def x000 {
 def O (0,0,0)
 def I [1,0,0]
 def J [0,1,0]
 def K [0,0,1]
 def eye (18,12,10)
 put { view( (eye) )
       then perspective(|(eye)-(O)|)
       then scale(3/8) } {
 def R 3
 def N 16
 def degrees_per_seg 15
 def pitch 1/7
 def darc degrees_per_seg / 360 * 2 * 3.14159 * R
 def dy darc * pitch
 def n_segs 114
 line[linecolor=red,linewidth=2pt](0,-1,0)(0, n_segs * dy + 1, 0)
 sweep { n_segs, rotate( degrees_per_seg, (O), [J] ) then translate([0, dy, 0]) }
   put { translate([R,0,0]) then rotate(atan2(dy, darc), (O), [I]) }
     sweep[fillcolor=lightgray] { N<>, rotate(360/N, (O), [K]) } (1,0)

 }
}

def x010 {
 put { view((5,4,8)) } {
   def L 1.5
   line[arrows=<->](L,0,0)(0,0,0)(0,L,0)
   line[arrows=->](0,0,0)(0,0,L)
   special|\uput[r]#1{$x$}
           \uput[u]#2{$y$}
           \uput[l]#3{$z$}|
     (L,0,0) % 1
     (0,L,0) % 2
     (0,0,L) % 3
 }
}

def x020 {
 polygon(0,0,1)(1,0,0)(0,1,0)
 line(-1,-1,-1)(2,2,2)
 special|\psline[linecolor=lightgray]{<->}#1#2#3
        \pscircle*[linecolor=lightgray,fillcolor=lightgray]#2{2pt}
        \pscircle[linecolor=lightgray]#2{4pt}|
   [lay=under](0,2,0)(0,0,0)(2,0,0)
}

def x030 {
 polygon[fillcolor=lightgray,linewidth=3pt](0,0,1)(1,0,0)(0,1,0)
 line[linestyle=dotted](-1,-1,-1)(2,2,2)
}

def x040 {
 % vertices of the tetrahedron
 def p1 (0,0,1)
 def p2 (1,0,0)
 def p3 (0,1,0)
 def p4 (-.3,-.5,-.8)

 % faces of the tetrahedron.
 polygon(p1)(p2)(p3) % original front polygon
 polygon(p1)(p4)(p2) % bottom
 polygon(p1)(p3)(p4) % left
 polygon(p3)(p2)(p4) % rear

 % line to pierce the tetrahedron
 line[linecolor=red](-1,-1,-1)(2,2,2)
}

def x042 {
 % vertices of the tetrahedron
 def p1 (0,0,1)
 def p2 (1,0,0)
 def p3 (0,1,0)
 def p4 (-.3,-.5,-.8)

 % faces of the tetrahedron.
 polygon(p1)(p2)(p3) % original front polygon
 polygon(p1)(p4)(p2) % bottom
 polygon(p1)(p3)(p4) % left
 polygon(p3)(p2)(p4) % rear

 % line to pierce the tetrahedron
 line[linecolor=red](-1,-1,-1)(2,2,2)

 % labels
 special |\footnotesize
          \uput{2pt}[ur]#1{$P1$}\uput[r]#2{$P2$}
          \uput[u]#3{$P3$}\uput[d]#4{$P4$}|
   (p1)(p2)(p3)(p4)
}

def x045 {
 def O (0,0,0)
 def K [0,0,1]
 def n_segs 60
 def degrees_per_seg 20
 def pitch 3
 put { view((20,7,4)) then perspective(22) } {
 sweep[cull=false] { n_segs, rotate(10, (O), [K]) then translate(pitch * degrees_per_seg / 360 * [K]) } line[cull=false](-1,0)(1,0)
 put { translate([0,2.5,0]) }
   sweep[cull=true]  { n_segs, rotate(10, (O), [K]) then translate(pitch * degrees_per_seg / 360 * [K]) } line[cull=false](-1,0)(1,0)
 }
}

def x050 {

 def pierced_tetrahedron {
   def p1 (0,0,1) def p2 (1,0,0)
   def p3 (0,1,0) def p4 (-.3,-.5,-.8)
   % faces of the tetrahedron.
   polygon(p1)(p2)(p3)                      % original
   polygon(p1)(p4)(p2)                      % bottom
   polygon(p1)(p3)(p4)                      % left
   polygon[fillcolor=lightgray](p3)(p2)(p4) % rear
   line[linecolor=red](-1,-1,-1)(2,2,2)
 }

 {pierced_tetrahedron}  % tetrahedron in original position

 put { rotate(90, (0,0,0), [1,0,0]) % copy in new position
       then translate([2.5,0,0]) } {pierced_tetrahedron}
}

def x060 {

 def pierced_tetrahedron {
   def p1 (0,0,1) def p2 (1,0,0)
   def p3 (0,1,0) def p4 (-.3,-.5,-.8)
   % faces of the tetrahedron.
   polygon(p1)(p2)(p3)                      % original
   polygon(p1)(p4)(p2)                      % bottom
   polygon(p1)(p3)(p4)                      % left
   polygon[fillcolor=lightgray](p3)(p2)(p4) % rear
   line[linecolor=red](-1,-1,-1)(2,2,2)
 }

 repeat { 7, rotate(15, (0,0,0), [1,0,0]) % copy in new position
             then translate([1.8,0,0]) } {pierced_tetrahedron}
}

def x070 {
 def n_segs 8
 sweep { n_segs, rotate(180 / n_segs, [0,0,1]) } (1,0,0)
}

def x080 {
 def n_segs 8
 sweep { n_segs<>, rotate(180 / n_segs, [0,0,1]) } (1,0,0)
}

% toroid
def x090 {
 put { view((4,5,10)) } {
   def n_toroid_segs 20
   def n_circle_segs 16
   def r_minor 1
   def r_major 1.5
   sweep { n_toroid_segs, rotate(360 / n_toroid_segs, [0,1,0]) }
     sweep { n_circle_segs, rotate(360 / n_circle_segs, (r_major,0,0)) }
       (r_major + r_minor, 0)
   def al 1.5
   line[linecolor=red,arrows=->](0,0,0)(r_major + r_minor + al,0,0)
   line[linecolor=red,arrows=->](0,0,0)(0,r_minor + al,0)
   line[linecolor=red,arrows=->](0,0,0)(0,0,r_major + r_minor + al)
   special|\uput[r]#1{$x$}
           \uput[u]#2{$y$}
           \uput[dl]#3{$z$}|(r_major + r_minor + al,0,0)(0,r_minor + al,0)(0,0,r_major + r_minor + al)
 }
}

% triangle with normal
def x100 {
 def p1 (1,0,0)
 def p2 (0,0.5,0)
 def p3 (-0.5,-1,2)
 def O (0,0,0)
 def N unit( ((p3) - (p2)) * ((p1) - (p2)) )
 def n1 ((p1) - (O) + (p2) - (O) + (p3) - (O)) / 3 + (O)
 def n2 (n1)+[N]
 polygon(p1)(p2)(p3)
 line[arrows=*->](n1)(n2)
}

% views of cylinder
def x110 {
 def n_cyl_segs 20
 def n_views 5
 def I [1,0,0]
 repeat { n_views, rotate(180/n_views, [I]) then translate([I] * 2.1) }
   sweep[fillcolor=lightgray]{ n_cyl_segs<>, rotate(360/n_cyl_segs, [0,1,0]) }
     line[fillcolor=white](1,-1)(1,1)
}

% mobius strip
def x120 {
 put { view ((3,5,10)) } {

 def R 4
 def N 64
 def T .3
 sweep[cull=false] {
   N,
   rotate(180/N, (R,0,0)),
   rotate(360/N, [0,1,0])
 } line(R - 1,-T)(R + 1,-T)(R + 1,T)(R - 1,T)(R - 1,-T)

 }
}

def x130_200 {
 % useful common defs
 def O (0,0,0)

 % right side (outside to right)
 def ht 2 % height of peak of house
 def R1 (1,1,1) def R2 (1,-1,1) def R3 (1,-1,-1) def R4 (1,1,-1)
 def R5 (1,ht,0)

 % left side (outside to right--backward)
 def W  [2,0,0]
 def L1 (R1)-[W] def L2 (R2)-[W] def L3 (R3)-[W] def L4 (R4)-[W]
 def L5 (R5)-[W]

 % door
 def e .01
 def D1 (0,-1,1+e) def D2 (.5,-1,1+e) def D3 (.5,0,1+e) def D4 (0,0,1+e)

 def hp <ex130> scale(1)
        <ex140> scale(1)
        <> rotate(-40, [0,1,0]) then translate([0,0,-12]) % house positioner
 def pR1 [[hp]]*(R1) def pR2 [[hp]]*(R2) def pR3 [[hp]]*(R3)
 def pR4 [[hp]]*(R4) def pR5 [[hp]]*(R5)
 def pL1 [[hp]]*(L1) def pL2 [[hp]]*(L2) def pL3 [[hp]]*(L3)
 def pL4 [[hp]]*(L4) def pL5 [[hp]]*(L5)
 def pD1 [[hp]]*(D1) def pD2 [[hp]]*(D2) def pD3 [[hp]]*(D3)
 def pD4 [[hp]]*(D4)

 % house
 def rgt polygon (pR1)(pR2)(pR3)(pR4)(pR5)
 def lft polygon (pL5)(pL4)(pL3)(pL2)(pL1)
 def frt polygon (pR2)(pR1)(pL1)(pL2)
 def bck polygon (pR4)(pR3)(pL3)(pL4)
 def tfr polygon (pR1)(pR5)(pL5)(pL1)
 def tbk polygon (pR5)(pR4)(pL4)(pL5)
 def bot polygon (pR2)(pL2)(pL3)(pR3)
 def door polygon[fillcolor=brown] (pD1)(pD2)(pD3)(pD4)
 def house { {rgt}{lft}{frt}{bck}{tfr}{tbk}{bot}{door} }

 % perspective system
 def axes {
   def sz 1
   line [arrows=<->] (sz,0,0)(O)(0,sz,0)
   line [arrows=->]  (O)(0,0,sz)
   line [linewidth=.2pt,linecolor=blue,linestyle=dashed] (O)(0,0,-12)
   special |\uput[r]#1{$x$}\uput[u]#2{$y$}\uput[l]#3{$z$}|
     (sz,0,0)(0,sz,0)(0,0,sz)
 }
 def p 5 % projection distance (plane at z=-p)
 def projection_plane {
   def sz 1.5
   polygon (-sz,-sz,-p)(sz,-sz,-p)(sz,sz,-p)(-sz,sz,-p)
   special |\rput[b]#1-2#3{\footnotesize\sf projection plane}|
     [lay=over](-sz,-sz,-p)(sz,-sz,-p)(0,-sz+.1,-p)
 }
 def projection_rays {
   def ray [linewidth=.3pt,linecolor=lightgray]
   % right
   line [ray](O)(pR1) line [ray](O)(pR2) line[ray](O)(pR3)
   line [ray](O)(pR4) line [ray](O)(pR5)
   % left
   line [ray](O)(pL1) line [ray](O)(pL2) line[ray](O)(pL5)
   %door
   line [ray](O)(pD1) line [ray](O)(pD2)
   line [ray](O)(pD3) line [ray](O)(pD4)
 }
 def projection {
   put { project(p) then translate([0,0,e])   } {house}
   put { project(p) then translate([0,0,2*e]) } {door}
 }
 def eye (5,2,2.5)
 def look_at (0,0,-5)
 def all
   <ex130>
     {house}
   <ex140>
       put { scale(.3) } repeat { 13, rotate(30, [1,2,3]), translate([3,0,0]) } {house}
   <ex150>
     put { view((eye), (look_at)) } {
       {house}
       {axes}
     }
   <ex160>
     put { view((eye), (look_at)) } {
       {house}
       {axes}
       {projection_plane}
     }
   <ex170>
     put { view((eye), (look_at)) } {
       {house}
       {axes}
       {projection_plane}
       {projection_rays}
     }
   <ex180>
     put { view((eye), (look_at)) } {
       {house}
       {axes}
       {projection_plane}
       {projection_rays}
       {projection}
     }
   <ex190>
     put { view((eye), (look_at)) then perspective(9)} {
       {house}
       {axes}
       {projection_plane}
       {projection_rays}
       {projection}
     }
   <> {house}
 {all}
}

def x210 { input {hand.sk} }
def x220 { def fist <> input {hand.sk} }
def x230 { def ok <> input {hand.sk} }
def x240 { def spread <> input {hand.sk} }
def x250 { input {truncatedcone.sk} }
def x260 { def labeled <> input {truncatedcone.sk} }

def tomake
 input{tags.sk}
 <> special|No case was selected!|

{tomake}

global {
 set [linewidth=.3pt]
}

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