Astronomical Applications Department, U.S. Naval Observatory Curves 3 D Page 1
Space Curves
Marc A. Murison
Astronomical Applications Department
U.S. Naval Observatory
murison@aa.usno.navy.mil
http://aa.usno.navy.mil/murison./
restart
(
)
with
curves
ParametrizedToImplicit arclength astroid binormal cardioid cassinian catenary circle cissoid
,
,
,
,
,
,
,
,
,
[
clotharg clothoid curvature cycloid deltoid ellipse evolute folium helix hyperbola inversion involute
,
,
,
,
,
,
,
,
,
,
,
,
lemniscate lissajous logspiral parabola pedal radial tangent torsion torusknot tractrix twicubic
,
,
,
,
,
,
,
,
,
,
,
unitnormal ]
Space Curves
Torus Knot
:=
TorusKnot
(
)
, , , , ,
a b c p q t
[
]
,
,
(
)
+
a b
(
)
cos
q t
(
)
cos
p t (
)
+
a b
(
)
cos
q t
(
)
sin
p t c
(
)
sin
q t
Plot (The Luge from Hell)
tubecurveplot
(
)
TorusKnot
, , , , ,
10 3 5 2 5
t 1.2
=
t
..
0
2
=
..
.5
2.0
=
axes box
,
,
,
,
,
(
=
grid [
]
,
100 12
=
orientation [
]
,
110 60
=
title Luge from Hell
,
,
)
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