How to make an "X" through circle in jython?

Question

I have no idea how to do this. I need to draw two lines that make an X through a circle, where the starting and end points would be on the circumference of the circle. If anybody could even give me a direction to go in to do this, it'd be appreciated.

Answer 1

Get the maths right first.

The most general case of circle-line intersection is described here: http://mathworld.wolfram.com/Circle-LineIntersection.html

But if the center of the circle is the origin, its radius is 1, and the lines are forming an x, so a 45 degree angle with the horizontal and vertical axes, it is quite a bit more simple:

The circle is defined by

x² + y² = 1

The line with 45 degree slope is defined by

y = x

Their intersections are the points (x,y) where both statements are true so

x² + x² = 1

2 x² = 1

x² = 1/2

x = sqrt(1/2) or x = -sqrt(1/2) and y = x

so points (sqrt(1/2), sqrt(1/2)) and (-sqrt(1/2), -sqrt(1/2))

Same for the other line.

One line goes from (-sqrt(0.5), -sqrt(0.5)) (bottom left) to (sqrt(0.5), sqrt(0.5)) (top right) and the other from (-sqrt(0.5), sqrt(0.5)) (top left) to (sqrt(0.5), -sqrt(0.5)) (bottom right).

On Wolfram Alpha