#############################
#
#  File:     /../tmp/Downloads/tmp/DiffGeom/MonkeySaddle/monkey_Saddle-parabola-darboux-frame.cs
#  Created:  Sun Oct 19 08:31:28 -040027 2025
#  By:       CenterStage v3.2
#

::cs::File Version 3.2


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

::class::Group Create 3D_Surface {
  {Slider t -0.94 0.94 -resolution 0.05
Animate n 1001 \{t -0.94 0.94\}

Transform Scale(1,1,1)
}
  {always 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 \{-0.98 0.98 101\}

Function \{u\} \{
  let (x,y,z) = (u,u^2,u^3-3*u^5)
\}}
  {always 1 none}
  {{ 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::Vectors Create 3D_Surface/CurveN {
  {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}
  {flat 1.0 3 1 0 0 0 0 0 0 0 0 1.0 3}
  {{} {}}
}

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

::class::Vectors Create 3D_Surface/CurveT {
  {Vectors \{
 \{(t,t^2,t^3-3*t^5) (1/sqrt(225*t^8-90*t^6+9*t^4+4*t^2+1),(2*t)/sqrt(225*t^8-90*t^6+9*t^4+4*t^2+1),-((15*t^4-3*t^2)/sqrt(225*t^8-90*t^6+9*t^4+4*t^2+1)))\}
\}
}
  {always 1 none}
  {{ list 0.75294118 0 0} 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}
  {constant 1.0 3 1 0 0 0 0 0 0 0 0 1.0 3}
  {{} {}}
}

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

::class::Vectors Create 3D_Surface/CurveU {
  {Vectors \{
 \{(t,t^2,t^3-3*t^5) (-((90*t^7-18*t^5+2*t)/(sqrt(9*t^8+18*t^6+9*t^4+1)*sqrt(225*t^8-90*t^6+9*t^4+4*t^2+1))),(45*t^8-54*t^6+9*t^4+1)/(sqrt(9*t^8+18*t^6+9*t^4+1)*sqrt(225*t^8-90*t^6+9*t^4+4*t^2+1)),(6*t^5-12*t^3)/(sqrt(9*t^8+18*t^6+9*t^4+1)*sqrt(225*t^8-90*t^6+9*t^4+4*t^2+1)))\}
\}
}
  {always 1 none}
  {{ list 0 0 1} 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}
  {constant 1.0 3 1 0 0 0 0 0 0 0 0 1.0 3}
  {{} {}}
}

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

::class::Surface Create 3D_Surface/Surface {
  {Domain \{\{0 1.4 100\} \{0 2*pi 100\}\}

Function \{r th\} \{
  let u=r*cos(th)
  let v=r*sin(th)
  let (x,y,z) = (u, v, u^3-3*u*v^2)
\}}
  {always 1 none}
  {{set z} 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 1 1 0 0 0 0 0 0 0 0 1.0 1}
  {{} {}}
  {::sd::Patch 0 0 .25}
}