# Triangle minimum enclosing disk solution

Model was written in NetLogo 5.3.1
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turtles-own [name] globals [Ix Iy radius ExtList wholist step pos slopes intercepts Ax Ay Bx By Cx Cy ABx ABy ABm ABb BCx BCy BCm BCb CAx CAy CAm CAb midx midy] to doit if step = 0 [triangle] if step = 1 [midpoints] if step = 2 [bisect] if step = 3 [bi_intersect] set step step + 1 if step > 4 [set step 0 ca clear-output] end to triangle ;make color set set pos 0 ;make points foreach ["A" "B" "C"][ crt 1 [set shape "square" set size 2 set color 48 set name ? set label name set heading random 360 jump (10 + random 10 + (random 100) / 100)] ] set wholist [] ask turtles[set wholist lput who wholist] set wholist sort wholist set pos 0 repeat (length wholist - 1) [ set pos pos + 1 ask turtle (item pos wholist) [create-link-with turtle (item (pos - 1) wholist)]] ask turtle (last wholist) [create-link-with turtle (first wholist)] ask links [set thickness 0.5 set color 5] end to midpoints set Ax [xcor] of one-of turtles with [name = "A"] set Ay [ycor] of one-of turtles with [name = "A"] set Bx [xcor] of one-of turtles with [name = "B"] set By [ycor] of one-of turtles with [name = "B"] set Cx [xcor] of one-of turtles with [name = "C"] set Cy [ycor] of one-of turtles with [name = "C"] set ABx first midpoint Ax Ay Bx By set ABy last midpoint Ax Ay Bx By crt 1 [set name "AB" set label name setxy ABx ABy set shape "triangle" set color yellow] set BCx first midpoint Bx By Cx Cy set BCy last midpoint Bx By Cx Cy crt 1 [set name "BC" set label name setxy BCx BCy set shape "triangle" set color yellow] set CAx first midpoint Cx Cy Ax Ay set CAy last midpoint Cx Cy Ax Ay crt 1 [set name "CA" set label name setxy CAx CAy set shape "triangle" set color yellow] end to bisect set ABm -1 / (slope Ax Ay Bx By) set ABb intercept ABx ABy ABm set BCm -1 / (slope Bx By Cx Cy) set BCb intercept BCx BCy BCm set CAm -1 / (slope Cx Cy Ax Ay) set CAb intercept CAx CAy CAm ;draw them ;find the intercept with the world-height and world-width? ;extend the lines let scale 0.95 set ExtList [] ;set the x to the world left edge and see of the y value is within the range of the height. If so keep the coordinates carefully [if abs ((ABm * ((world-width * scale) / -2.0)) + ABb) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / -2.0) ((ABm * ((world-width * scale) / -2.0)) + ABb)) ExtList]][] carefully [if abs ((ABm * ((world-width * scale) / 2.0)) + ABb) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / 2.0) ((ABm * ((world-width * scale) / 2.0)) + ABb)) ExtList]][] carefully [if abs ((((world-height * scale) / 2.0) - ABb) / ABm) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / 2.0) - ABb) / ABm) ((world-height * scale) / 2.0)) ExtList]][] carefully [if abs ((((world-height * scale) / -2.0) - ABb) / ABm) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / -2.0) - ABb) / ABm) ((world-height * scale) / -2.0)) ExtList]][] carefully [create-turtles 1 [set name "AB1" set xcor first first ExtList set ycor last first ExtList set color white set shape "dot"]][] carefully [create-turtles 1 [set name "AB2" set xcor first last ExtList set ycor last last ExtList set color white set shape "dot"]][] carefully [ask one-of turtles with [name = "AB1"] [create-link-with one-of turtles with [name = "AB2"]]][] carefully[ask link ([who] of one-of turtles with [name = "AB1"]) ([who] of one-of turtles with [name = "AB2"]) [set thickness 0.2 set color red]][] set ExtList [] carefully [if abs ((BCm * ((world-width * scale) / -2.0)) + BCb) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / -2.0) ((BCm * ((world-width * scale) / -2.0)) + BCb)) ExtList]][] carefully [if abs ((BCm * ((world-width * scale) / 2.0)) + BCb) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / 2.0) ((BCm * ((world-width * scale) / 2.0)) + BCb)) ExtList]][] carefully [if abs ((((world-height * scale) / 2.0) - BCb) / BCm) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / 2.0) - BCb) / BCm) ((world-height * scale) / 2.0)) ExtList]][] carefully [if abs ((((world-height * scale) / -2.0) - BCb) / BCm) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / -2.0) - BCb) / BCm) ((world-height * scale) / -2.0)) ExtList]][] carefully [create-turtles 1 [set name "BC1" set xcor first first ExtList set ycor last first ExtList set color white set shape "dot"]][] carefully [create-turtles 1 [set name "BC2" set xcor first last ExtList set ycor last last ExtList set color white set shape "dot"]][] carefully [ask one-of turtles with [name = "BC1"] [create-link-with one-of turtles with [name = "BC2"]]][] carefully[ask link ([who] of one-of turtles with [name = "BC1"]) ([who] of one-of turtles with [name = "BC2"]) [set thickness 0.2 set color red]][] set ExtList [] carefully [if abs ((CAm * ((world-width * scale) / -2.0)) + CAb) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / -2.0) ((CAm * ((world-width * scale) / -2.0)) + CAb)) ExtList]][] carefully [if abs ((CAm * ((world-width * scale) / 2.0)) + CAb) < ((world-height * scale) / 2) [set ExtList lput (list ((world-width * scale) / 2.0) ((CAm * ((world-width * scale) / 2.0)) + CAb)) ExtList]][] carefully [if abs ((((world-height * scale) / 2.0) - CAb) / CAm) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / 2.0) - CAb) / CAm) ((world-height * scale) / 2.0)) ExtList]][] carefully [if abs ((((world-height * scale) / -2.0) - CAb) / CAm) < ((world-width * scale) / 2) [set ExtList lput (list ((((world-height * scale) / -2.0) - CAb) / CAm) ((world-height * scale) / -2.0)) ExtList]][] ;show ExtList carefully [create-turtles 1 [set name "CA1" set xcor first first ExtList set ycor last first ExtList set color white set shape "dot"]][] carefully [create-turtles 1 [set name "CA2" set xcor first last ExtList set ycor last last ExtList set color white set shape "dot"]][] carefully [ask one-of turtles with [name = "CA1"] [create-link-with one-of turtles with [name = "CA2"]]][] carefully[ask link ([who] of one-of turtles with [name = "CA1"]) ([who] of one-of turtles with [name = "CA2"]) [set thickness 0.2 set color red]][] end to bi_intersect set Ix ((ABb - BCb) / (BCm - ABm)) set Iy (ABm * Ix + ABb) ifelse abs Ix < world-width / 2 and abs Iy < world-height / 2 [ set radius (((Ix - Ax) ^ 2) + ((Iy - Ay) ^ 2)) ^ 0.5 set pos 0 carefully[ repeat 179 [ set pos pos + 2 crt 1 [set name "circle" setxy Ix Iy set size 3 set shape "dot" set color white set size 1 set heading pos] ] ] [] ][show "outside of view"] ask turtles with [name = "circle"] [carefully[jump radius set shape "line" set heading heading + 90][die]] end to-report slope [x1 y1 x2 y2] report ((y1 - y2) / (x1 - x2)) end to-report intercept [x y m] report (y - (m * x)) end to-report midpoint [px py qx qy] set midx ((px + qx) / 2) set midy ((py + qy) / 2) ;show (list px py qx qy midx midy) report (list midx midy) end

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File | Type | Description | Last updated | |
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Triangle minimum enclosing disk solution.png | preview | Preview for 'Triangle minimum enclosing disk solution' | about 5 years ago, by Eugene Martin | Download |

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