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Copy pathspaces.go
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755 lines (696 loc) · 17.9 KB
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// SPDX-FileCopyrightText: 2024 Dominik Honnef and contributors
//
// SPDX-License-Identifier: MIT
package color
import (
"fmt"
"math"
"slices"
"strings"
"sync"
)
func init() {
RegisterSpace(XYZ_D50)
RegisterSpace(XYZ_D65)
RegisterSpace(LinearDisplayP3)
RegisterSpace(DisplayP3)
RegisterSpace(LinearSRGB)
RegisterSpace(SRGB)
RegisterSpace(Oklab)
RegisterSpace(Oklch)
RegisterSpace(ProPhoto)
RegisterSpace(LinearProPhoto)
RegisterSpace(Lab)
RegisterSpace(LCh)
RegisterSpace(LinearRec2020)
RegisterSpace(Rec2020)
RegisterSpace(Rec2100PQ)
}
var (
spacesMu sync.RWMutex
spaces = map[string]*Space{}
infty = [2]float64{math.Inf(-1), math.Inf(1)}
norm = [2]float64{0, 1}
)
// LookupSpace looks up a registered (see [RegisterSpace]) color space by ID.
func LookupSpace(id string) (*Space, bool) {
id = strings.TrimPrefix(id, "--")
spacesMu.RLock()
defer spacesMu.RUnlock()
cs, ok := spaces[id]
return cs, ok
}
// RegisterSpace registers a color space. This allows it to be referenced
// by ID in 'color()' expressions as parsed by [Parse] and looked up by
// [LookupSpace].
//
// All color spaces provided by this package are automatically registered.
func RegisterSpace(cs *Space) {
spacesMu.Lock()
defer spacesMu.Unlock()
registerSpace(cs)
}
func registerSpace(cs *Space) {
if _, ok := spaces[cs.ID]; ok {
// Trying to register the same color space ID more than once might point
// to a mistake, but it might also be the result of us registering base
// spaces, so we can't panic here.
return
}
spaces[cs.ID] = cs
if cs.Base != nil {
if _, ok := spaces[cs.Base.ID]; !ok {
registerSpace(cs.Base)
}
}
}
// Space describes a color space, such as sRGB or HSV.
//
// Color spaces form a tree. Every space, except for [XYZ_D65], has a base space
// and can be converted to and from it. Every space can be converted to any
// other space by finding a common "connection space". Often, the common space
// is XYZ D65.
//
// Color spaces are bit-width-agnostic and values are often stored in a
// normalized form. For example, the R, G, and B coordinates in sRGB will be in
// the range [0, 1], not [0, 255].
//
// The white point of a color space is described by the White field. This field
// only serves as documentation and does not affect how conversions are carried
// out. That is, simply changing the white point of an existing color space will
// not have the intended effect.
//
// When creating new color spaces, you must call [Space.Init] once you're
// done.
type Space struct {
ID string
Name string
White Chromaticity
Base *Space
Coords [3]Coordinate
FromBase func(c [3]float64) [3]float64
ToBase func(c [3]float64) [3]float64
path []*Space
}
func (cs *Space) Init() *Space {
if cs.Coords == ([3]Coordinate{}) {
cs.Coords = cs.Base.Coords
}
if cs.White == (Chromaticity{}) && cs.Base != nil {
cs.White = cs.Base.White
}
for i := range cs.Coords {
coord := &cs.Coords[i]
if coord.RefRange == ([2]float64{}) {
coord.RefRange = coord.Range
}
}
// if cs.GamutSpace == nil {
// var isPolar bool
// for _, coord := range cs.Coords {
// if coord.IsAngle {
// isPolar = true
// break
// }
// }
// if isPolar {
// cs.GamutSpace = cs.Base
// } else {
// cs.GamutSpace = cs
// }
// }
orig := cs
var out []*Space
for cs != nil {
out = append(out, cs)
cs = cs.Base
}
slices.Reverse(out)
orig.path = out
return orig
}
func (cs *Space) InGamut(values [3]float64) bool {
const ϵ = 0.000075
// if cs.GamutSpace != cs {
// values = cs.Convert(cs.GamutSpace, values)
// return cs.GamutSpace.InGamut(values)
// }
for i, v := range values {
meta := cs.Coords[i]
if !meta.IsAngle {
min := meta.Range[0]
max := meta.Range[1]
if !(v >= min-ϵ && v <= max+ϵ) {
return false
}
}
}
return true
}
func (cs *Space) Convert(to *Space, coords [3]float64) [3]float64 {
ourPath := cs.path
theirPath := to.path
// Determine the connection space by finding the lowest common ancestor of
// the source and destination spaces in the color space tree.
connIdx := -1
for i := range min(len(ourPath), len(theirPath)) {
if ourPath[i] == theirPath[i] {
connIdx = i
} else {
break
}
}
if connIdx == -1 {
// Every space should be connectable through XYZ.
panic(fmt.Sprintf("internal error: couldn't find connection space for %s and %s",
cs.Name, to.Name))
}
// Convert from our space to the connection space
for i := len(ourPath) - 1; i > connIdx; i-- {
coords = ourPath[i].ToBase(coords)
}
// Convert from connection space to destination space
for i := connIdx + 1; i < len(theirPath); i++ {
coords = theirPath[i].FromBase(coords)
}
return coords
}
// NewXYZSpace returns a new CIE XYZ color space with the specified name, ID, and
// white point.
func NewXYZSpace(name, id string, white Chromaticity) *Space {
// OPT(dh): because all white point conversions go through D65, converting
// between two non-D65 white points uses two instead of one matrix. For
// example, we'd do D50->D65->D75, instead of the more direct D50->D75. This
// is slower, and introduces more floating point error.
//
// In practice, most color spaces use D65 or D50, anyway.
toD65 := Bradford.Matrix(white, XYZ_D65.White)
fromD65 := Bradford.Matrix(XYZ_D65.White, white)
return (&Space{
ID: id,
Name: name,
White: white,
Base: XYZ_D65,
FromBase: func(c [3]float64) [3]float64 {
return Adapt(c, &fromD65)
},
ToBase: func(c [3]float64) [3]float64 {
return Adapt(c, &toD65)
},
}).Init()
}
var XYZ_D50 = NewXYZSpace("XYZ D50", "xyz-d50", WhitesCSSD50)
var XYZ_D65 = (&Space{
ID: "xyz-d65",
Name: "XYZ D65",
Coords: [3]Coordinate{
{Name: "X", Range: infty, RefRange: norm},
{Name: "Y", Range: infty, RefRange: norm},
{Name: "Z", Range: infty, RefRange: norm},
},
White: WhitesSRGBD65,
}).Init()
var LinearDisplayP3 = newRGBSpace(
&rgbSpace{
ID: "display-p3-linear",
Name: "Linear Display P3",
Base: XYZ_D65,
ToBase: [3][3]float64{
{0.4865709486482162, 0.26566769316909306, 0.1982172852343625},
{0.2289745640697488, 0.6917385218365064, 0.079286914093745},
{0.0000000000000000, 0.04511338185890264, 1.043944368900976},
},
FromBase: [3][3]float64{
{2.493496911941425, -0.9313836179191239, -0.40271078445071684},
{-0.8294889695615747, 1.7626640603183463, 0.023624685841943577},
{0.03584583024378447, -0.07617238926804182, 0.9568845240076872},
},
},
)
var DisplayP3 = (&Space{
ID: "display-p3",
Name: "Display P3",
Base: LinearDisplayP3,
// Gamma encoding is the same as sRGB
ToBase: SRGB.ToBase,
FromBase: SRGB.FromBase,
}).Init()
var LinearSRGB = newRGBSpace(
&rgbSpace{
ID: "srgb-linear",
Name: "Linear sRGB",
Base: XYZ_D65,
// sRGB Matrices taken from
// https://github.com/w3c/csswg-drafts/pull/7320/commits/e835926c83e10342c0c43fd2f1ccbff1b35c3f07
ToBase: [3][3]float64{
{506752.0 / 1228815.0, 87881.0 / 245763.0, 12673.0 / 70218.0},
{87098.0 / 409605.0, 175762.0 / 245763.0, 12673.0 / 175545.0},
{7918.0 / 409605
8000
.0, 87881.0 / 737289.0, 1001167.0 / 1053270.0},
},
FromBase: [3][3]float64{
{12831.0 / 3959.0, -329.0 / 214.0, -1974.0 / 3959.0},
{-851781.0 / 878810.0, 1648619.0 / 878810.0, 36519.0 / 878810.0},
{705.0 / 12673.0, -2585.0 / 12673.0, 705.0 / 667.0},
},
},
)
type rgbSpace struct {
ID string
Name string
Base *Space
ToBase [3][3]float64
FromBase [3][3]float64
}
func newRGBSpace(space *rgbSpace) *Space {
return (&Space{
ID: space.ID,
Name: space.Name,
Coords: RGBCoordinates,
Base: space.Base,
ToBase: func(c [3]float64) [3]float64 {
return mulVecMat(c, &space.ToBase)
},
FromBase: func(c [3]float64) [3]float64 {
return mulVecMat(c, &space.FromBase)
},
}).Init()
}
// SRGB is the sRGB color space. Conversion to sRGB uses the piece-wise OETF.
// Conversion from sRGB uses the inverse of the piece-wise OETF. This is not the
// same as the EOTF that is commonly used by consumer displays, which uses gamma
// 2.2.
var SRGB = (&Space{
ID: "srgb",
Name: "sRGB",
Base: LinearSRGB,
FromBase: func(c [3]float64) [3]float64 {
f := func(ch float64) float64 {
var sign float64
if ch < 0 {
sign = -1.0
} else {
sign = 1.0
}
abs := math.Abs(ch)
if abs > 0.0031308 {
return sign * (1.055*(math.Pow(abs, 1.0/2.4)) - 0.055)
} else {
return 12.92 * ch
}
}
return [3]float64{f(c[0]), f(c[1]), f(c[2])}
},
ToBase: func(c [3]float64) [3]float64 {
f := func(ch float64) float64 {
var sign float64
if ch < 0 {
sign = -1
} else {
sign = 1
}
abs := ch * sign
if abs <= 0.04045 {
return ch / 12.92
} else {
return sign * math.Pow((abs+0.055)/1.055, 2.4)
}
}
return [3]float64{f(c[0]), f(c[1]), f(c[2])}
},
}).Init()
// Matrices have been recalculated for consistent reference white;
// see https://github.com/w3c/csswg-drafts/issues/6642#issuecomment-943521484
var (
oklabXyzToLms = [3][3]float64{
{0.8190224379967030, 0.3619062600528904, -0.1288737815209879},
{0.0329836539323885, 0.9292868615863434, 0.0361446663506424},
{0.0481771893596242, 0.2642395317527308, 0.6335478284694309},
}
oklabLmsToLab = [3][3]float64{
{0.2104542683093140, 0.7936177747023054, -0.0040720430116193},
{1.9779985324311684, -2.4285922420485799, 0.4505937096174110},
{0.0259040424655478, 0.7827717124575296, -0.8086757549230774},
}
oklabLabToLms = [3][3]float64{
{1.0000000000000000, 0.3963377773761749, 0.2158037573099136},
{1.0000000000000000, -0.1055613458156586, -0.0638541728258133},
{1.0000000000000000, -0.0894841775298119, -1.2914855480194092},
}
oklabLmsToXyz = [3][3]float64{
{1.2268798758459243, -0.5578149944602171, 0.2813910456659647},
{-0.0405757452148008, 1.1122868032803170, -0.0717110580655164},
{-0.0763729366746601, -0.4214933324022432, 1.5869240198367816},
}
)
var Oklab = (&Space{
ID: "oklab",
Name: "Oklab",
Coords: [3]Coordinate{
{Name: "Lightness", Range: infty, RefRange: norm},
{Name: "a", Range: infty, RefRange: [2]float64{-0.4, 0.4}},
{Name: "b", Range: infty, RefRange: [2]float64{-0.4, 0.4}},
},
Base: XYZ_D65,
FromBase: func(c [3]float64) [3]float64 {
lms := mulVecMat(c, &oklabXyzToLms)
lms_ := [3]float64{
math.Cbrt(lms[0]),
math.Cbrt(lms[1]),
math.Cbrt(lms[2]),
}
lab := mulVecMat(lms_, &oklabLmsToLab)
return lab
},
ToBase: func(c [3]float64) [3]float64 {
lms := mulVecMat(c, &oklabLabToLms)
lms_ := [3]float64{
lms[0] * lms[0] * lms[0],
lms[1] * lms[1] * lms[1],
lms[2] * lms[2] * lms[2],
}
xyz := mulVecMat(lms_, &oklabLmsToXyz)
return xyz
},
}).Init()
var Oklch = (&Space{
ID: "oklch",
Name: "Oklch",
Coords: [3]Coordinate{
{Name: "Lightness", Range: infty, RefRange: norm},
{Name: "Chroma", Range: infty, RefRange: [2]float64{0, 0.4}},
{Name: "Hue", Range: infty, IsAngle: true, RefRange: [2]float64{0, 360}},
},
Base: Oklab,
FromBase: func(c [3]float64) [3]float64 {
return labToLCH(c, 0.8/1e5)
},
ToBase: LCh.ToBase,
}).Init()
var Lab = (&Space{
ID: "lab",
Name: "Lab",
Coords: [3]Coordinate{
{Name: "Lightness", Range: infty, RefRange: [2]float64{0, 100}},
{Name: "a", Range: infty, RefRange: [2]float64{-125, 125}},
{Name: "b", Range: infty, RefRange: [2]float64{-125, 125}},
},
Base: XYZ_D50,
FromBase: func(c [3]float64) [3]float64 {
const (
ϵ = 216.0 / 24389.0
ϵ3 = 24.0 / 116.0
κ = 24389.0 / 27.0
)
white := WhitesCSSD50.XYZ()
xyz := c
xyz[0] /= white[0]
xyz[1] /= white[1]
xyz[2] /= white[2]
f := func(x float64) float64 {
if x > ϵ {
return math.Cbrt(x)
} else {
return (κ*x + 16) / 116.0
}
}
x_ := f(xyz[0])
y_ := f(xyz[1])
z_ := f(xyz[2])
l := 116.0*y_ - 16
a := 500.0 * (x_ - y_)
b := 200.0 * (y_ - z_)
return [3]float64{l, a, b}
},
ToBase: func(c [3]float64) [3]float64 {
const (
ϵ = 216.0 / 24389.0
ϵ3 = 24.0 / 116.0
κ = 24389.0 / 27.0
)
l, a, b := c[0], c[1], c[2]
f1 := (l + 16.0) / 116.0
f0 := a/500.0 + f1
f2 := f1 - b/200.0
var x, y, z float64
if f0 > ϵ3 {
x = f0 * f0 * f0
} else {
x = (116*f0 - 16) / κ
}
if l > 8 {
n := (l + 16.0) / 116.0
y = n * n * n
} else {
y = l / κ
}
if f2 > ϵ3 {
z = f2 * f2 * f2
} else {
z = (116.0*f2 - 16) / κ
}
white := WhitesCSSD50.XYZ()
x *= white[0]
y *= white[1]
z *= white[2]
return [3]float64{x, y, z}
},
}).Init()
var LCh = (&Space{
ID: "lch",
Name: "LCh",
Coords: [3]Coordinate{
{Name: "Lightness", Range: infty, RefRange: [2]float64{0, 100}},
{Name: "Chroma", Range: infty, RefRange: [2]float64{0, 150}},
{Name: "Hue", Range: infty, IsAngle: true, RefRange: [2]float64{0, 360}},
},
Base: Lab,
FromBase: func(c [3]float64) [3]float64 {
return labToLCH(c, 250.0/1e5)
},
ToBase: func(cl [3]float64) [3]float64 {
// XXX handle achromatic h
l, c, h := cl[0], cl[1], cl[2]
if c < 0 {
c = 0
}
a := c * math.Cos(h*math.Pi/180.0)
b := c * math.Sin(h*math.Pi/180)
return [3]float64{l, a, b}
},
}).Init()
func labToLCH(lab [3]float64, ϵ float64) [3]float64 {
l, a, b := lab[0], lab[1], lab[2]
achromatic := math.Abs(a) < ϵ && math.Abs(b) < ϵ
var c, h float64
if achromatic {
c = 0
// XXX color.js uses null for achromatic
h = 0
} else {
c = math.Sqrt(a*a + b*b)
h_ := math.Atan2(b, a) * 180 / math.Pi
h = math.Mod(h_+360, 360)
}
return [3]float64{l, c, h}
}
var LinearProPhoto = newRGBSpace(
&rgbSpace{
ID: "prophoto-rgb-linear",
Name: "Linear ProPhoto",
Base: XYZ_D50,
ToBase: [3][3]float64{
{0.79776664490064230, 0.13518129740053308, 0.03134773412839220},
{0.28807482881940130, 0.71183523424187300, 0.00008993693872564},
{0.00000000000000000, 0.00000000000000000, 0.82510460251046020},
},
FromBase: [3][3]float64{
{1.34578688164715830, -0.25557208737979464, -0.05110186497554526},
{-0.54463070512490190, 1.50824774284514680, 0.02052744743642139},
{0.00000000000000000, 0.00000000000000000, 1.21196754563894520},
},
},
)
var ProPhoto = (&Space{
ID: "prophoto-rgb",
Name: "ProPhoto",
Base: LinearProPhoto,
Coords: RGBCoordinates,
ToBase: func(c [3]float64) [3]float64 {
f := func(v float64) float64 {
var sign float64
if v < 0 {
sign = -1
} else {
sign = 1
}
abs := math.Abs(v)
if abs <= 16.0/512.0 {
return v / 16.0
} else {
return sign * math.Pow(abs, 1.8)
}
}
return [3]float64{
f(c[0]),
f(c[1]),
f(c[2]),
}
},
FromBase: func(c [3]float64) [3]float64 {
f := func(v float64) float64 {
var sign float64
if v < 0 {
sign = -1
} else {
sign = 1
}
abs := math.Abs(v)
if abs > 1.0/512.0 {
return sign * math.Pow(abs, 1.0/1.8)
} else {
return 16 * v
}
}
return [3]float64{
f(c[0]),
f(c[1]),
f(c[2]),
}
},
}).Init()
var LinearRec2020 = newRGBSpace(
&rgbSpace{
ID: "rec2020-linear",
Name: "Linear Rec. 2020",
Base: XYZ_D65,
ToBase: [3][3]float64{
{6.36953507e-01, 1.44619185e-01, 1.68855854e-01},
{2.62698339e-01, 6.78008766e-01, 5.92928953e-02},
{4.99407097e-17, 2.80731358e-02, 1.06082723},
},
FromBase: [3][3]float64{
{1.71666343, -0.35567332, -0.25336809},
{-0.66667384, 1.61645574, 0.0157683},
{0.01764248, -0.04277698, 0.94224328},
},
},
)
var Rec2020 = (&Space{
ID: "rec2020",
Name: "Rec. 2020",
Base: LinearRec2020,
Coords: RGBCoordinates,
ToBase: func(c [3]float64) [3]float64 {
f := func(v float64) float64 {
const b = 0.018053968510807
const a = 1 + 5.5*b
var sign float64
if v < 0 {
sign = -1
} else {
sign = 1
}
abs := math.Abs(v)
if abs < 4.5*b {
return v / 4.5
} else {
return sign * math.Pow(((abs+(a-1))/a), 1.0/0.45)
}
}
return [3]float64{
f(c[0]),
f(c[1]),
f(c[2]),
}
},
FromBase: func(c [3]float64) [3]float64 {
f := func(v float64) float64 {
const b = 0.018053968510807
const a = 1 + 5.5*b
var sign float64
if v < 0 {
sign = -1
} else {
sign = 1
}
abs := math.Abs(v)
if abs < b {
return 4.5 * v
} else {
return sign*a*math.Pow(abs, 0.45) - (a - 1)
}
}
return [3]float64{
f(c[0]),
f(c[1]),
f(c[2]),
}
},
}).Init()
var Rec2100PQ = (&Space{
ID: "rec2100-pq",
Name: "Rec. 2100 PQ",
Base: LinearRec2020,
Coords: RGBCoordinates,
ToBase: func(c [3]float64) [3]float64 {
f := func(v float64) float64 {
const m1 = 2610.0 / 16384.0
const m2 = 128 * (2523.0 / 4096.0)
const c3 = 32 * (2392.0 / 4096.0)
const c2 = 32 * (2413.0 / 4096.0)
const c1 = c3 - c2 + 1
EtoM2Recip := math.Pow(v, 1.0/m2)
nom := max(EtoM2Recip-c1, 0)
denom := c2 - c3*EtoM2Recip
return 10_000 * math.Pow(nom/denom, 1.0/m1)
}
return [3]float64{
f(c[0]) / 203,
f(c[1]) / 203,
f(c[2]) / 203,
}
},
FromBase: func(c [3]float64) [3]float64 {
f := func(v float64) float64 {
const m1 = 2610.0 / 16384.0
const m2 = 128 * (2523.0 / 4096.0)
const c3 = 32 * (2392.0 / 4096.0)
const c2 = 32 * (2413.0 / 4096.0)
const c1 = c3 - c2 + 1
Y := v / 10_000
YtoM1 := math.Pow(Y, m1)
return math.Pow((c1+c2*YtoM1)/(1+c3*YtoM1), m2)
}
return [3]float64{
f(c[0] * 203),
f(c[1] * 203),
f(c[2] * 203),
}
},
}).Init()
func mulVecMat(vec [3]float64, m *[3][3]float64) [3]float64 {
return [3]float64{
m[0][0]*vec[0] + m[0][1]*vec[1] + m[0][2]*vec[2],
m[1][0]*vec[0] + m[1][1]*vec[1] + m[1][2]*vec[2],
m[2][0]*vec[0] + m[2][1]*vec[1] + m[2][2]*vec[2],
}
}
func mulMatMat(m1, m2 *[3][3]float64) [3][3]float64 {
return [3][3]float64{
{
m1[0][0]*m2[0][0] + m1[0][1]*m2[1][0] + m1[0][2]*m2[2][0],
m1[0][0]*m2[0][1] + m1[0][1]*m2[1][1] + m1[0][2]*m2[2][1],
m1[0][0]*m2[0][2] + m1[0][1]*m2[1][2] + m1[0][2]*m2[2][2],
},
{
m1[1][0]*m2[0][0] + m1[1][1]*m2[1][0] + m1[1][2]*m2[2][0],
m1[1][0]*m2[0][1] + m1[1][1]*m2[1][1] + m1[1][2]*m2[2][1],
m1[1][0]*m2[0][2] + m1[1][1]*m2[1][2] + m1[1][2]*m2[2][2],
},
{
m1[2][0]*m2[0][0] + m1[2][1]*m2[1][0] + m1[2][2]*m2[2][0],
m1[2][0]*m2[0][1] + m1[2][1]*m2[1][1] + m1[2][2]*m2[2][1],
m1[2][0]*m2[0][2] + m1[2][1]*m2[1][2] + m1[2][2]*m2[2][2],
},
}
}