#############################
#
#  File:     /../tmp/Downloads/tmp/DiffGeom/MonkeySaddle/monkey_Saddle_parabola_darboux_princ_curve-anim.cs
#  Created:  Sun Oct 19 08:16:56 -040027 2025
#  By:       CenterStage v3.2
#

::cs::File Version 3.2


####################

::class::Group Create 3D_Surface {
  {Slider t -0.95 0.95 -resolution 0.015
Animate n 101 \{t -0.95 0.95\}
Transform Scale(\{1,1,1\})
}
  {selected 1 none}
  {{set z} 0 0 {{{1 0 0} 50 Red} {{1 .5 0} 0     Orange} {{1 1 0} 50 Yellow} {{0 1 0} 50 Green} {{0 1 1} 50 Cyan} {{0 0 1} 50 Blue} {{1 0 1} 50 Purple} {{0 0 0} 0      Black} {{1 1 1} 0      White}} 1}
  {smooth 1.0 1 1 0 0 0 0 0 0 0 0 1.0 1}
  {{} {}}
}

####################

::class::Curve Create 3D_Surface/Curve {
  {Domain \{-1 1 101\}

Function \{t\} \{
  let (x,y,z) = (t,t^2,t^3-3*t^5)
\}}
  {always 1 all}
  {{ list 0 0 0} 0 1 {{{1 0 0} 50 Red} {{1 .5 0} 0     Orange} {{1 1 0} 50 Yellow} {{0 1 0} 50 Green} {{0 1 1} 50 Cyan} {{0 0 1} 50 Blue} {{1 0 1} 50 Purple} {{0 0 0} 0      Black} {{1 1 1} 0      White}} 1}
  {flat 1.0 3 1 0 0 0 0 0 0 0 0 1.0 3}
  {{} {}}
  {::cd::Solid}
}

####################

::class::Surface Create 3D_Surface/Plane {
  {Domain \{\{-0.125 0.125 200\} \{-0.125 0.125 200\}\}

Function \{u v\} \{
  let (x,y,z) = (u+t,v+t^2,-(6*t^3*v)+(3*t^2-3*t^4)*u-3*t^5+t^3)
\}
}
  {selected 1 none}
  {{ list 1 .5 0} 0 1 {{{1 0 0} 50 Red} {{1 .5 0} 0     Orange} {{1 1 0} 50 Yellow} {{0 1 0} 50 Green} {{0 1 1} 50 Cyan} {{0 0 1} 50 Blue} {{1 0 1} 50 Purple} {{0 0 0} 0      Black} {{1 1 1} 0      White}} 1}
  {smooth 1.0 2 1 0 0 0 0 0 0 0 0 1.0 2}
  {{} {}}
  {::sd::Grid 0 0 .25}
}

####################

::class::Vectors Create 3D_Surface/PrincCurve1 {
  {Vectors \{
\{(t,t^2,t^3-3*t^5) (
-((sqrt(648*t^16+1296*t^14+648*t^12+72*t^10+72*t^8+2*t^4)*(3*sqrt(t^4+t^2)*sqrt(729*t^14+243*t^12-405*t^10+117*t^8+72*t^6+36*t^4+4)-81*t^9-54*t^7+27*t^5))/((9*t^8+18*t^6+9*t^4+1)^(3/2)*sqrt(26244*t^24+34992*t^22-5832*t^20-9639*t^18+7776*t^16+sqrt(t^4+t^2)*sqrt(729*t^14+243*t^12-405*t^10+117*t^8+72*t^6+36*t^4+4)*(972*t^15+648*t^13-324*t^11+45*t^9+54*t^7+9*t^5+2*t)+3726*t^14+1008*t^12+333*t^10+252*t^8+36*t^6+4*t^4+4*t^2))),
(sqrt(648*t^16+1296*t^14+648*t^12+72*t^10+72*t^8+2*t^4)*(sqrt(t^4+t^2)*(27*t^8-27*t^4-3)*sqrt(729*t^14+243*t^12-405*t^10+117*t^8+72*t^6+36*t^4+4)-729*t^17-486*t^15+972*t^13+432*t^11-324*t^9-108*t^7-81*t^5-6*t^3-6*t))/(sqrt(9*t^8+18*t^6+9*t^4+1)*(162*t^15+486*t^13+486*t^11+171*t^9+36*t^7+27*t^5+t)*sqrt(26244*t^24+34992*t^22-5832*t^20-9639*t^18+7776*t^16+sqrt(t^4+t^2)*sqrt(729*t^14+243*t^12-405*t^10+117*t^8+72*t^6+36*t^4+4)*(972*t^15+648*t^13-324*t^11+45*t^9+54*t^7+9*t^5+2*t)+3726*t^14+1008*t^12+333*t^10+252*t^8+36*t^6+4*t^4+4*t^2)),
(sqrt(648*t^16+1296*t^14+648*t^12+72*t^10+72*t^8+2*t^4)*(sqrt(t^4+t^2)*(9*t^4+9*t^2)*sqrt(729*t^14+243*t^12-405*t^10+117*t^8+72*t^6+36*t^4+4)+81*t^13+567*t^11+891*t^9+405*t^7+36*t^5+36*t^3))/(sqrt(9*t^8+18*t^6+9*t^4+1)*(162*t^14+486*t^12+486*t^10+171*t^8+36*t^6+27*t^4+1)*sqrt(26244*t^24+34992*t^22-5832*t^20-9639*t^18+7776*t^16+sqrt(t^4+t^2)*sqrt(729*t^14+243*t^12-405*t^10+117*t^8+72*t^6+36*t^4+4)*(972*t^15+648*t^13-324*t^11+45*t^9+54*t^7+9*t^5+2*t)+3726*t^14+1008*t^12+333*t^10+252*t^8+36*t^6+4*t^4+4*t^2))
)\}
\}
}
  {always 1 none}
  {{ list 1 0 0} 0 1 {{{1 0 0} 50 Red} {{1 .5 0} 0     Orange} {{1 1 0} 50 Yellow} {{0 1 0} 50 Green} {{0 1 1} 50 Cyan} {{0 0 1} 50 Blue} {{1 0 1} 50 Purple} {{0 0 0} 0      Black} {{1 1 1} 0      White}} 1}
  {constant 1.0 3 1 0 0 0 0 0 0 0 0 1.0 3}
  {{} {}}
}

####################

::class::Vectors Create 3D_Surface/PrincCurve2 {
  {Vectors \{
\{(t,t^2,t^3-3*t^5) (
(sqrt(648*t^16+1296*t^14+648*t^12+72*t^10+72*t^8+2*t^4)*(3*sqrt(t^4+t^2)*sqrt(729*t^14+243*t^12-405*t^10+117*t^8+72*t^6+36*t^4+4)+81*t^9+54*t^7-27*t^5))/((9*t^8+18*t^6+9*t^4+1)^(3/2)*sqrt(26244*t^24+34992*t^22-5832*t^20-9639*t^18+7776*t^16+sqrt(t^4+t^2)*sqrt(729*t^14+243*t^12-405*t^10+117*t^8+72*t^6+36*t^4+4)*(-(972*t^15)-648*t^13+324*t^11-45*t^9-54*t^7-9*t^5-2*t)+3726*t^14+1008*t^12+333*t^10+252*t^8+36*t^6+4*t^4+4*t^2)),
-((sqrt(648*t^16+1296*t^14+648*t^12+72*t^10+72*t^8+2*t^4)*(sqrt(t^4+t^2)*(27*t^8-27*t^4-3)*sqrt(729*t^14+243*t^12-405*t^10+117*t^8+72*t^6+36*t^4+4)+729*t^17+486*t^15-972*t^13-432*t^11+324*t^9+108*t^7+81*t^5+6*t^3+6*t))/(sqrt(9*t^8+18*t^6+9*t^4+1)*(162*t^15+486*t^13+486*t^11+171*t^9+36*t^7+27*t^5+t)*sqrt(26244*t^24+34992*t^22-5832*t^20-9639*t^18+7776*t^16+sqrt(t^4+t^2)*sqrt(729*t^14+243*t^12-405*t^10+117*t^8+72*t^6+36*t^4+4)*(-(972*t^15)-648*t^13+324*t^11-45*t^9-54*t^7-9*t^5-2*t)+3726*t^14+1008*t^12+333*t^10+252*t^8+36*t^6+4*t^4+4*t^2))),
-((sqrt(648*t^16+1296*t^14+648*t^12+72*t^10+72*t^8+2*t^4)*(sqrt(t^4+t^2)*(9*t^4+9*t^2)*sqrt(729*t^14+243*t^12-405*t^10+117*t^8+72*t^6+36*t^4+4)-81*t^13-567*t^11-891*t^9-405*t^7-36*t^5-36*t^3))/(sqrt(9*t^8+18*t^6+9*t^4+1)*(162*t^14+486*t^12+486*t^10+171*t^8+36*t^6+27*t^4+1)*sqrt(26244*t^24+34992*t^22-5832*t^20-9639*t^18+7776*t^16+sqrt(t^4+t^2)*sqrt(729*t^14+243*t^12-405*t^10+117*t^8+72*t^6+36*t^4+4)*(-(972*t^15)-648*t^13+324*t^11-45*t^9-54*t^7-9*t^5-2*t)+3726*t^14+1008*t^12+333*t^10+252*t^8+36*t^6+4*t^4+4*t^2)))
)\}
\}
}
  {always 1 none}
  {{ list 0 0 1} 0 1 {{{1 0 0} 50 Red} {{1 .5 0} 0     Orange} {{1 1 0} 50 Yellow} {{0 1 0} 50 Green} {{0 1 1} 50 Cyan} {{0 0 1} 50 Blue} {{1 0 1} 50 Purple} {{0 0 0} 0      Black} {{1 1 1} 0      White}} 1}
  {constant 1.0 3 1 0 0 0 0 0 0 0 0 1.0 3}
  {{} {}}
}

####################

::class::Surface Create 3D_Surface/Surface {
  {Domain \{\{-1 1 100\} \{-1 1 100\}\}

Function \{u v\} \{
  let (x,y,z) = (u, v, u^3-3*u*v^2)
\}
}
  {always 1 none}
  {{set z} 1 1 {{{1 0 0} 50 Red} {{1 .5 0} 0     Orange} {{1 1 0} 50 Yellow} {{0 1 0} 50 Green} {{0 1 1} 50 Cyan} {{0 0 1} 50 Blue} {{1 0 1} 50 Purple} {{0 0 0} 0      Black} {{1 1 1} 0      White}} 0}
  {smooth 1.0 1 1 0 0 0 0 0 0 0 0 1.0 1}
  {{} {}}
  {::sd::Patch 0 0 .25}
}

####################

::class::Vectors Create 3D_Surface/SurfaceNormal {
  {Vectors \{
 \{(t,t^2,t^3-3*t^5) ((3*t^4-3*t^2)/sqrt(9*t^8+18*t^6+9*t^4+1),(6*t^3)/sqrt(9*t^8+18*t^6+9*t^4+1),1/sqrt(9*t^8+18*t^6+9*t^4+1))\}
\}
}
  {always 1 none}
  {{ list 1 1 0} 0 1 {{{1 0 0} 50 Red} {{1 .5 0} 0     Orange} {{1 1 0} 50 Yellow} {{0 1 0} 50 Green} {{0 1 1} 50 Cyan} {{0 0 1} 50 Blue} {{1 0 1} 50 Purple} {{0 0 0} 0      Black} {{1 1 1} 0      White}} 1}
  {constant 1.0 3 1 0 0 0 0 0 0 0 0 1.0 3}
  {{} {}}
}