[Resolved] Finding Min X on a circle

[THEROB]

How is it possible to find the minimum X coordinate on the circle between the two lines?
Y1, Y2, R are known. The centre of the circle is at (0, 0)

In the picture the MinX would be –R, but the boundary lines can be placed anywhere in the circle, they are always parallel with the X axis.

Thanks

Robert

[zaza]

Just check the values of Y1 and Y2. There are only 3 possibilities:

One >= 0, one <= 0 as in your picture - in this case the minimum must be -R because the lines enclose the overall minimum point at 180 degrees.

Both >= 0 - in this case the minimum is at Y2. Since you know R and the value of Y2, you can easily work out the X value by Pythagoras or trig.

Both <= 0 - as above, except that now the minimum is at Y1.



zaza

[krtxmrtz]

How is it possible to find the minimum X coordinate on the circle between the two lines?
Y1, Y2, R are known. The centre of the circle is at (0, 0)

In the picture the MinX would be –R, but the boundary lines can be placed anywhere in the circle, they are always parallel with the X axis.

Thanks

Robert

Well, if (Y1 - R)*(Y2 - R) <= 0 then the 2 lines are on opposite sides with rerspect to the x axis, so the min. x coordinate is -R as in your example.
Otherwise, let H = Min[Abs(Y1),Abs(Y2)], i.e. make H the distance between the origin and the closest of those lines. Then you find the negative x coordinate of the intercept with the circle.

Equation of the circle:

X² + y² = R²

Substitute y by H:

X² + H² = R²

so that the required minimum x is:

X_min = -Sqr(R² - H²)

[THEROB]

Thanks thats really helped me out.

Robert