plotOptimals: Plot Optimal Colors

In colorSpec: Color Calculations with Emphasis on Spectral Data

Plot Optimal Colors

Description

Consider a colorSpec object x with type equal to 'responsivity.material' and 3 responsivity spectra. The function plotOptimals3D() makes a plot of the object-color solid for x. This solid is a zonohedron in 3D. The 3D drawing package rgl is required.
Consider a colorSpec object x with type equal to 'responsivity.material' and 2 responsivity spectra. The function plotOptimals2D() makes a plot of the object-color solid for x. This solid is a zonogon in 2D. The 3D drawing package rgl is not required.
The set of all possible material reflectance functions (or transmittance functions) is convex, closed, and bounded (in any reasonable function space), and this implies that the set of all possible output responses from x is also convex, closed, and bounded. The latter set is called the object-color solid, or Rösch Farbkörper, for x. A color on the boundary of the object-color solid is called an optimal color. For more discussion see sectionOptimalColors().

Usage

## S3 method for class 'colorSpec'
plotOptimals3D( x, size=50, type='w', both=TRUE )

## S3 method for class 'colorSpec'
plotOptimals2D( x )

Arguments

x	a colorSpec object with type equal to 'responsivity.material' and 2 or 3 spectra, as appropriate.
size	an integer giving the number of wavelengths at which to resample x. To skip resampling, set size=NA.
type	type='w' for a wireframe plot of the parallelogram faces. type='p' for a point plot with points at the centers of the parallelograms.
both	the color solid is symmetric about its center, so only half of it must be computed. If both=TRUE it plots one half in black and the other half in red. If both=FALSE it only plots one half in black.

Value

The functions return TRUE or FALSE.

Details for 3D

If n is the number of wavelengths, the number of parallelogram faces of the zonohedron is n*(n-1). The time to compute these faces increase with n even faster, so that is why the default size=50 is a fairly small number. It was chosen to be a reasonable compromise between detail and performance.
In addition to the wireframe or points, it draws the box with opposite vertices at the "poles" 0 and W and the diagonal segment of neutral grays that connects 0 and W.

Details for 2D

If n is the number of wavelengths, the number of edges in the zonogon is 2*n. Computing these edges is fast and visualization is easy, so there are no plotting options at this time.

Note

If all responsivity functions of x are non-negative, the object-color solid of x is inside the box. If the responsivity functions of x have negative lobes, the object-color solid of x extends outside the box. Indeed, the box may actually be inside the optimals.

References

Centore, Paul. A Zonohedral Approach to Optimal Colours. Color Research & Application. Vol. 38. No. 2. pp. 110-119. April 2013.

Logvinenko, A. D. An object-color space. Journal of Vision. 9(11):5, 1-23, (2009).
https://jov.arvojournals.org/article.aspx?articleid=2203976. doi:10.1167/9.11.5.

West, G. and M. H. Brill. Conditions under which Schrödinger object colors are optimal. Journal of the Optical Society of America. 73. pp. 1223-1225. 1983.

See Also

type(), probeOptimalColors(), sectionOptimalColors(), vignette Plotting Chromaticity Loci of Optimal Colors

Examples

human = product( D50.5nm, 'slot', xyz1931.5nm, wave=seq(400,770,by=5) )
plotOptimals3D( human )

plotOptimals2D( subset(human,2:3) )     # y and z only

scanner = product( D50.5nm, 'slot', BT.709.RGB, wave=seq(400,770,by=5) )
plotOptimals3D( scanner )

colorSpec documentation built on May 29, 2024, 6 a.m.