# formula list, multiline format.
# line 1 is presentation formula.
# line 2 is gnuplot formula.
# line 3 is presentation phrase, language-dependent.
# the rest is gnuplot parameters.
# line 4 is boundaries: u,v,xyz
# line 5 is sample rate: sample1,sample2

: x^2+y^2+z^2+t^2=1
  sqrt(1-t^2)*cos(u)*cos(v),sqrt(1-t^2)*sin(u)*cos(v),sqrt(1-t^2)*sin(v)
  sphere S<sup>3</sup>
  0,2*pi,-pi/2,pi/2,1
  25,15

: x^2+y^2+z^2-t^2=0
  t*cos(u)*cos(v),t*sin(u)*cos(v),t*sin(v)
  spherical cone with principal axis on the axis of t
  0,2*pi,-pi/2,pi/2,0.8
  25,15

: x^2+y^2-z^2+t^2=0
  sqrt(v^2-t^2)*cos(u),sqrt(v^2-t^2)*sin(u),v
  spherical cone with principal axis on the axis of z
  0,2*pi,-1,1,1
  20,30

: x^2-y^2+z^2+t^2=0
  sqrt(v^2-t^2)*cos(u),v,sqrt(v^2-t^2)*sin(u)
  spherical cone with principal axis on the axis of y
  0,2*pi,-1,1,1
  20,30

: x^2+y^2-zt=0
  sqrt(v*t)*cos(u),sqrt(v*t)*sin(u),v
  spherical cone whose principal axis is the line x=y=z+t=0
  0,2*pi,-1,1,1.2
  20,20
  
: x^2+z^2-yt=0
  sqrt(v*t)*cos(u),-v,sqrt(v*t)*sin(u)
  spherical cone whose principal axis is the line x=z=y+t=0
  0,2*pi,-1,1,1.2
  20,20
  
: x^2+y^2+z^2-t^2=1
  sqrt(1+t^2)*cos(u)*cos(v),sqrt(1+t^2)*sin(u)*cos(v),sqrt(1+t^2)*sin(v)
  spherical hyperboloid whose principal axis is the axis of t
  0,2*pi,-pi/2,pi/2,1.8
  25,15
  
: x^2+y^2-z^2+t^2=1
  sqrt(1+v^2-t^2)*cos(u),sqrt(1+v^2-t^2)*sin(u),v
  spherical hyperboloid whose principal axis is the axis of z
  0,2*pi,-1,1,1.5
  20,20

: x^2-y^2+z^2+t^2=1
  sqrt(1+v^2-t^2)*cos(u),v,sqrt(1+v^2-t^2)*sin(u)
  spherical hyperboloid whose principal axis is the axis of y
  0,2*pi,-1,1,1.5
  20,20

: x^2+y^2-zt=1
  sqrt(1+v*t)*cos(u),sqrt(1+v*t)*sin(u),v
  spherical hyperboloid whose principal axis is the line x=y=z+t=0
  0,2*pi,-2,2,2
  20,20
  
: x^2+z^2-yt=1
  sqrt(1+v*t)*cos(u),-v,sqrt(1+v*t)*sin(u)
  spherical hyperboloid whose principal axis is the line x=z=y+t=0
  0,2*pi,-2,2,2
  20,20
  
: x^2+y^2-z^2-t^2=0
  sqrt(v^2+t^2)*cos(u),sqrt(v^2+t^2)*sin(u),v
  vertical hyperboloidal cone
  0,2*pi,-1,1,1.6
  20,15
  
: x^2-y^2+z^2-t^2=0
  sqrt(v^2+t^2)*cos(u),v,sqrt(v^2+t^2)*sin(u)
  horizontal hyperboloidal cone
  0,2*pi,-1,1,1.6
  20,15
  
: x^2-y^2-zt=0
  sqrt(abs(t))*u,sqrt(abs(t))*v,u^2-v^2
  hyperboloidal cone
  -1,1,-1,1,1
  20,20

: x^2-z^2-yt=0
  sqrt(abs(t))*u,u^2-v^2,sqrt(abs(t))*v
  hyperboloidal cone
  -1,1,-1,1,1
  20,20

: x^2+y^2-z^2-t^2=1
  sqrt(0.6+v^2+t^2)*cos(u),sqrt(0.6+v^2+t^2)*sin(u),v
  hyperboloidal hyperboloid
  0,2*pi,-1.5,1.5,2
  20,16

: x^2-y^2+z^2-t^2=1
  sqrt(0.6+v^2+t^2)*cos(u),v,sqrt(0.6+v^2+t^2)*sin(u)
  hyperboloidal hyperboloid
  0,2*pi,-1.5,1.5,2
  20,16

: x^2+y^2-z^2-t^2=-1
  sqrt(-1+v^2+t^2)*cos(u),sqrt(-1+v^2+t^2)*sin(u),v
  hyperboloidal hyperboloid
  0,2*pi,-1.5,1.5,1.5
  20,25

: x^2-y^2+z^2-t^2=-1
  sqrt(-1+v^2+t^2)*cos(u),v,sqrt(-1+v^2+t^2)*sin(u)
  hyperboloidal hyperboloid
  0,2*pi,-1.5,1.5,1.5
  20,25

: x^2-y^2-zt=1
  u,v,(u^2-v^2-1)/t/5
  hyperboloidal hyperboloid
  -2,2,-2,2,2.5
  25,25

: x^2-z^2-yt=1
  u,(u^2-v^2-1)/t/5,v
  hyperboloidal hyperboloid
  -2,2,-2,2,2.5
  25,25

: x^2+y^2+z^2-t=0
  sqrt(t)*cos(u)*cos(v),sqrt(t)*sin(u)*cos(v),sqrt(t)*sin(v)
  spherical paraboloid oriented towards the axis of t
  0,2*pi,-pi/2,pi/2,1.3
  20,20

: x^2+y^2-z+t^2=0
  sqrt(v-t^2)*cos(u),sqrt(v-t^2)*sin(u),v
  spherical paraboloid oriented towards the axis of z
  0,2*pi,-1,1,1
  25,25

: x^2-y+z^2+t^2=0
  sqrt(v-t^2)*cos(u),-v,sqrt(v-t^2)*sin(u)
  spherical paraboloid oriented towards the axis of y
  0,2*pi,-1,1,1
  20,30

: x^2+y^2-z^2-t=0
  sqrt(v^2+t)*cos(u),sqrt(v^2+t)*sin(u),v
  hyperboloidal paraboloid oriented towards the axis of t, vertical
  0,2*pi,-1,1,1
  20,25

: x^2-y^2+z^2-t=0
  sqrt(v^2+t)*cos(u),-v,sqrt(v^2+t)*sin(u)
  hyperboloidal paraboloid oriented towards the axis of t, horizontal
  0,2*pi,-1,1,1
  20,25

: x^2+y^2-z-t^2=0
  sqrt(t^2+v)*cos(u),sqrt(t^2+v)*sin(u),v
  hyperboloidal paraboloid oriented towards the axis of z
  0,2*pi,-2,2,2
  20,25

: x^2-y^2-z+t^2=0
  u,v,u^2-v^2+t^2
  hyperboloidal paraboloid oriented towards the axis of z
  -1.5,1.5,-1.5,1.5,2
  20,20

: x^2-y+z^2-t^2=0
  sqrt(t^2+v)*cos(u),-v,sqrt(t^2+v)*sin(u)
  hyperboloidal paraboloid oriented towards the axis of y
  0,2*pi,-2,2,2
  20,25

: x^2-y-z^2+t^2=0
  u,u^2-v^2+t^2,v
  hyperboloidal paraboloid oriented towards the axis of y
  -1.5,1.5,-1.5,1.5,2
  20,20

: x^2+y^2+t^2=1
  sqrt(1-t^2)*cos(u),sqrt(1-t^2)*sin(u),v
  vertical spherical cylinder
  0,2*pi,-1.2,1.2,1
  20,18

: x^2+z^2+t^2=1
  sqrt(1-t^2)*cos(u),-v,sqrt(1-t^2)*sin(u)
  horizontal spherical cylinder
  0,2*pi,-1.2,1.2,1
  20,18

: x^2+y^2-t^2=0
  cos(u)*t,sin(u)*t,v
  conic cylinder with a singular line on the axis of z
  0,2*pi,-1.5,1.5,1.4
  20,20

: x^2+z^2-t^2=0
  cos(u)*t,-v,sin(u)*t
  conic cylinder with a singular line on the axis of y
  0,2*pi,-1.5,1.5,1.4
  20,20

: x^2+y^2-t^2=1
  cos(u)*sqrt(1+t^2),sin(u)*sqrt(1+t^2),v
  hyperboloidal cylinder with one sheet, vertical
  0,2*pi,-1.8,1.8,1.8
  20,20

: x^2+z^2-t^2=1
  cos(u)*sqrt(0.7+t^2),-v,sin(u)*sqrt(0.7+t^2)
  hyperboloidal cylinder with one sheet, horizontal
  0,2*pi,-2,2,2
  20,20

: x^2+y^2-t^2=-1
  cos(u)*sqrt(t^2-0.7),sin(u)*sqrt(t^2-0.7),v
  hyperboloidal cylinder with two sheets, vertical
  0,2*pi,-1,1,1
  20,20

: x^2+z^2-t^2=-1
  cos(u)*sqrt(t^2-0.6),-v,sin(u)*sqrt(t^2-0.6)
  hyperboloidal cylinder with two sheets, horizontal
  0,2*pi,-1,1,1.1
  20,20


