Convex_Hull

Here is code that computes the convex hull of a given set of points. This is primarily based on the algorithm from the book "Introduction to Algorithms". The wiki had trouble with the link so I will just post it here as it is: https://www.amazon.com/Introduction-Algorithms-3rd-MIT-Press/dp/0262033844/ref=sr_1_1?crid=1J4MH8H1F4B0G&keywords=rivest&qid=1672008537&sprefix=rivest%2Caps%2C134&sr=8-1

I know there is another page here with a different implementation. A few of reasons for this new page:

  1. It is a different algorithm.
  2. This uses a new structure to represent points. It includes a point id/name in addition to x/y coordinates.
  3. A quick glance showed some comments about buggy behavior on certain inputs.

Here is the code with all its related proc's:

proc point {id x y} {
     global tsp_points

     ;## get point's x
     set tsp_points($id,id) $id
     set tsp_points($id,x) $x
     set tsp_points($id,y) $y

     return $id
}


proc make_points {triplets} {
    global tsp_points
   
   ;## make point objects from a list of point number and its x,y coordinates
    set pList {}
    foreach tuple $triplets {
        lappend pList [point [lindex $tuple 0] [lindex $tuple 1] [lindex $tuple 2]]
    }
    return $pList
}


proc make_points_from_xy_only {xyList} {
    global tsp_points
   
   ;## make point objects from a list of (x,y) coordinates
    set i 0
    set pList {}
    foreach pair $xyList {
        incr i
        lappend pList [point $i [lindex $pair 0] [lindex $pair 1]]
    }
    return $pList
}

proc pointGetX {p} {
     global tsp_points

     ;## get point's x
     return tsp_points($p,x)
}


proc pointGetY {p} {
     global tsp_points

     ;## get point's x
     return tsp_points($p,y)
}


proc pointIsSamePoint {p1 p2} {
     ;## given two points,
     ;## determine whether they are the same point
     ;## (either by their id's or by their coordinate values)

     if {([string compare $p1 $p2] == 0) || \
              ( ([pointGetX $p1] == [pointGetX $p2]) && \
           ([pointGetY $p1] == [pointGetY $p2]) )} {
             return 1
     } else {
             return 0
     }
}


proc pointGetDistanceToPoint {p1 p2} {
     ;## given two points,
     ;## compute the distance between them
     set x1 [pointGetX $p1]
     set y1 [pointGetY $p1]
     set x2 [pointGetX $p2]
     set y2 [pointGetY $p2]

     return [expr {sqrt (($x1 - $x2) * ($x1 - $x2) + \
                              ($y1 - $y2) * ($y1 - $y2))}]
}


proc convexHull_Theta {p1 p2} {
     ;## given two points,
     ;## compute the theta (in degrees) between them
     if {[pointIsSamePoint $p1 $p2]} {
          set result 361.0

     } else {
          set dx [expr {[pointGetX $p2] - [pointGetX $p1]}]
          set ax [expr {abs($dx)}]
          set dy [expr {[pointGetY $p2] - [pointGetY $p1]}]
          set ay [expr {abs($dy)}]


          set absSum [expr {$ax + $ay}]
          if {$absSum == 0} {
               set t 0
          } else {
               set t [expr {$dy / $absSum}]
          }


          if {$dx < 0} {
               set t [expr {2 - $t}]
          } elseif {$dy < 0} {
               set t [expr {$t + 4}]
          }


          set result [expr {$t * 90}]
     }


     return $result
}


proc computeConvexHull {pointList} {
     ;## given a list of points,
     ;## return a list of points that lie on the convex hull

     if {[llength $pointList] == 0} {
          ;## nothing to do
          return
     }


     ;## create a local array for efficient swap operations
     set pCount 0
     foreach pointID $pointList {
        set pArray($pCount) $pointID
        incr pCount
     }


     ;## find the point with the minimum y-coordinate
     set min 0
     for {set i 0} {$i < $pCount} {incr i} {
          set pi   $pArray($i)
          set pmin $pArray($min)
          if {[pointGetY $pi] < [pointGetY $pmin]} {
               set min $i
          }
     }


     ;## duplicate the min-y point at the end as a safeguard
     set pArray($pCount) $pArray($min)


     ;## put the min-y point first
     ;## swap the 0-th and min-th elements
     set temp         $pArray(0)
     set pArray(0)    $pArray($min)
     set pArray($min) $temp


     set min       0
     set prev     -1
     set hullSize -1
     set changed   1


     for {set i 0} {$i < $pCount} {incr i} {
          ;## swap the i-th and min-th elements
          set temp         $pArray($i)
          set pArray($i)   $pArray($min)
          set pArray($min) $temp


          set polar   360
          set changed 0


          for {set j [expr $i + 1]} {$j <= $pCount} {incr j} {
               set current [convexHull_Theta $pArray($i) $pArray($j)]
               if {($current > $prev) && ($current < $polar)} {
                     set min $j
                     set polar $current
                     set changed 1

               } elseif {$current == $polar} {
                     set distI_J   [pointGetDistanceToPoint $pArray($i) \
                                                                 $pArray($j)]
                     set distI_Min [pointGetDistanceToPoint $pArray($i) \
                                                                 $pArray($min)]
                     if {$distI_J > $distI_Min} {
                          set min $j
                          set polar $current
                          set changed 1
                     }
               }
          }


          ;## convex hull complete?
          if {(! $changed) || [pointIsSamePoint $pArray(0) $pArray($min)]} {
                 set hullSize [expr $i + 1]
                 break
          }


          set prev $polar
     }


     if {$hullSize == -1} {
          ;## all points are on the convex hull
          ;## (did not break out of the above loop)
          set hullSize $pCount
     }


     ;## collect the convex hull points in a list
     set convexList {}
     for {set i 0} {$i < $hullSize} {incr i} {
          lappend convexList $pArray($i)
     }


     ;## destroy the temporary array
     for {set i 0} {$i < $pCount} {incr i} {
          unset pArray($i)
     }


     ;## return the list of convex hull points
     return $convexList
}