puts "======================="
puts "Test for Circle/Sphere extrema algorithm"
puts "Touch case (circle is just touching the sphere)"
puts "======================="
puts ""

# Make sphere
set x0 0.
set y0 0.
set z0 0.
set sph_radius 10.
sphere s $x0 $y0 $z0 $sph_radius

# Initially the circle will be made at the same place as sphere with different radius
# and will shifted many times to touch the sphere.
# The distance should always be close to zero.

# Number of different radius of initial circle
set nb_radius 7
# Number of circle's rotations 
set nbstep 8
set angle [expr 180. / $nbstep]

# Iteration step
set iStep 1

for {set i 1} {$i < $nb_radius} {incr i} {
  set circ_radius [expr $i*2.]
  if {$circ_radius == $sph_radius} {
    set circ_radius [expr $circ_radius + 0.1]
  }
  circle c $x0 $y0 $z0 0 0 1 $circ_radius

  # Circle will be rotated around the line
  line rotation_line $x0 $y0 $z0 1 0 0
  # Line rotation
  for {set j 1} {$j <= $nbstep} {incr j} {
    rotate rotation_line $x0 $y0 $z0 0 0 1 $angle
    
    # Get direction for circle's rotation
    regexp {Axis   :([-0-9.+eE]*), ([-0-9.+eE]*), ([-0-9.+eE]*)} [dump rotation_line] full dx dy dz
    
    # Circle rotation
    copy c c_rotated
    for {set k 1} {$k <= $nbstep} {incr k} {
      rotate c_rotated $x0 $y0 $z0 $dx $dy $dz $angle
      
      # Get translation axis for the circle
      regexp {XAxis  :([-0-9.+eE]*), ([-0-9.+eE]*), ([-0-9.+eE]*)} [dump c_rotated] full dxx dxy dxz
      
      # Get rotation plane for translation line
      regexp {YAxis  :([-0-9.+eE]*), ([-0-9.+eE]*), ([-0-9.+eE]*)} [dump c_rotated] full dyx dyy dyz
      
      line translation_line $x0 $y0 $z0 $dxx $dxy $dxz
      
      for {set n 1} {$n <= $nbstep} {incr n} {
        rotate translation_line $x0 $y0 $z0 $dyx $dyy $dyz $angle
        
        # Get direction for circle's translation
        regexp {Axis   :([-0-9.+eE]*), ([-0-9.+eE]*), ([-0-9.+eE]*)} [dump translation_line] full dtx dty dtz
        
        # Circle's translation
        copy c_rotated c_shifted
        translate c_shifted $sph_radius*$dtx $sph_radius*$dty $sph_radius*$dtz 
    
        # Shift circle to touch sphere
        set shift -1
        repeat 2 {
          copy c_shifted c_touch
          translate c_touch $shift*$circ_radius*$dxx $shift*$circ_radius*$dxy $shift*$circ_radius*$dxz

          set log [extrema c_touch s]

          # save each circle if necessary
          # copy c_touch c_$iStep

          if {![regexp "ext_1" $log]} {
            if {![regexp "Extrema 1 is point" $log]} {
              puts "Error: Extrema has not detected the touching case on step $iStep"
            } else {
              puts "Check of Step $iStep, min distance  OK"
            }              
          } else {
            set ext_dist [lindex [length ext_1] end]
            checkreal "Step $iStep, min distance " $ext_dist 0 1.e-7 1.e-7
          }
          incr iStep
          set shift 1
        }
      }
    }
  }
}