# Intersecting Lines Example

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## WHAT IS IT?

This shows how to determine whether line segments cross, and if they do, where.

## 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, 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 segment variables instead and compute them for all segments before checking for any intersections.

The math assumes that the turtles 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 Links Example: same as this example, but for links instead of line turtles
- 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 [ segments segment ] breed [ markers marker ] to setup clear-all set-default-shape markers "circle" set-default-shape segments "line" create-segments 9 [ setxy (random-xcor / 2) (random-ycor / 2) set size 10 + random 5 ] place-markers reset-ticks end to go ask segments [ rt 0.1 + who / 30 ] place-markers tick end to place-markers ask markers [ die ] ;; each pair of segments checks for intersections once ask segments [ ;; performing this check on the who numbers keeps ;; us from checking every pair twice ask segments with [self > myself] [ let result intersection self myself if not empty? result [ 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 - heading)] of t1 let m2 [tan (90 - 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 [ycor - xcor * m1] of t1 ;; t2 is vertical so we know x already let x [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 [ycor - xcor * m1] of t1 let c2 [ycor - 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 (xcor - x) <= abs (size / 2 * dx) end to-report y-within? [y] ;; turtle procedure report abs (ycor - y) <= abs (size / 2 * dy) 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 Lines Example.png | preview | Preview for 'Intersecting Lines Example' | over 11 years ago, by Uri Wilensky | Download |

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