3DXM Space Curve Gallery

Classic Space Curves

helix tube frenet 024
lissajous2 5 13 knot 024
lissajous space curve
Two Cylinder 45557-s265x236
Intersection of Two Cylinders


torus knot 7 3
torus knot
genus2 knot 0colorchoice
genus 2 knot
cinquefoil rotate x 024
(2,5)-Cinquefoil knot to (5,2)
trefoil knot strip 006
Trefoil knot
figure8 harmonic
Figure 8 Knot
grannyknot tube rot 012
Granny Knot
square knot z axis.jpg 001
Square Knot
prime knots 5 4 3 036
Prime Knots

Curves on Sphere

loxodrome tube 001 s265x236
viviani 2tube 008-s274x229
Viviani Curve
spherical ellipse const 001 s265x236
Spherical Ellipse
spherical cycloid const 006-s264x237
Spherical Cycloid
spherical lemniscate co 001 s258x243
Spherical Lemniscate

Differential Geometry

constant curvature 8knot11
constant curvature curve
constant torsion sym3
constant torsion curve

    How to construct closed constant curvature space curves

About Space Curves


We gratefully acknowledge support for the development of the 3D-XplorMath program and this website by The National Science Foundation through a CCLI Grant (DUE Award # 0514781).