[Last Call] Learn about multicloud storage options and how to improve your company's cloud strategy. Register Now

x
Solved

# Converting lines to polygons

Posted on 2003-12-11
Medium Priority
289 Views
I have a set of 2D lines that make up one or more polygons (which can share sides). Can anyone describe an algorithm that will give me the polygon vertices?
0
Question by:JamieR
[X]
###### Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

• Help others & share knowledge
• Earn cash & points

LVL 11

Expert Comment

ID: 9925267
Coplanar lines are either coincident, parallel, or they intersect at a point. Assume you have the slope-intercept form of the line: the lines are coincident if the slope and intercept are the same. They are parallel if the slope is the same and they are not coincident. They intersect if they are neither of the above and the point of intersection is the point that satisfies the two simultaneous equations

y = m*x + b
y = n*x + c

where m,n are slopes and b,c are intercepts.

The union of the pair-wise intersection points of the lines is the collection of all of the vertices of all of the polygons formed by the lines.

Hope this helps, -bcl
0

LVL 84

Expert Comment

ID: 9933182
How is your set of 2D lines represented?
0

LVL 1

Author Comment

ID: 9935427
Each line is represented by it's two end points - a pair of (x, y) co-ordinates.

I'm nearly there I think. Each point (that potentially comprises a polygon) has two or more lines associated with it. Basically I navigate around each point always turning left (taking the line with the smallest relative angle). Once I reach the start point I output a polygon comprisied of each point visited. I only allow one journey down each line (in both directions) for dealing with polygons that overlap.
0

LVL 84

Expert Comment

ID: 9954879
That could work.   Do any of the lines intersect other than at their end points?  Can polygons that "overlap" share more than their borders?
0

LVL 1

Author Comment

ID: 9955787
Yes, two polygons can share one or more sides.
0

LVL 84

Expert Comment

ID: 9955846
Sharing sides should pose no problem.  I was wondering if they could share area.
0

LVL 1

Author Comment

ID: 9955884
Yes they can. I don't think this poses a problem either, but I'd be interested in your train of thought.
0

LVL 84

Expert Comment

ID: 9955906
Actually I was wondering if you'd need to trace vertices of your polygons not in your list of endpoints but formed by the intersection of two of your line segments.
0

LVL 5

Accepted Solution

Netminder earned 0 total points
ID: 10144470
Points (250) refunded and question closed.

Netminder
0

## Featured Post

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

As game developers, we quickly learn that Artificial Intelligence (AI) doesnâ€™t need to be so tough.  To reference Space Ghost: â€œMoltar, I have a giant brain that is able to reduce any complex machine into a simple yes or no answer. (http://www.youtuâ€¦
Recently, in one of the tech-blogs I usually read, I saw a post about the best-selling video games through history. The first place in the list is for the classic, extremely addictive Tetris. Well, a long time ago, in a galaxy far far away, I wasâ€¦
This tutorial will teach you the special effect of super speed similar to the fictional character Wally West aka "The Flash" After Shake : http://www.videocopilot.net/presets/after_shake/ All lightning effects with instructions : http://www.mediafâ€¦