Artistic variation on a geometrical inversion of a shell (Jeener surface 1) [Variation artistique sur une inversion géométrique d'un coquillage (surface de Jeener 1)].




The parametric equations of the Jeener surface 1 are:


                               ku
                    F (u,v) = e  (1+cos(v))cos(u)
                     x

ku F (u,v) = e (1+cos(v))sin(u) y
ku F (u,v) = e (2+sin(v)) z

                         log(2)
                    k = --------
                          2.pi

u E [-2.pi,+2.pi]
pi v E [- ----,+pi] 2

The attributes of each sphere are chosen as follows:


                    RADIUS = constant

dF (u,v) dF (u,v) x x RED = 1 - K (----------Du + ----------Dv) R du dv
dF (u,v) dF (u,v) y y GREEN = 1 - K (----------Du + ----------Dv) V du dv
dF (u,v) dF (u,v) z z BLUE = 1 - K (----------Du + ----------Dv) B du dv

                          8.pi
                    Du = ------
                           200

3.pi Dv = ------ 200

The atomization process (displaying a continuous object with a finite number of colored spheres) reveals the intricate inner details of the surface without the ambiguities of transparencies, when the apparent variation of the size of spheres (due to the projection) gives a good depth cue.


See the original shell.


(CMAP28 WWW site: this page was created on 04/27/2006 and last updated on 01/26/2019 11:53:19 -CET-)



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