# Manuel Díaz Regueiro

My 3d art is currently formed by a set of several hundred figures,
most of them “wire sculptures” with axial symmetry given abstract and
beautiful objects. Finding rules governing objects and beauty is one
of my goals. Finding distinguished and / or spectacular copies, one of
my hobbies.

In this occasion the theme is about the spherical curves that are
represented in three examples:

-Infinite on the sphere lemniscate: a curve related to the Viviani
curve that is completed by extending the lines between two points
giving place to the infinite symbol or the spherical version of the
lemniscate curve.

-Triskel in the spherical Lissajous world: This other spherical wire
sculpture is formed by an own variant of the 3d Lissajous curve.

-The third one is, again, a combination of cosine and sine functions
completed with a 3d program to result a Rose.

All of them, in this kind of 3d curves, have in common that we can see a 2d rhodonea in the z axis direction. In this case, too. Related to both the Viviani and the rhodonea curves, this one is completed extending the lines between two points giving place to the infinite symbol or the spherical version of the lemniscate curve.

Triskel in the spherical Lissajous world: This spherical wire
sculpture is formed by my own variant of the 3d Lissajous curve, a
Lissajous pattern on a spherical surface. It`s possible to create
spherical artistic designs with Lissajous 3d curves that are 2d
curves but generated using spherical coordinates.

Azimuthal and polar angles undergo oscillations while the radius
is kept constant.

Well, this is one of the multiple 3d curves possible in the
sphere, but very many others, even no spherical curves, are
related.

You can see some of these spherical and not spherical Lissajous
curves in shapeways.com searching for regueiro.

There are many 2d curves with flower form like many cases of
rhodonea, of equation

r=a*cos(k*theta)

An example is r=a*cos(5/6*theta)

But there are no examples of the same curve in 3d. Until this
curve with simple equation with cosines and sines. Which are the
equations?

A problem to resolve. In fact, the equation allows us to construct
many other similar 3d curves.

If you visit shapeways.com site and search for regueiro you will
see many other variants of rhodonea 3d curves, which have as a
characteristic that we can always see 2d rhodoneas in the z axis
direction.