3-D Zoetrope at SIGGRAPH 2000
A Mathematica animation in physical
3D was one of the works on display in the Art Gallery at last month's SIGGRAPH 2000 (the
27th International Conference on Computer Graphics and Interactive
Techniques). Simply titled 3-D Zoetrope, the subject of the animation
was the homotopy, or metamorphosis, of a ring torus (a
donut-shaped object) into a Costa
A zoetrope, according to Webster's Dictionary, is "an optical toy, in
which figures made to revolve on the inside of a cylinder, and viewed
through slits in its circumference, appear like a single figure passing
through a series of natural motions as if animated or mechanically moved."
In 3-D Zoetrope, 60 phases of the torus-Costa surface
transformation are attached to the edge of a wheel. The rotation of the
wheel is then "frozen" using a stroboscopic light optically synchronized
to the "spokes" of the wheel, where the objects project from its edge.
computer-rendered proposal for the zoetrope had previously won first
prize at the 1999 First International Digital Sculpture Competition. Stewart
Dickson, the artist, is a pioneer in using computer-aided, rapid mechanical
prototyping technologies to visualize mathematical objects in
three physical dimensions.
Dickson, a technical director at Walt Disney Feature Animation and a
long-time Mathematica user, found Mathematica to be uniquely
this project since the Costa surface depends upon the WeierstrassP
function, which is not available in most computer math packages. In
Mathematica, it is a built-in function that renders the code
compact. Dickson added, "The fact that Mathematica makes the
the page both dynamic and concrete (in regard to 3D CAD/CAM
compatibility), I find extremely powerful."
A detailed description of the construction of the zoetrope, including
several QuickTime animations, is included in the original proposal. For
more information on Mr. Dickson and his work, visit the MathArt web site.
click for animation