Spherical Path Example 3D

globals [ radius ]

to setup
  clear-all
  set radius ( world-width - 2 ) / 2

  crt 12 [
    ;; move to a random point on the sphere
    tilt-up ( random 180 ) - 90
    fd radius
    ;; lie tangent to the sphere
    tilt-down 90
    ;; turn again so that not all turtles are moving
    ;; to north and south poles
    rt random 360
    pen-down
  ]
end 

to go-distance
  ask turtles [
    arc-forward-by-distance step-size
    lt random wiggle-range rt random wiggle-range
  ]
  tick
end 

to go-angle
  ask turtles [
    arc-forward-by-angle arc-angle
    lt random wiggle-range rt random wiggle-range
  ]
  tick
end 

;; This procedure moves the turtle to the next point
;; on the sphere the given distance along the curve.

to arc-forward-by-distance [dist] ;; turtle procedure
  ;; calculate how much of an angle we'll be turning through
  ;; (essentially converting radians to degrees)
  let theta dist * 180 / ( pi * radius )
  ;; turn to face the next point we're going to
  tilt-down theta / 2
  ;; go there
  fd dist
  ;; turn to face tangent to the circle
  tilt-down theta / 2
end 

;; This procedure moves the turtle to the next point
;; on the sphere the given angle measure along the curve.

to arc-forward-by-angle [angle] ;; turtle procedure
  ;; turn to face the next point we're going to
  tilt-down angle / 2
  ;; calculate the distance we'll have to move forward
  ;; in order to stay on the circle. Go there.
  fd 2 * radius * sin (angle / 2)
  ;; turn to face tangent to the circle
  tilt-down angle / 2
end 


; Copyright 2007 Uri Wilensky. This code may be freely copied, distributed,
; altered, or otherwise used by anyone for any legal purpose.