PlanckianLoci: Planckian Loci - stored as Lookup Tables

In spacesXYZ: CIE XYZ and some of Its Derived Color Spaces

Planckian Loci - stored as Lookup Tables

Description

RobertsonLocus	the table from Robertson, with 31 points from 0 to 600 mired
PrecisionLocus	a precomputed table, with 65 points from 0 to 1000 mired

Format

Both objects are data.frames with these columns

mired	the reciprocal temperature 10^6/T
u	the u chromaticity, in 1960 CIE
v	the v chromaticity, in 1960 CIE

The PrecisionLocus data.frame has these additional columns:

up	the 1st derivative of u with respect to mired
vp	the 1st derivative of v with respect to mired
upp	the 2nd derivative of u with respect to mired
vpp	the 2nd derivative of v with respect to mired

Details

For RobertsonLocus, the values are taken from Wyszecki & Stiles. The lookup table on page 228 contains an error at 325 mired, which was corrected by Bruce Lindbloom (see Source).

For PrecisionLocus, the chromaticity values u and v are computed from first principles, from the famous equation for the Planckian radiator (with c_2 = 1.4388 \times 10^{-2}) and from the tabulated CIE 1931 standard observer color matching functions, by summing from 360 to 830nm. Let \beta denote the reciprocal temperature 10^6/T. We think of u as a function u(\beta). The column up is u'(\beta), and upp is u''(\beta). And similarly for v. The derivatives are computed from first principles, by summing the derivatives of the Planckian formula from 360 to 830nm. This includes the limiting case \beta=0.

When this package is loaded (during .onLoad()), cubic splines are computed from RobertsonLocus, using stats::splinefun() with method="fmm"). And quintic splines are computed from PrecisionLocus. Both splines are C^2 continuous.

Source

http://www.brucelindbloom.com/index.html?Eqn_XYZ_to_T.html

References

Robertson, A. R. Computation of correlated color temperature and distribution temperature. Journal of the Optical Society of America. 58. pp. 1528-1535. 1968.

Wyszecki, Günther and W. S. Stiles. Color Science: Concepts and Methods, Quantitative Data and Formulae, Second Edition. John Wiley & Sons, 1982. Table 1(3.11). pp. 227-228.

See Also

CCTfromuv(), planckLocus()

Examples

RobertsonLocus[ 1:10, ]
##    mired       u       v
## 1      0 0.18006 0.26352
## 2     10 0.18066 0.26589
## 3     20 0.18133 0.26846
## 4     30 0.18208 0.27119
## 5     40 0.18293 0.27407
## 6     50 0.18388 0.27709
## 7     60 0.18494 0.28021
## 8     70 0.18611 0.28342
## 9     80 0.18740 0.28668
## 10    90 0.18880 0.28997

PrecisionLocus[ 1:10, ]
##    mired         u         v           up           vp          upp          vpp
## 1      0 0.1800644 0.2635212 5.540710e-05 0.0002276279 7.115677e-07 1.977793e-06
## 2     10 0.1806553 0.2658948 6.291429e-05 0.0002469232 7.900243e-07 1.873208e-06
## 3     20 0.1813253 0.2684554 7.120586e-05 0.0002649377 8.679532e-07 1.722425e-06
## 4     30 0.1820820 0.2711879 8.026143e-05 0.0002812384 9.423039e-07 1.531723e-06
## 5     40 0.1829329 0.2740733 9.002982e-05 0.0002954676 1.010028e-06 1.309700e-06
## 6     50 0.1838847 0.2770894 1.004307e-04 0.0003073613 1.068393e-06 1.066350e-06
## 7     60 0.1849432 0.2802122 1.113592e-04 0.0003167582 1.115240e-06 8.120582e-07
## 8     70 0.1861132 0.2834161 1.226923e-04 0.0003235990 1.149155e-06 5.566812e-07
## 9     80 0.1873980 0.2866757 1.342971e-04 0.0003279171 1.169532e-06 3.088345e-07
## 10    90 0.1887996 0.2899664 1.460383e-04 0.0003298241 1.176525e-06 7.543963e-08

spacesXYZ documentation built on June 8, 2025, 12:56 p.m.