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Math Help - Elliptical Arc-Midpoint determination

  1. #1
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    Elliptical Arc-Midpoint determination

    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 start angle is the angle from center point to start point in radian


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

    Where
    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 itís not giving correct result.

    I have attached the picture and also provided sample values

    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

    Mid Point = B =?

    Thanks
    Attached Thumbnails Attached Thumbnails Elliptical Arc-Midpoint determination-example-elliptical-arc-picture.jpg  
    Last edited by mrajee; November 27th 2009 at 03:25 AM. Reason: uploading picture
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