Planckian Loci: 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

Arguments

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.

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.

Examples

Run this code

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