#############################
#
#  File:     /mnt/misc/LAPIET.INFO/HTML/mathphys/diffgeo/diffgeo2/geomview/sphere-w-geodesic-basis-plus-general-covd.cs
#  Created:  Sun May 10 10:42:22 -040027 2026
#  By:       CenterStage v3.2
#

::cs::File Version 3.2


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

::class::Group Create 3D_Surface {
  {Slider t -pi/2 pi/2 -resolution 0.05
Animate n 101 \{t -pi/2 pi/2\}}
  {always 1 none}
  {{ list 0.33333333 0.53333333 0.56470588} 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}
  {flat 1.0 1 1 0 0 0 0 0 0 0 0 1.0 1}
  {{} {}}
}

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

::class::Vectors Create 3D_Surface/Basis {
  {Vectors \{
 \{(cos(t),-(sin(t)/2),(sqrt(3)*sin(t))/2) ((sqrt(3)*cos(t)*sin(t))/sqrt(3*cos(t)^2+1),-((sqrt(3)*sin(t)^2)/(2*sqrt(3*cos(t)^2+1))),-(sqrt(3*cos(t)^2+1)/2))\}
 \{(cos(t),-(sin(t)/2),(sqrt(3)*sin(t))/2) (sin(t)/2,cos(t),0)\}
\}
}
  {always 1 none}
  {{ list 0 0.50196078 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}
  {smooth 1.0 3 1 0 0 0 0 0 0 0 0 1.0 3}
  {{} {}}
}

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

::class::Vectors Create 3D_Surface/Covd {
  {Vectors \{
 \{(cos(t),-(sin(t)/2),(sqrt(3)*sin(t))/2) ((sqrt(3)*cos(t)^2-sqrt(3))/(3*cos(t)^2+1)^(3/2),-((sqrt(3*cos(t)^2+1)*(9*cos(t)^2+3)*sin(t)+8*sqrt(3)*cos(t)*sin(t))/(sqrt(3*cos(t)^2+1)*(12*cos(t)^2+4))),-((sqrt(3)*sin(t))/4))\}
\}
}
  {always 1 none}
  {{ list 0 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}
  {flat 1.0 3 1 0 0 0 0 0 0 0 0 1.0 3}
  {{} {}}
}

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

::class::Curve Create 3D_Surface/Curve {
  {Domain \{-pi/2 pi/2 101\}

Function \{t\} \{
  let (x,y,z) = (cos(t),-(sin(t)/2),(sqrt(3)*sin(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}
  {flat 1.0 3 1 0 0 0 0 0 0 0 0 1.0 3}
  {{} {}}
  {::cd::Solid}
}

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

::class::Vectors Create 3D_Surface/General {
  {Vectors \{
 \{(cos(t),-(sin(t)/2),(sqrt(3)*sin(t))/2) ((sqrt(3*cos(t)^2+1)*sin(t)+2*sqrt(3)*cos(t)*sin(t))/(2*sqrt(3*cos(t)^2+1)),(2*cos(t)*sqrt(3*cos(t)^2+1)-sqrt(3)*sin(t)^2)/(2*sqrt(3*cos(t)^2+1)),-(sqrt(3*cos(t)^2+1)/2))\}
\}
}
  {always 1 none}
  {{ list 0.65098039 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}
  {flat 1.0 3 1 0 0 0 0 0 0 0 0 1.0 3}
  {{} {}}
}

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

::class::Surface Create 3D_Surface/Surface {
  {Domain \{\{0 pi 50\} \{0 2*pi 100\}\}

Function \{u v\} \{
  let (x,y,z) = (sin(u)*cos(v), sin(u)*sin(v), cos(u))
\}
}
  {always 1 none}
  {{ list 0.69019608 0.69411765 0.70196078} 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}
  {csmooth 1.0 1 1 1 0 0 0 0 0 0 0 other 1}
  {{} {}}
  {::sd::Patch 0 1 0.5}
}