I found this page which gave me some equations on solving the intersection of a line with an ellipse given a point on the line and the slope of the line:
There Isn't much explanation but I presume that after solving for a, b, and c, you can then find the roots to the newly formed quadratic, which will give 2 possible k values.
Here's where the questions come in:
- Which of the two k values do I use in solving for r' and z' ?
- How can you tell when the line doesn't intersect the ellipse? Is the quadratic equation for k not have any real roots?
Earlier, the site states:
- Is it important for r to be >0 in for this equation even though I'm not testing a point, but a line instead?
Why is the semi-minor axis being defined as 'ae(1-f)'? I usually just define the semi-minor axis the same way I define the major, so could I just replace all the '(1-f)'s in the above equations with my desired semi-minor axis length?
Finally, is there any simpler, faster way to see if and were an ellipse and line intersect?