 Minor radius of elliptical arc

    Angle (in radian) =StartAngle + (CenterAngle / 2)
    Where strat angle is the angle from center point to start point in radian


    MidX = CenterX +Cos(Angle) * Distance
    MidY = CenterY+ Sin(Angle) * Distance


    Distance is the Distance from center point to MidPoint on the elliptical arc which is unknown.

    Please do help in finding the Distance which is unknown or specify some other approch to do so.

    I have tried by substituting the major radius and minor radius as X and Y Distance, but its not giving correct result.

    Thanks
    Last edited by mrajee; November 24th 2009 at 09:38 PM.
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  2. #2
    Super Member bigwave's Avatar
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    can you post a drawing of what you are doing
    might be easier for us to answer
    and label the elements...
    Last edited by bigwave; November 25th 2009 at 11:27 PM. Reason: wording
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  3. #3
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    Mid point on elliptical arc

    Quote Originally Posted by bigwave View Post
    can you post a drawing of what you are doing
    might be easier for us to answer
    and label the elements...

    Thank You for your reply.


    I have attached the sample picture.

    Actually my elliptical arc may be horizontal(fig 1) or vertical(fig 2) or rotated (fig 3) as shown in sample picture


    For Fig 1, I have provided the point details.

    A = Start Point = ( 170.6004 , 159.3217)

    C = End Point = ( 196.1697 , 129.754)

    O = Center Point = (206.7051 , 146.6791)

    Center Angle = 283

    Start Angle = 161 ( Angle form center point to start point)

    End Angle = 283 ( Angle from center point to End point)

    Major Radius = 52.9993

    Minor Radius = 17.2697
    Attached Thumbnails Attached Thumbnails Midpoint on the elliptical arc-example-elliptical-arc-picture.jpg  
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