# Intersecting Links Example

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## WHAT IS IT?

This code example shows how to determine if two links intersect.

## HOW IT WORKS

The work is done in the procedure called `intersection`

. First the code computes the intersection point of the lines containing the segments between the two nodes of the link, then checks to see if that intersection point is actually within both segments. (The second check is easy to do because we already know the intersection point is on the lines, so we only need to check that the point's x coordinate.) If two segments have the same slope, no intersections are marked.

Since slope is undefined for vertical lines, special case code is used if either of the segments is vertical.

## THINGS TO NOTICE

The `intersection`

procedure computes m and c for both segments every time it is called. This is wasteful if we are checking every turtle against every other turtle looking for intersections. To speed up the model, make m and c link variables instead and compute them for all segments before checking for any intersections.

The math assumes that the links don't extend beyond the edges of the world. If you need to intersect turtles which go off the edges of the world, you'll need to add extra code.

## RELATED MODELS

- Code Examples -> Intersecting Lines Example: same as this example, but for line turtles instead of links
- Games -> Planarity: has shorter code for determining whether two line segments intersect, without bothering to compute the location of the intersection point

## CREDITS AND REFERENCES

To keep the math relatively simple, the code represents lines in slope-intercept form (y=mx+c); see http://mathworld.wolfram.com/Slope.html.

Thanks to Gagandeep Singh for his work on this example.

## Comments and Questions

breed [ markers marker ] breed [ endpoints endpoint ] to setup clear-all set-default-shape markers "circle" create-endpoints 9 [ setxy random-xcor random-ycor ] ask endpoints [ hatch-endpoints 1 [ setxy random-xcor random-ycor create-link-with myself ] ] place-markers reset-ticks end to go ask endpoints [ rt random-float .5 fd 0.01 ] place-markers tick end to place-markers ask markers [ die ] ;; each pair of segments checks for intersections once ask links [ ;; performing this check on the who numbers keeps ;; us from checking every pair twice ask links with [self > myself] [ let result intersection self myself if not empty? result [ ask end1 [ hatch-markers 1 [ set color gray set size 1 setxy (first result) (last result) ] ] ] ] ] end ;; reports a two-item list of x and y coordinates, or an empty ;; list if no intersection is found to-report intersection [t1 t2] let m1 [tan (90 - link-heading)] of t1 let m2 [tan (90 - link-heading)] of t2 ;; treat parallel/collinear lines as non-intersecting if m1 = m2 [ report [] ] ;; is t1 vertical? if so, swap the two turtles if abs m1 = tan 90 [ ifelse abs m2 = tan 90 [ report [] ] [ report intersection t2 t1 ] ] ;; is t2 vertical? if so, handle specially if abs m2 = tan 90 [ ;; represent t1 line in slope-intercept form (y=mx+c) let c1 [link-ycor - link-xcor * m1] of t1 ;; t2 is vertical so we know x already let x [link-xcor] of t2 ;; solve for y let y m1 * x + c1 ;; check if intersection point lies on both segments if not [x-within? x] of t1 [ report [] ] if not [y-within? y] of t2 [ report [] ] report list x y ] ;; now handle the normal case where neither turtle is vertical; ;; start by representing lines in slope-intercept form (y=mx+c) let c1 [link-ycor - link-xcor * m1] of t1 let c2 [link-ycor - link-xcor * m2] of t2 ;; now solve for x let x (c2 - c1) / (m1 - m2) ;; check if intersection point lies on both segments if not [x-within? x] of t1 [ report [] ] if not [x-within? x] of t2 [ report [] ] report list x (m1 * x + c1) end to-report x-within? [x] ;; turtle procedure report abs (link-xcor - x) <= abs (link-length / 2 * sin link-heading) end to-report y-within? [y] ;; turtle procedure report abs (link-ycor - y) <= abs (link-length / 2 * cos link-heading) end to-report link-xcor report ([xcor] of end1 + [xcor] of end2) / 2 end to-report link-ycor report ([ycor] of end1 + [ycor] of end2) / 2 end ; Public Domain: ; To the extent possible under law, Uri Wilensky has waived all ; copyright and related or neighboring rights to this model.

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## Attached files

File | Type | Description | Last updated | |
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Intersecting Links Example.png | preview | Preview for 'Intersecting Links Example' | almost 10 years ago, by Uri Wilensky | Download |

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