genlist {zonohedra}

zonohedra generators useful for testing and plotting

Description

classics.genlist	13 classic zonohedra generators
colorimetry.genlist	4 sets of Color Matching Functions (each set is a 3xN matrix)

Format

Each is an S3 class genlist object organized as a list of 3xN matrices (N varies). The list must have names, preferably short names or abbreviations. Each matrix can have optional attributes "shortname" and "fullname" which are useful when printing with print.genlist().

Note

Making these S3 class genlist makes it possible to easily print a short summary using print.genlist().

For colorimetry.genlist[[2]] a few remarks are in order. These generators come from the xyz CIE color matching functions of 1931, from 360 to 830 nm with 1 nm step. From 699 to 830 nm, the angles between the generators only differ by a few microradians, and it apparent that the designers tapered all 3 functions identically in that nm range. For an illustration of this in the chromaticity domain, see Burns, Figure 10. When the zonohedron is constructed from these 132 generators, with the default options, all these generators a 'collapsed' into a single one. In the original matroid these 132 points form a multiple group, and in the simplified matroid they are collapsed to a single point, labeled with 699.

Source

David Eppstein. Zonohedra and Zonotopes.
https://www.ics.uci.edu/~eppstein/junkyard/ukraine/ukraine.html

Colour & Vision Research Laboratory. University College London. http://www.cvrl.org

References

ASTM E 308 - 01. Standard Practice for Computing the Colors of Objects by Using the CIE System. Table 1

Scott A Burns. The location of optimal object colors with more than two transitions. Color Research & Application. Vol. 46. No. 6. pp 1180-1193. 2021.

Günther Wyszecki and W.S. Stiles. Color Science : Concepts and Methods, Quantitative Data and Formulae. Second Edition. Wiley-Interscience. 1982. Table I(3.3.1). pp. 723-735.

See Also

print.genlist()

Examples

# get the names of 3 sets of color matching functions
names(colorimetry.genlist)
# [1] "xyz1931.5nm" "xyz1931.1nm" "lms2000.1nm"


# print zonohedra metrics associated with 3 sets of color matching functions
colorimetry.genlist
#                            fullname generators vertices  edges facets      area     volume pointed
# xyz1931.5nm  xyz at 5nm step                81     5100  10146   5048  1582.722   4070.345    TRUE
# xyz1931.1nm  xyz at 1nm step               471   112910 225720 112812 39586.707 509434.149    TRUE
# lms2000.1nm  lms at 1nm step               441   146642 292860 146220 22736.652 181369.085    TRUE
# ciexyzjv.5nm xyz at 5nm step (1978)         90     8012  16020   8010  1553.535   3951.899    TRUE