How to say if two random curves intersects?

[helloansuman]

Given- 1. A set of finite curves which are randomly distributed on a finite surface. Some of the curves intersects with some curves and some are separate.
2. I have discrete coordinates of each curve including starting and ending points.

Question: Does a curve let curve number 1 intersects with curve number 5?
Answer- Yes/ No.

How to determine?

One solution may be take the two curves and find their tangents if they meet at some points then their tangents have same slop.

1. But problem is I have discrete points of those curves. They may meet in between two discrete points.

2. Finding tangent at every point is computational very expensive

 

[stapel]

What is the exact text of the exercise? What precise information have you been given? How does the picture relate, if at all?

Please be complete. Thank you!

 

[DrPhil]

Given- 1. A set of finite curves which are randomly distributed on a finite surface. Some of the curves intersects with some curves and some are separate.
2. I have discrete coordinates of each curve including starting and ending points.

Question: Does a curve let curve number 1 intersects with curve number 5?
Answer- Yes/ No.

How to determine?

One solution may be take the two curves and find their tangents if they meet at some points then their tangents have same slop.

1. But problem is I have discrete points of those curves. They may meet in between two discrete points.

2. Finding tangent at every point is computational very expensive

You are making it too hard - "intersections" are generally where two curves meet or cross. The slopes are not relevant in this case. I assume that if the curves are defined at some set of points, there is a continuous line joining the points. If the two lines cross between given points, then there is an intersection. If y1 is greater than y5 at some point and less at another (and the two curves are continuous), there is an intersection.

 

[daon2]

What is a finite curve?

What do you mean by a set of curves being randomly distributed?

To what space to these curves belong? Just a general 3-dimensional surface? In that case, have you thought of looking at the "shadows" under a projection? This is what knot theory does.
.