CTTKmodel {colourvision} | R Documentation |

Chittka (1992) colour hexagon extended to animals with any number of photoreceptors types.

```
CTTKmodel(photo=ncol(C)-1, R, I, Rb, C,
interpolate=TRUE, nm=seq(300,700,1))
```

`photo` |
Number of photoreceptor types. Model accepts any number of photoreceptor types ( |

`R` |
Reflectance of observed objects. A data frame with first column corresponding to wavelength values and following columns with reflectance values. |

`I` |
Irradiance spectrum. A data frame with two columns only: first column corresponding to wavelength values and second column with irradiance values. Irradiance values must be in quantum flux units. |

`Rb` |
Background reflectance. A data frame with two columns only: first column corresponding to wavelength values and second column with reflectance values. |

`C` |
Photoreceptor sensitivity curves, from lowest to longest lambda-max. A data frame: first column corresponding to wavelength values and following columns with photoreceptor sensitivity values (see function |

`interpolate` |
Whether data files should be interpolated before further calculations. See |

`nm` |
A sequence of numeric values specifying where interpolation is to take place. See |

The original model is available for trichromatic animals only. Thery and Casas (2002) derived a version for tetrachromatic animals which is implemented here. In `colourvision`

, this model was extended to any number of photoreceptors types (Gawryszewski 2018; see also Pike 2012). The colour hexagon in Chittka (1992) has a vector of length = 1.0 The chromaticity coordinates in `colourvision`

preserve the same vector length.

Photoreceptor outputs (`E_i`

) are calculated by:

`E_i = \frac{q_i}{q_i+1}`

where `q_i`

is given by `Qr`

.

Then, for trichromatic vision, coordinates in the colour space are found by (Chittka 1992):

`X_1 = \frac{\sqrt{3}}{2}(E_3-E_1)`

`X_2 = E_2-\frac{1}{2}(E_1+E_3)`

For tetrachromatic vision (Thery and Casas 2002):

`X_1 = \frac{\sqrt{3}\sqrt{2}}{3}(E_3-E_4)`

`X_2 = E_1-\frac{1}{3}(E_2+E_3+E_4)`

`X_3 = \frac{2\sqrt{2}}{3}(\frac{1}{2}(E_3+E_4)-E_2)`

For a pentachromatic animal following the same vector length:

`X_1 = \frac{5}{2\sqrt{2}\sqrt{5}}(E_2-E_1)`

`X_2 = \frac{5\sqrt{2}}{2\sqrt{3}\sqrt{5}}(E_3-\frac{E_1+E_2}{2})`

`X_3 = \frac{5\sqrt{3}}{4\sqrt{5}}(E_4-\frac{E_1+E_2+E_3}{3})`

`X_4 = E_5-\frac{E1+E2+E3+E4}{4}`

`Qri` |
Photoreceptor photon catch values after the von Kries transformation (see function |

`Ei` |
Photoreceptor output values. Values can vary from 0 to 1. |

`Xi` |
Coordinates in the colour space. |

`deltaS` |
Euclidean distance to the origin of the colour space. It represents the conspicuousness of the stimulus ( |

Felipe M. Gawryszewski f.gawry@gmail.com

Chittka, L. 1992. The colour hexagon: a chromaticity diagram based on photoreceptor excitations as a generalized representation of colour opponency. J Comp Physiol A 170:533-543.

Gawryszewski, F.M. 2018. Colour vision models: Some simulations, a general n-dimensional model, and the colourvision R package. Ecology and Evolution, 10.1002/ece3.4288.

Pike, T.W. 2012. Generalised chromaticity diagrams for animals with n-chromatic colour vision. Journal of Insect Behavior 255: 277-286.

Thery, M., and J. Casas. 2002. Predator and prey views of spider camouflage. Nature 415:133-133.

`CTTKhexagon`

, `CTTKhexagon3D`

, `photor`

, `RNLmodel`

, `EMmodel`

, `deltaS`

```
##Photoreceptor sensitivity curves
##with lambda max at 350nm, 450nm and 550nm:
C<-photor(lambda.max=c(350,450,550))
## Grey background
## with 10 percent reflectance from 300 to 700nm:
Rb <- data.frame(300:700, rep(10, length(300:700)))
## Read CIE D65 standard illuminant
data("D65")
## Reflectance data
## with a sigmoid spectrum and midpoint at 500nm
R<-logistic(x=seq(300,700,1), x0=500, L=50, k=0.04)
## Run model
model<-CTTKmodel(photo=3, R=R, I=D65,
Rb=Rb, C=C)
#plot
plot(model)
```

[Package *colourvision* version 2.0.4 Index]