Elliptical Arc-Midpoint determination
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
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 =?