Curves and surfaces — Gnuplot
Denis Potapov
March 3, 2015
Contents
1 Ellipse
2
2 Hyperbola
3
3 Ellipsoid
4
4 Hyperboloid of one sheet
5
5 Hyperboloid of two sheets
6
6 Elliptic paraboloid
7
7 Hyperbolic paraboloid
8
8 Elliptic cone
9
9 Torus
10
1
1
Ellipse
Canonical implicit form:
x2 y 2
+ 2 =1
a2
b
Canonical parametric form:
(
x = a cos t
, t ∈ [−π, π]
y = b sin t
Gnuplot:
gnuplot>
gnuplot>
gnuplot>
gnuplot>
gnuplot>
gnuplot>
gnuplot>
set parametric
unset border
set xtics axis
set ytics axis
set xzeroaxis
set yzeroaxis
plot [-pi:pi] 2*cos(t), sin(t)
2
2
Hyperbola
Canonical implicit form:
x2 y 2
− 2 =1
a2
b
Canonical parametric form:
(
x = ±a cosh t
, t∈R
y = b sinh t
Gnuplot:
gnuplot>
gnuplot>
gnuplot>
gnuplot>
gnuplot>
gnuplot>
gnuplot>
set parametric
unset border
set xtics axis
set ytics axis
set xzeroaxis
set yzeroaxis
plot [-2:2] 2*cosh(t), sinh(t), -2*cosh(t), sinh(t)
3
3
Ellipsoid
Ellipsoid – Google Search
Canonical implicit form:
x2 y 2 z 2
+ 2 + 2 =1
a2
b
c
Canonical parametric form:


 x = a cos u cos v
h π πi
y = b sin u cos v u ∈ [−π, π], v ∈ − ,
.

2 2
 z = c sin v
Gnuplot:
gnuplot> set parametric
gnuplot> set isosamples 50
gnuplot> splot [-pi:pi][-pi/2:pi/2] cos(u)*cos(v), 2*sin(u)*cos(v), 3*sin(v)
4
4
Hyperboloid of one sheet
Hyperboloid of one sheet – Google Search
Canonical implicit form:
x2 y 2 z 2
+ 2 − 2 =1
a2
b
c
Canonical parametric form:


 x = a cos u cosh v
y = b sin u cosh v u ∈ [−π, π], v ∈ R.

 z = c sinh v
Gnuplot:
gnuplot> set parametric
gnuplot> set isosamples 50
gnuplot> splot [-pi:pi][-1.5:1.5] cos(u)*cosh(v), sin(u)*cosh(v), sinh(v)
5
5
Hyperboloid of two sheets
Hyperboloid of two sheets – Google Search
Canonical implicit form:
x2 y 2 z 2
+ 2 − 2 = −1
a2
b
c
Canonical parametric form:


 x = a cos u sinh v
y = b sin u sinh v u ∈ [−π, π], v ∈ R+ .

 z = ±c cosh v
Gnuplot:
gnuplot> set parametric
gnuplot> set isosamples 50
gnuplot> set view equal
gnuplot> splot [-pi:pi][-2.5:2.5] cos(u)*sinh(v), sin(u)*sinh(v), cosh(v); \
cos(u)*sinh(v), sin(u)*sinh(v), -cosh(v)
6
6
Elliptic paraboloid
Elliptic Paraboloid – Google Search
Canonical form:
y 2 x2
z
= 2 + 2
c
b
a
Gnuplot:
gnuplot> splot [-2:2][-2:2] y**2 + x**2
7
7
Hyperbolic paraboloid
Hyperbolic Paraboloid – Google Search
Canonical form:
y 2 x2
z
= 2 − 2
c
b
a
Gnuplot:
gnuplot> splot [-2:2][-2:2] y**2 - x**2
8
8
Elliptic cone
Elliptic Cone – Google Search
Canonical implicit form:
z2
y 2 x2
=
+ 2
c2
b2
a
Canonical parametric form:


 x = v cos u
y = v sin u u ∈ [−π, π], v ∈ R.

z =v
Gnuplot:
gnuplot> set parametric
gnuplot> set isosamples 50
gnuplot> splot [-pi:pi][-5:5] v*cos(u), v*sin(u), v
9
9
Torus
Torus – Google Search
Canonical parametric form:


 x = (R + r cos u) cos v
y = (R + r cos u) sin v u, v ∈ [−π, π].

 z = r sin u
Gnuplot:
gnuplot> set parametric
gnuplot> set isosamples 50
gnuplot> splot [-pi:pi][-pi:pi] (5 + cos(u))*cos(v), (5 + cos(u))*sin(v), sin(u)
10