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Amy G. Dalin
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module smariot.com/oklab
go 1.22.1

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// Based on: https://bottosson.github.io/posts/oklab/
//
// OkLab first defines a transform from xyz, and multiplies by this matrix:
// [+0.8189330101, +0.3618667424, -0.1288597137]
// [+0.0329845436, +0.9293118715, +0.0361456387]
// [+0.0482003018, +0.2643662691, +0.633851707 ]
//
// Wikipedia lists this matrix for converting from linear sRGB to D65 CIE XYZ, so
// I'm considering it canonical:
// [+0.4124, +0.3576, +0.1805]
// [+0.2126, +0.7152, +0.0722]
// [+0.0193, +0.1192, +0.9505]
//
// Combined, we get:
// [+0.41217385032507, +0.5362974607032, +0.05146302925248]
// [+0.21187214048845, +0.6807476834212, +0.10740645682645]
// [+0.08831541121808, +0.2818663070584, +0.63026344660742]
//
// And its inverse:
// [+4.0767584135565013494237930518854, -3.3072279873944731418619352916485, +0.230721459944885632473018834049 ]
// [-1.2681810851624033989047813181437, +2.6092932102856398573991970933594, -0.3411121165477535569679616041822]
// [-0.0040984077180314400491332639337372, -0.70350366010241732765095902557887, +1.7068604529788013559365593912662]
//
// After a non-linear transformation (cube root), OkLab applies a second matrix:
// [+0.2104542553, +0.793617785, -0.0040720468]
// [+1.9779984951, -2.428592205, +0.4505937099]
// [+0.0259040371, +0.7827717662, -0.808675766 ]
//
// And its inverse:
// [+0.99999999845051981426207542502031, +0.39633779217376785682345989261573, +0.21580375806075880342314146183004 ]
// [+1.0000000088817607767160752456705, -0.10556134232365634941095687705472, -0.063854174771705903405254198817796]
// [+1.0000000546724109177012928651534, -0.089484182094965759689052745863391, -1.2914855378640917399489287529148 ]
//
// It should be noted that the numbers in the first column were supposed to be 1, and other implementations skip
// multiplying by that column altogether. I however am insane, and shall continue barging forward.
package oklab
import (
"image/color"
"math"
)
type Color struct {
Lightness, ChromaA, ChromaB, A float64
}
func linearize(c uint32) float64 {
l := float64(c) / 0xffff
if l <= 0.039285714285714285714285714285714 {
return l / 12.923210180787861094641554898407
}
return math.Pow((l+0.055)/1.055, 2.4)
}
func delinearize(l float64) uint32 {
switch {
case l <= 0:
return 0
case l <= 0.0030399346397784299969770436366690:
return uint32(l*846922.57919793247683733430026710 + 0.5)
case l >= 1:
return 0xffff
default:
return uint32(69139.425*math.Pow(l, 1/2.4) - 3603.925)
}
}
// FromNRGBA create an OkLab color from non-pre-multiplied RGBA.
func FromNRGBA(r, g, b, a uint32) Color {
rLin, gLin, bLin := linearize(r), linearize(g), linearize(b)
l := math.Cbrt(0.41217385032507*rLin + 0.5362974607032*gLin + 0.05146302925248*bLin)
m := math.Cbrt(0.21187214048845*rLin + 0.6807476834212*gLin + 0.10740645682645*bLin)
s := math.Cbrt(0.08831541121808*rLin + 0.2818663070584*gLin + 0.63026344660742*bLin)
return Color{
0.2104542553*l + 0.793617785*m - 0.0040720468*s,
1.9779984951*l - 2.428592205*m + 0.4505937099*s,
0.0259040371*l + 0.7827717662*m - 0.808675766*s,
float64(a) / float64(0xffff),
}
}
// FromRGBA create an OkLab color from pre-multiplied RGBA.
func FromRGBA(r, g, b, a uint32) Color {
switch a {
case 0xffff:
// do nothing.
case 0:
// completely transparent, color information was lost.
// pretend it was gray.
r, g, b = 0x7fff, 0x7fff, 0x7fff
default:
// un-premultiply rgb.
//
// Note that I'm rounding up here, which is the opposite of what the NRGBA/NRGBA64 colors do,
// which may be a bug as RGBA64->NRGBA64->RGBA64 is lossy.
r = (r*0xffff + a - 1) / a
g = (g*0xffff + a - 1) / a
b = (b*0xffff + a - 1) / a
}
return FromNRGBA(r, g, b, a)
}
func cube(v float64) float64 {
return v * v * v
}
// NRGBA converts to non-premultiplied RGBA.
func (c Color) NRGBA() (r, g, b, a uint32) {
l := cube(0.99999999845051981426207542502031*c.Lightness + 0.39633779217376785682345989261573*c.ChromaA + 0.21580375806075880342314146183004*c.ChromaB)
m := cube(1.0000000088817607767160752456705*c.Lightness - 0.10556134232365634941095687705472*c.ChromaA - 0.063854174771705903405254198817796*c.ChromaB)
s := cube(1.0000000546724109177012928651534*c.Lightness - 0.089484182094965759689052745863391*c.ChromaA - 1.2914855378640917399489287529148*c.ChromaB)
r = delinearize(4.0767584135565013494237930518854*l - 3.3072279873944731418619352916485*m + 0.230721459944885632473018834049*s)
g = delinearize(-1.2681810851624033989047813181437*l + 2.6092932102856398573991970933594*m - 0.3411121165477535569679616041822*s)
b = delinearize(-0.0040984077180314400491332639337372*l - 0.70350366010241732765095902557887*m + 1.7068604529788013559365593912662*s)
a = uint32(c.A*0xffff + 0.5)
return
}
// RGBA converts to premultiplied RGBA.
func (c Color) RGBA() (r, g, b, a uint32) {
r, g, b, a = c.NRGBA()
r = r * a / 0xffff
g = g * a / 0xffff
b = b * a / 0xffff
return
}
func sqr(a float64) float64 {
return a * a
}
func Distance(a, b Color) float64 {
dL := a.Lightness*a.A - b.Lightness*b.A
da := a.ChromaA*a.A - b.ChromaA*b.A
db := a.ChromaB*a.A - b.ChromaB*b.A
dA := a.A - b.A
return math.Sqrt(max(sqr(dL), sqr(dL+dA)) + max(sqr(da), sqr(da+dA)) + max(sqr(db), sqr(db+dA)))
//return math.Sqrt((sqr(dL)+sqr(da)+sqr(db))*(a.A*b.A) + sqr(dA))
}
func okLabModel(c color.Color) color.Color {
switch c := c.(type) {
case Color:
return c
// Special handling for color.NRGBA and color.NRGBA64
case color.NRGBA:
return FromNRGBA(uint32(c.R)*0x101, uint32(c.G)*0x101, uint32(c.B)*0x101, uint32(c.A)*0x101)
case color.NRGBA64:
return FromNRGBA(uint32(c.R), uint32(c.G), uint32(c.B), uint32(c.A))
// This isn't a standard interface, but I'm going to check for it regardless.
case interface{ NRGBA() (r, g, b, a uint32) }:
return FromNRGBA(c.NRGBA())
default:
return FromRGBA(c.RGBA())
}
}
// Implements a color model for converting arbitrary colors to OKLab.
var Model = color.ModelFunc(okLabModel)

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package oklab
import (
"image/color"
"math"
"reflect"
"testing"
)
func TestColor_NRGBA(t *testing.T) {
// Not checking the whole space because that would be slow, and alpha is given less resolution in this test.
// The increments were chosen because they're factors of 0xffff, so we'll end on the maximum value.
for a := uint32(0); a < 0x10000; a += 4369 {
for b := uint32(0); b < 0x10000; b += 1285 {
for g := uint32(0); g < 0x10000; g += 1285 {
for r := uint32(0); r < 0x10000; r += 1285 {
_r, _g, _b, _a := FromNRGBA(r, g, b, a).NRGBA()
if r != _r || g != _g || b != _b || a != _a {
t.Errorf("NRGBA(0x%04x,0x%04x,0x%04x,0x%04x) -> OkLab -> NRGBA(0x%04x,0x%04x,0x%04x,0x%04x)", r, g, b, a, _r, _g, _b, _a)
return
}
}
}
}
}
}
func TestColor_RGBA(t *testing.T) {
// This is similar to the NRGBA test, except the components step by a/17 instead of a fixed 1285.
// a/17 was chosen because 17 is a factor of 4369, so the components will end equalling a.
for a := uint32(0); a < 0x10000; a += 4369 {
step := max(1, a/17)
for b := uint32(0); b <= a; b += step {
for g := uint32(0); g <= a; g += step {
for r := uint32(0); r <= a; r += step {
_r, _g, _b, _a := FromRGBA(r, g, b, a).RGBA()
if r != _r || g != _g || b != _b || a != _a {
t.Errorf("RGBA(0x%04x,0x%04x,0x%04x,0x%04x) -> OkLab -> RGBA(0x%04x,0x%04x,0x%04x,0x%04x)", r, g, b, a, _r, _g, _b, _a)
return
}
}
}
}
}
}
func Test_delinearize(t *testing.T) {
for c := uint32(0); c < 0x10000; c++ {
got := delinearize(linearize(c))
if got != c {
t.Errorf("delinearize(linearize(0x%04x)) != 0x%04x", c, got)
return
}
}
}
// The NRGBA and NRGBA64 models don't have sensible ways to recover transparent colors from types it
// doesn't know about, so I'm going to help them out.
func fixedNRGBAModel(c color.Color) color.Color {
if c, ok := c.(interface{ NRGBA() (r, g, b, a uint32) }); ok {
r, g, b, a := c.NRGBA()
return color.NRGBA{R: uint8(r >> 8), G: uint8(g >> 8), B: uint8(b >> 8), A: uint8(a >> 8)}
}
return color.NRGBAModel.Convert(c)
}
func fixedNRGBA64Model(c color.Color) color.Color {
if c, ok := c.(interface{ NRGBA() (r, g, b, a uint32) }); ok {
r, g, b, a := c.NRGBA()
return color.NRGBA64{R: uint16(r), G: uint16(g), B: uint16(b), A: uint16(a)}
}
return color.NRGBA64Model.Convert(c)
}
func Test_Model(t *testing.T) {
// test to make sure we can reproduce some test colors.
// In particular, I want to make sure the colors can be recovered from transparent NRGBA and NRGBA64.
for _, tt := range [...]struct {
name string
color color.Color
model color.Model
}{
{
"OkLab: nop",
Color{math.Inf(1), math.Inf(-1), math.MaxFloat64, 0},
Model,
}, {
"NRGBA: opaque Sapphire",
color.NRGBA{R: 0x0f, G: 0x52, B: 0xba, A: 0xff},
color.ModelFunc(fixedNRGBAModel),
}, {
"NRGBA: translucent Orchid",
color.NRGBA{R: 0xda, G: 0x70, B: 0xd6, A: 0x7f},
color.ModelFunc(fixedNRGBAModel),
}, {
"NRGBA: invisible Floral White",
color.NRGBA{R: 0xff, G: 0xfa, B: 0xf0, A: 0x00},
color.ModelFunc(fixedNRGBAModel),
}, {
"NRGBA64: opaque Amethyst",
color.NRGBA64{R: 0x9999, G: 0x6666, B: 0xcccc, A: 0xffff},
color.ModelFunc(fixedNRGBA64Model),
}, {
"NRGBA64: translucent Smoke",
color.NRGBA64{R: 0xf5f5, G: 0xf5f5, B: 0xf5f5, A: 0x7fff},
color.ModelFunc(fixedNRGBA64Model),
}, {
"NRGBA64: invisible Emerald",
color.NRGBA64{R: 0x5050, G: 0xC8C8, B: 0x7878, A: 0x0000},
color.ModelFunc(fixedNRGBA64Model),
}, {
"RGBA64: opaque Chartreuse",
color.RGBA64{R: 0xb2b2, G: 0xd6d6, B: 0x3f3f, A: 0xffff},
color.RGBA64Model,
}, {
"RGBA64: transparent Mauveine",
color.RGBA64{R: 0x577c, G: 0x013e, B: 0x602b, A: 0x9e37},
color.RGBA64Model,
}, {
"RGBA64: invisible nothing",
color.RGBA64{R: 0x0, G: 0x0, B: 0x0, A: 0x0},
color.RGBA64Model,
}, {
"RGBA: opaque Chartreuse",
color.RGBA{R: 0xb2, G: 0xd6, B: 0x3f, A: 0xff},
color.RGBAModel,
}, {
"RGBA: transparent Mauveine",
color.RGBA{R: 0x57, G: 0x01, B: 0x60, A: 0x9e},
color.RGBAModel,
}, {
"RGBA: invisible nothing",
color.RGBA{R: 0x0, G: 0x0, B: 0x0, A: 0x0},
color.RGBAModel,
},
} {
t.Run(tt.name, func(t *testing.T) {
c := Model.Convert(tt.color).(Color)
if got := tt.model.Convert(c); !reflect.DeepEqual(got, tt.color) {
t.Errorf("%#+v -> %#+v -> %#+v, want %#+v", tt.color, c, got, tt.color)
return
}
})
}
}
func TestDistance(t *testing.T) {
colours := []Color{
FromNRGBA(0xffff, 0xffff, 0xffff, 0xffff),
FromNRGBA(0xffff, 0xffff, 0xffff, 0x7fff),
FromNRGBA(0xffff, 0xffff, 0xffff, 0x0000),
FromNRGBA(0x0000, 0x0000, 0x0000, 0xffff),
FromNRGBA(0x0000, 0x0000, 0x0000, 0x7fff),
FromNRGBA(0x0000, 0x0000, 0x0000, 0x0000),
}
for i, c0 := range colours {
for j, c1 := range colours {
d := Distance(c0, c1)
if i == j || (c0.A == 0 && c1.A == 0) {
// if they're the same color, or both are completely transparent,
// they should be perceived as identical.
if d != 0 {
t.Errorf("Distance(%v, %v) = %v, want 0", c0, c1, d)
}
} else {
// otherwise, there should be some kind of difference between them.
if d <= 0 {
t.Errorf("Distance(%v, %v) = %v, want > 0", c0, c1, d)
}
}
mid := Color{
Lightness: (c0.Lightness + c1.Lightness) * 0.5,
ChromaA: (c0.ChromaA + c1.ChromaA) * 0.5,
ChromaB: (c0.ChromaB + c1.ChromaB) * 0.5,
A: (c0.A + c1.A) * 0.5,
}
// traveling from c0 to c1 via mid can't possibly be
// shorter than traveling from c0 to c1 directly.
d2 := Distance(c0, mid) + Distance(mid, c1)
if d2 < d {
t.Errorf("Distance(%v, %v)+Distance(%v, %v) < Distance(%v, %v), want %f >= %f", c0, mid, mid, c1, c0, c1, d2, d)
}
}
}
}