CIE(2012) 10-deg XYZ “physiologically-relevant” color matching functions Matrix

CIE(2012) 2-deg XYZ “physiologically-relevant” color matching functions Matrix

CIE White Points in CIE [X,Y,Z] coordinates

CAM16 Surround Parameters [Surround F c Nc]

CAM16 [h,e,H] for Unique Hue [Red Yellow Green Blue Red]

CIE 2016 Chromatic Adaptation Transformation

CIE 2016 Chromatic Adaptation Inverse Transformation

Spectral intensity of R, G, B primaries of a linearized ROGPG279Q LCD display

Stiles & Burch (1959) 10-deg r̄(λ), ḡ(λ), b̄(λ) color matching functions

Stiles & Burch (1955) 2-deg r̄(λ), ḡ(λ), b̄(λ) color matching functions

Stiles & Burch (1955, 1959) color matching primaries, wavelength(nm) for 𝑹, 𝑮, 𝑩.

10-deg cone fundamentals based on the Stiles & Burch 10-deg CMFs, Stockman & Sharpe (2000). Each row are the wavelength(nm), L, M, S Cone spectral sensitivity(Linear Energy).

2-deg cone fundamentals based on the Stiles & Burch 10-deg CMFs (adjusted to 2-deg), Stockman & Sharpe (2000). Each row are the wavelength(nm), L, M, S Cone spectral sensitivity(Linear Energy).

10-deg CIE(2008) "physiologically-relevant" luminous efficiency function V(λ), consistent with the Stockman & Sharpe(2000) 10-deg cone fundamentals. Each row are the wavelength(nm), photopic luminous efficiency(Linear Energy).

2-deg CIE(2008) "physiologically-relevant" luminous efficiency function V(λ), consistent with the Stockman & Sharpe(2000) 2-deg cone fundamentals. Each row are the wavelength(nm), photopic luminous efficiency(Linear Energy).

Convert CIE Color Appearance Model 2016 to CIE XYZ

CAM16 Uniform Color Space in polar[J′, M′, h] or cartesian[J′, a′, b′] Luo, M.R., Cui, G., and Li, C. (2006). Uniform colour spaces based on CIECAM02 colour appearance model. Color Research & Application 31, 320–330.

Solve System of Linear Equations to get converting matrices between X and Y

Converting Matrices between LMS and Cone Contrast(Weber) color spaces. (DH Brainard, Cone contrast and opponent modulation color spaces, human color vision, 1996)

Converting Matrices between LMS and DKL[L+M, L-M, S-(L+M)] color spaces.

Converting Matrices between RGB and LMS color spaces, based on spectral measurement and cone fundamentals

Converting Matrices between RGB and CIE XYZ color spaces, based on spectral measurement and CIE xyz matching functions

Convert CIE XYZ to CIE Color Appearance Model 2016 Li, C., Li, Z., Wang, Z., Xu, Y., Luo, M.R., Cui, G., Melgosa, M., Brill, M.H., and Pointer, M. (2017). Comprehensive color solutions: CAM16, CAT16, and CAM16‐UCS.

return: J is the lightness C is the chroma h is the hue angle Q is the brightness M is the colourfulness s is the saturation

Convert CIE XYZ to CIE xyY.

CAM16 Viewing Conditions

W: White in test illuminant [Xw, Yw, Zw] Yb: Background in test conditions La: Luminance of test adapting field (cd/m2) Surround: Surround condition {Average, Dim, Dark}, Nc and F are functions of c, and their values can be linearly interpolated. Sr = Lsw / Ldw, where Lsw is the luminance of reference white in surround and Ldw in the display area. Sr == 0: Dark 0 < Sr < 0.2: Dim Sr >= 0.2: Average

new color matching functions by transform existing ones

Michelson Contrast, where $michelson(Lmax, Lmin) = weber(Lmax, Lmean), Lmean = (Lmax+Lmin)/2$

Weber Contrast, where $weber(L, Lb) = michelson(L, 2Lb-L)$

Converting Matrices between differential LMS relative to background and DKL[L+M, L-M, S-(L+M)] color spaces. (DH Brainard, Cone contrast and opponent modulation color spaces, human color vision, 1996)

De-Augmenting Homogeneous Transformation Matrix to Linear Transformation Matrix

De-Augmenting Homogeneous Coordinates(each column) to Cartesian Coordinates

De-Augmenting Homogeneous Coordinate to Cartesian Coordinate

Desaturate perceptible but not displayable CIE colors(each column) into the gamut of a display

Convert Absolute Coordinates[X,Y,Z] to Relative Coordinates[x,y,z] where $x=X/X+Y+Z, y=Y/X+Y+Z, z=Z/X+Y+Z$

Augmenting Linear Transformation Matrix to Homogeneous Transformation Matrix

Augmenting Cartesian Coordinates(each column) to Homogeneous Coordinates

Augmenting Cartesian Coordinate to Homogeneous Coordinate

Intersection point of a line and a plane. points of a line are defined as a direction(Dₗ) through a point(Pₗ): P = Pₗ + λDₗ , where λ is a scaler. points of a plane are defined as a plane through a point(Pₚ) and with normal vector(Nₚ) : Nₚᵀ(P - Pₚ) = 0 , where Nᵀ is the transpose of N.

return the point of intersection and if it's on direction.

Intersection point of a line and the six faces of the unit cube with origin as a vertex and three axies as edges[0:1,0:1,0:1]. points of the line are defined as a direction(Dₗ) through a point(Pₗ).

return the intersection point on direction.

Points of a line segment defined by two points P₀ and P₁.

• d: points density of unit line length

Tristimulus values, based on spectral measurement and matching functions

Cone activations of colors, based on spectral measurement and cone fundamentals

CIE “physiologically-relevant” XYZ of colors, based on following formula:

$XYZ = 683∫S(λ)x̄ȳz̄(λ)dλ$

where S(λ) is the power spectrum, x̄ȳz̄(λ) are the matching functions and Y will be the luminance(cd/m²).

Tristimulus matching values of single wavelength unit spectral

Convert CIE xyY to CIE XYZ.