# Volume by cross sections
# Calculus visualization models
# by Lloyd for James
# Intended to 3-D print
#
# Smooth example
#
define pi 3.14159265
# object dimensions
define tri_edge 1.0
define length 6.0
define maxsize 5.0
# Define an equilateral triangle shape with unit sides 
define tan60 60 * $pi / 180 %tan
define tri_height $tri_edge / 2. * $tan60
curve interpolated etri
  start -1.0 * $tri_edge / 2.0 0.0
  line 0.0 $tri_height
  line $tri_edge / 2.0 0.0
  line -1.0 * $tri_edge / 2.0 0.0
# 
object dome paratri
  curve1 etri
  c1_xscale $maxsize
  c1_yscale $maxsize
  length -1.0 * $length
  taper para
  nodes_axial 20
  nodes_circ 4
object dome endcap
  taper bulk
#
move
  flip
list variables
write vrml para-tri1.wrl
write stl para-tri1.stl
#
# discrete version
new
define nseg 10
define seglen $length / $nseg
define scale $nseg - 0.5 / $nseg %sqrt
object section section1
  curve1 etri
  curve2 etri
  c1_xscale $maxsize * $scale
  c1_yscale $maxsize * $scale
  c2_xscale $maxsize * $scale
  c2_yscale $maxsize * $scale
  length -1.0 * $seglen
  nodes_circ 4
  nodes_axial 2
object dome cap1
  taper bulk
  transz 0.0
object dome cap1
  taper bulk
  transz -1.0 * $seglen
define scale $nseg - 1.5 / $nseg %sqrt
object section section1
  curve1 etri
  curve2 etri
  c1_xscale $maxsize * $scale
  c1_yscale $maxsize * $scale
  c2_xscale $maxsize * $scale
  c2_yscale $maxsize * $scale
  length -1.0 * $seglen
  nodes_circ 4
  nodes_axial 2 
object dome cap1
  taper bulk
define scale $nseg - 2.5 / $nseg %sqrt
object section section1
  curve1 etri
  curve2 etri
  c1_xscale $maxsize * $scale
  c1_yscale $maxsize * $scale
  c2_xscale $maxsize * $scale
  c2_yscale $maxsize * $scale
  length -1.0 * $seglen
  nodes_circ 4
  nodes_axial 2 
object dome cap1
  taper bulk
define scale $nseg - 3.5 / $nseg %sqrt
object section section1
  curve1 etri
  curve2 etri
  c1_xscale $maxsize * $scale
  c1_yscale $maxsize * $scale
  c2_xscale $maxsize * $scale
  c2_yscale $maxsize * $scale
  length -1.0 * $seglen
  nodes_circ 4
  nodes_axial 2 '
object dome cap1
  taper bulk
define scale $nseg - 4.5 / $nseg %sqrt
object section section1
  curve1 etri
  curve2 etri
  c1_xscale $maxsize * $scale
  c1_yscale $maxsize * $scale
  c2_xscale $maxsize * $scale
  c2_yscale $maxsize * $scale
  length -1.0 * $seglen
  nodes_circ 4
  nodes_axial 2 
object dome cap1
  taper bulk
define scale $nseg - 5.5 / $nseg %sqrt
object section section1
  curve1 etri
  curve2 etri
  c1_xscale $maxsize * $scale
  c1_yscale $maxsize * $scale
  c2_xscale $maxsize * $scale
  c2_yscale $maxsize * $scale
  length -1.0 * $seglen
  nodes_circ 4
  nodes_axial 2 
object dome cap1
  taper bulk
define scale $nseg - 6.5 / $nseg %sqrt
object section section1
  curve1 etri
  curve2 etri
  c1_xscale $maxsize * $scale
  c1_yscale $maxsize * $scale
  c2_xscale $maxsize * $scale
  c2_yscale $maxsize * $scale
  length -1.0 * $seglen
  nodes_circ 4
  nodes_axial 2 
object dome cap1
  taper bulk
define scale $nseg - 7.5 / $nseg %sqrt
object section section1
  curve1 etri
  curve2 etri
  c1_xscale $maxsize * $scale
  c1_yscale $maxsize * $scale
  c2_xscale $maxsize * $scale
  c2_yscale $maxsize * $scale
  length -1.0 * $seglen
  nodes_circ 4
  nodes_axial 2 
object dome cap1
  taper bulk
define scale $nseg - 8.5 / $nseg %sqrt
object section section1
  curve1 etri
  curve2 etri
  c1_xscale $maxsize * $scale
  c1_yscale $maxsize * $scale
  c2_xscale $maxsize * $scale
  c2_yscale $maxsize * $scale
  length -1.0 * $seglen
  nodes_circ 4
  nodes_axial 2 
object dome cap1
  taper bulk
define scale $nseg - 9.5 / $nseg %sqrt
object section section1
  curve1 etri
  curve2 etri
  c1_xscale $maxsize * $scale
  c1_yscale $maxsize * $scale
  c2_xscale $maxsize * $scale
  c2_yscale $maxsize * $scale
  length -1.0 * $seglen
  nodes_circ 4
  nodes_axial 2 
object dome cap1
  taper bulk
move
  flip
write vrml para-tri2.wrl
write stl para-tri2.stl
end