gemini-browser

colors.go (27612B)

---

 // The colorful package provides all kinds of functions for working with colors.
 package colorful
 
 import (
 	"fmt"
 	"image/color"
 	"math"
 )
 
 // A color is stored internally using sRGB (standard RGB) values in the range 0-1
 type Color struct {
 	R, G, B float64
 }
 
 // Implement the Go color.Color interface.
 func (col Color) RGBA() (r, g, b, a uint32) {
 	r = uint32(col.R*65535.0 + 0.5)
 	g = uint32(col.G*65535.0 + 0.5)
 	b = uint32(col.B*65535.0 + 0.5)
 	a = 0xFFFF
 	return
 }
 
 // Constructs a colorful.Color from something implementing color.Color
 func MakeColor(col color.Color) (Color, bool) {
 	r, g, b, a := col.RGBA()
 	if a == 0 {
 		return Color{0, 0, 0}, false
 	}
 
 	// Since color.Color is alpha pre-multiplied, we need to divide the
 	// RGB values by alpha again in order to get back the original RGB.
 	r *= 0xffff
 	r /= a
 	g *= 0xffff
 	g /= a
 	b *= 0xffff
 	b /= a
 
 	return Color{float64(r) / 65535.0, float64(g) / 65535.0, float64(b) / 65535.0}, true
 }
 
 // Might come in handy sometimes to reduce boilerplate code.
 func (col Color) RGB255() (r, g, b uint8) {
 	r = uint8(col.R*255.0 + 0.5)
 	g = uint8(col.G*255.0 + 0.5)
 	b = uint8(col.B*255.0 + 0.5)
 	return
 }
 
 // Used to simplify HSLuv testing.
 func (col Color) values() (float64, float64, float64) {
 	return col.R, col.G, col.B
 }
 
 // This is the tolerance used when comparing colors using AlmostEqualRgb.
 const Delta = 1.0 / 255.0
 
 // This is the default reference white point.
 var D65 = [3]float64{0.95047, 1.00000, 1.08883}
 
 // And another one.
 var D50 = [3]float64{0.96422, 1.00000, 0.82521}
 
 // Checks whether the color exists in RGB space, i.e. all values are in [0..1]
 func (c Color) IsValid() bool {
 	return 0.0 <= c.R && c.R <= 1.0 &&
 		0.0 <= c.G && c.G <= 1.0 &&
 		0.0 <= c.B && c.B <= 1.0
 }
 
 // clamp01 clamps from 0 to 1.
 func clamp01(v float64) float64 {
 	return math.Max(0.0, math.Min(v, 1.0))
 }
 
 // Returns Clamps the color into valid range, clamping each value to [0..1]
 // If the color is valid already, this is a no-op.
 func (c Color) Clamped() Color {
 	return Color{clamp01(c.R), clamp01(c.G), clamp01(c.B)}
 }
 
 func sq(v float64) float64 {
 	return v * v
 }
 
 func cub(v float64) float64 {
 	return v * v * v
 }
 
 // DistanceRgb computes the distance between two colors in RGB space.
 // This is not a good measure! Rather do it in Lab space.
 func (c1 Color) DistanceRgb(c2 Color) float64 {
 	return math.Sqrt(sq(c1.R-c2.R) + sq(c1.G-c2.G) + sq(c1.B-c2.B))
 }
 
 // DistanceLinearRGB computes the distance between two colors in linear RGB
 // space. This is not useful for measuring how humans perceive color, but
 // might be useful for other things, like dithering.
 func (c1 Color) DistanceLinearRGB(c2 Color) float64 {
 	r1, g1, b1 := c1.LinearRgb()
 	r2, g2, b2 := c2.LinearRgb()
 	return math.Sqrt(sq(r1-r2) + sq(g1-g2) + sq(b1-b2))
 }
 
 // Check for equality between colors within the tolerance Delta (1/255).
 func (c1 Color) AlmostEqualRgb(c2 Color) bool {
 	return math.Abs(c1.R-c2.R)+
 		math.Abs(c1.G-c2.G)+
 		math.Abs(c1.B-c2.B) < 3.0*Delta
 }
 
 // You don't really want to use this, do you? Go for BlendLab, BlendLuv or BlendHcl.
 func (c1 Color) BlendRgb(c2 Color, t float64) Color {
 	return Color{c1.R + t*(c2.R-c1.R),
 		c1.G + t*(c2.G-c1.G),
 		c1.B + t*(c2.B-c1.B)}
 }
 
 // Utility used by Hxx color-spaces for interpolating between two angles in [0,360].
 func interp_angle(a0, a1, t float64) float64 {
 	// Based on the answer here: http://stackoverflow.com/a/14498790/2366315
 	// With potential proof that it works here: http://math.stackexchange.com/a/2144499
 	delta := math.Mod(math.Mod(a1-a0, 360.0)+540, 360.0) - 180.0
 	return math.Mod(a0+t*delta+360.0, 360.0)
 }
 
 /// HSV ///
 ///////////
 // From http://en.wikipedia.org/wiki/HSL_and_HSV
 // Note that h is in [0..360] and s,v in [0..1]
 
 // Hsv returns the Hue [0..360], Saturation and Value [0..1] of the color.
 func (col Color) Hsv() (h, s, v float64) {
 	min := math.Min(math.Min(col.R, col.G), col.B)
 	v = math.Max(math.Max(col.R, col.G), col.B)
 	C := v - min
 
 	s = 0.0
 	if v != 0.0 {
 		s = C / v
 	}
 
 	h = 0.0 // We use 0 instead of undefined as in wp.
 	if min != v {
 		if v == col.R {
 			h = math.Mod((col.G-col.B)/C, 6.0)
 		}
 		if v == col.G {
 			h = (col.B-col.R)/C + 2.0
 		}
 		if v == col.B {
 			h = (col.R-col.G)/C + 4.0
 		}
 		h *= 60.0
 		if h < 0.0 {
 			h += 360.0
 		}
 	}
 	return
 }
 
 // Hsv creates a new Color given a Hue in [0..360], a Saturation and a Value in [0..1]
 func Hsv(H, S, V float64) Color {
 	Hp := H / 60.0
 	C := V * S
 	X := C * (1.0 - math.Abs(math.Mod(Hp, 2.0)-1.0))
 
 	m := V - C
 	r, g, b := 0.0, 0.0, 0.0
 
 	switch {
 	case 0.0 <= Hp && Hp < 1.0:
 		r = C
 		g = X
 	case 1.0 <= Hp && Hp < 2.0:
 		r = X
 		g = C
 	case 2.0 <= Hp && Hp < 3.0:
 		g = C
 		b = X
 	case 3.0 <= Hp && Hp < 4.0:
 		g = X
 		b = C
 	case 4.0 <= Hp && Hp < 5.0:
 		r = X
 		b = C
 	case 5.0 <= Hp && Hp < 6.0:
 		r = C
 		b = X
 	}
 
 	return Color{m + r, m + g, m + b}
 }
 
 // You don't really want to use this, do you? Go for BlendLab, BlendLuv or BlendHcl.
 func (c1 Color) BlendHsv(c2 Color, t float64) Color {
 	h1, s1, v1 := c1.Hsv()
 	h2, s2, v2 := c2.Hsv()
 
 	// We know that h are both in [0..360]
 	return Hsv(interp_angle(h1, h2, t), s1+t*(s2-s1), v1+t*(v2-v1))
 }
 
 /// HSL ///
 ///////////
 
 // Hsl returns the Hue [0..360], Saturation [0..1], and Luminance (lightness) [0..1] of the color.
 func (col Color) Hsl() (h, s, l float64) {
 	min := math.Min(math.Min(col.R, col.G), col.B)
 	max := math.Max(math.Max(col.R, col.G), col.B)
 
 	l = (max + min) / 2
 
 	if min == max {
 		s = 0
 		h = 0
 	} else {
 		if l < 0.5 {
 			s = (max - min) / (max + min)
 		} else {
 			s = (max - min) / (2.0 - max - min)
 		}
 
 		if max == col.R {
 			h = (col.G - col.B) / (max - min)
 		} else if max == col.G {
 			h = 2.0 + (col.B-col.R)/(max-min)
 		} else {
 			h = 4.0 + (col.R-col.G)/(max-min)
 		}
 
 		h *= 60
 
 		if h < 0 {
 			h += 360
 		}
 	}
 
 	return
 }
 
 // Hsl creates a new Color given a Hue in [0..360], a Saturation [0..1], and a Luminance (lightness) in [0..1]
 func Hsl(h, s, l float64) Color {
 	if s == 0 {
 		return Color{l, l, l}
 	}
 
 	var r, g, b float64
 	var t1 float64
 	var t2 float64
 	var tr float64
 	var tg float64
 	var tb float64
 
 	if l < 0.5 {
 		t1 = l * (1.0 + s)
 	} else {
 		t1 = l + s - l*s
 	}
 
 	t2 = 2*l - t1
 	h /= 360
 	tr = h + 1.0/3.0
 	tg = h
 	tb = h - 1.0/3.0
 
 	if tr < 0 {
 		tr++
 	}
 	if tr > 1 {
 		tr--
 	}
 	if tg < 0 {
 		tg++
 	}
 	if tg > 1 {
 		tg--
 	}
 	if tb < 0 {
 		tb++
 	}
 	if tb > 1 {
 		tb--
 	}
 
 	// Red
 	if 6*tr < 1 {
 		r = t2 + (t1-t2)*6*tr
 	} else if 2*tr < 1 {
 		r = t1
 	} else if 3*tr < 2 {
 		r = t2 + (t1-t2)*(2.0/3.0-tr)*6
 	} else {
 		r = t2
 	}
 
 	// Green
 	if 6*tg < 1 {
 		g = t2 + (t1-t2)*6*tg
 	} else if 2*tg < 1 {
 		g = t1
 	} else if 3*tg < 2 {
 		g = t2 + (t1-t2)*(2.0/3.0-tg)*6
 	} else {
 		g = t2
 	}
 
 	// Blue
 	if 6*tb < 1 {
 		b = t2 + (t1-t2)*6*tb
 	} else if 2*tb < 1 {
 		b = t1
 	} else if 3*tb < 2 {
 		b = t2 + (t1-t2)*(2.0/3.0-tb)*6
 	} else {
 		b = t2
 	}
 
 	return Color{r, g, b}
 }
 
 /// Hex ///
 ///////////
 
 // Hex returns the hex "html" representation of the color, as in #ff0080.
 func (col Color) Hex() string {
 	// Add 0.5 for rounding
 	return fmt.Sprintf("#%02x%02x%02x", uint8(col.R*255.0+0.5), uint8(col.G*255.0+0.5), uint8(col.B*255.0+0.5))
 }
 
 // Hex parses a "html" hex color-string, either in the 3 "#f0c" or 6 "#ff1034" digits form.
 func Hex(scol string) (Color, error) {
 	format := "#%02x%02x%02x"
 	factor := 1.0 / 255.0
 	if len(scol) == 4 {
 		format = "#%1x%1x%1x"
 		factor = 1.0 / 15.0
 	}
 
 	var r, g, b uint8
 	n, err := fmt.Sscanf(scol, format, &r, &g, &b)
 	if err != nil {
 		return Color{}, err
 	}
 	if n != 3 {
 		return Color{}, fmt.Errorf("color: %v is not a hex-color", scol)
 	}
 
 	return Color{float64(r) * factor, float64(g) * factor, float64(b) * factor}, nil
 }
 
 /// Linear ///
 //////////////
 // http://www.sjbrown.co.uk/2004/05/14/gamma-correct-rendering/
 // http://www.brucelindbloom.com/Eqn_RGB_to_XYZ.html
 
 func linearize(v float64) float64 {
 	if v <= 0.04045 {
 		return v / 12.92
 	}
 	return math.Pow((v+0.055)/1.055, 2.4)
 }
 
 // LinearRgb converts the color into the linear RGB space (see http://www.sjbrown.co.uk/2004/05/14/gamma-correct-rendering/).
 func (col Color) LinearRgb() (r, g, b float64) {
 	r = linearize(col.R)
 	g = linearize(col.G)
 	b = linearize(col.B)
 	return
 }
 
 // A much faster and still quite precise linearization using a 6th-order Taylor approximation.
 // See the accompanying Jupyter notebook for derivation of the constants.
 func linearize_fast(v float64) float64 {
 	v1 := v - 0.5
 	v2 := v1 * v1
 	v3 := v2 * v1
 	v4 := v2 * v2
 	//v5 := v3*v2
 	return -0.248750514614486 + 0.925583310193438*v + 1.16740237321695*v2 + 0.280457026598666*v3 - 0.0757991963780179*v4 //+ 0.0437040411548932*v5
 }
 
 // FastLinearRgb is much faster than and almost as accurate as LinearRgb.
 // BUT it is important to NOTE that they only produce good results for valid colors r,g,b in [0,1].
 func (col Color) FastLinearRgb() (r, g, b float64) {
 	r = linearize_fast(col.R)
 	g = linearize_fast(col.G)
 	b = linearize_fast(col.B)
 	return
 }
 
 func delinearize(v float64) float64 {
 	if v <= 0.0031308 {
 		return 12.92 * v
 	}
 	return 1.055*math.Pow(v, 1.0/2.4) - 0.055
 }
 
 // LinearRgb creates an sRGB color out of the given linear RGB color (see http://www.sjbrown.co.uk/2004/05/14/gamma-correct-rendering/).
 func LinearRgb(r, g, b float64) Color {
 	return Color{delinearize(r), delinearize(g), delinearize(b)}
 }
 
 func delinearize_fast(v float64) float64 {
 	// This function (fractional root) is much harder to linearize, so we need to split.
 	if v > 0.2 {
 		v1 := v - 0.6
 		v2 := v1 * v1
 		v3 := v2 * v1
 		v4 := v2 * v2
 		v5 := v3 * v2
 		return 0.442430344268235 + 0.592178981271708*v - 0.287864782562636*v2 + 0.253214392068985*v3 - 0.272557158129811*v4 + 0.325554383321718*v5
 	} else if v > 0.03 {
 		v1 := v - 0.115
 		v2 := v1 * v1
 		v3 := v2 * v1
 		v4 := v2 * v2
 		v5 := v3 * v2
 		return 0.194915592891669 + 1.55227076330229*v - 3.93691860257828*v2 + 18.0679839248761*v3 - 101.468750302746*v4 + 632.341487393927*v5
 	} else {
 		v1 := v - 0.015
 		v2 := v1 * v1
 		v3 := v2 * v1
 		v4 := v2 * v2
 		v5 := v3 * v2
 		// You can clearly see from the involved constants that the low-end is highly nonlinear.
 		return 0.0519565234928877 + 5.09316778537561*v - 99.0338180489702*v2 + 3484.52322764895*v3 - 150028.083412663*v4 + 7168008.42971613*v5
 	}
 }
 
 // FastLinearRgb is much faster than and almost as accurate as LinearRgb.
 // BUT it is important to NOTE that they only produce good results for valid inputs r,g,b in [0,1].
 func FastLinearRgb(r, g, b float64) Color {
 	return Color{delinearize_fast(r), delinearize_fast(g), delinearize_fast(b)}
 }
 
 // XyzToLinearRgb converts from CIE XYZ-space to Linear RGB space.
 func XyzToLinearRgb(x, y, z float64) (r, g, b float64) {
 	r = 3.2409699419045214*x - 1.5373831775700935*y - 0.49861076029300328*z
 	g = -0.96924363628087983*x + 1.8759675015077207*y + 0.041555057407175613*z
 	b = 0.055630079696993609*x - 0.20397695888897657*y + 1.0569715142428786*z
 	return
 }
 
 func LinearRgbToXyz(r, g, b float64) (x, y, z float64) {
 	x = 0.41239079926595948*r + 0.35758433938387796*g + 0.18048078840183429*b
 	y = 0.21263900587151036*r + 0.71516867876775593*g + 0.072192315360733715*b
 	z = 0.019330818715591851*r + 0.11919477979462599*g + 0.95053215224966058*b
 	return
 }
 
 /// XYZ ///
 ///////////
 // http://www.sjbrown.co.uk/2004/05/14/gamma-correct-rendering/
 
 func (col Color) Xyz() (x, y, z float64) {
 	return LinearRgbToXyz(col.LinearRgb())
 }
 
 func Xyz(x, y, z float64) Color {
 	return LinearRgb(XyzToLinearRgb(x, y, z))
 }
 
 /// xyY ///
 ///////////
 // http://www.brucelindbloom.com/Eqn_XYZ_to_xyY.html
 
 // Well, the name is bad, since it's xyY but Golang needs me to start with a
 // capital letter to make the method public.
 func XyzToXyy(X, Y, Z float64) (x, y, Yout float64) {
 	return XyzToXyyWhiteRef(X, Y, Z, D65)
 }
 
 func XyzToXyyWhiteRef(X, Y, Z float64, wref [3]float64) (x, y, Yout float64) {
 	Yout = Y
 	N := X + Y + Z
 	if math.Abs(N) < 1e-14 {
 		// When we have black, Bruce Lindbloom recommends to use
 		// the reference white's chromacity for x and y.
 		x = wref[0] / (wref[0] + wref[1] + wref[2])
 		y = wref[1] / (wref[0] + wref[1] + wref[2])
 	} else {
 		x = X / N
 		y = Y / N
 	}
 	return
 }
 
 func XyyToXyz(x, y, Y float64) (X, Yout, Z float64) {
 	Yout = Y
 
 	if -1e-14 < y && y < 1e-14 {
 		X = 0.0
 		Z = 0.0
 	} else {
 		X = Y / y * x
 		Z = Y / y * (1.0 - x - y)
 	}
 
 	return
 }
 
 // Converts the given color to CIE xyY space using D65 as reference white.
 // (Note that the reference white is only used for black input.)
 // x, y and Y are in [0..1]
 func (col Color) Xyy() (x, y, Y float64) {
 	return XyzToXyy(col.Xyz())
 }
 
 // Converts the given color to CIE xyY space, taking into account
 // a given reference white. (i.e. the monitor's white)
 // (Note that the reference white is only used for black input.)
 // x, y and Y are in [0..1]
 func (col Color) XyyWhiteRef(wref [3]float64) (x, y, Y float64) {
 	X, Y2, Z := col.Xyz()
 	return XyzToXyyWhiteRef(X, Y2, Z, wref)
 }
 
 // Generates a color by using data given in CIE xyY space.
 // x, y and Y are in [0..1]
 func Xyy(x, y, Y float64) Color {
 	return Xyz(XyyToXyz(x, y, Y))
 }
 
 /// L*a*b* ///
 //////////////
 // http://en.wikipedia.org/wiki/Lab_color_space#CIELAB-CIEXYZ_conversions
 // For L*a*b*, we need to L*a*b*<->XYZ->RGB and the first one is device dependent.
 
 func lab_f(t float64) float64 {
 	if t > 6.0/29.0*6.0/29.0*6.0/29.0 {
 		return math.Cbrt(t)
 	}
 	return t/3.0*29.0/6.0*29.0/6.0 + 4.0/29.0
 }
 
 func XyzToLab(x, y, z float64) (l, a, b float64) {
 	// Use D65 white as reference point by default.
 	// http://www.fredmiranda.com/forum/topic/1035332
 	// http://en.wikipedia.org/wiki/Standard_illuminant
 	return XyzToLabWhiteRef(x, y, z, D65)
 }
 
 func XyzToLabWhiteRef(x, y, z float64, wref [3]float64) (l, a, b float64) {
 	fy := lab_f(y / wref[1])
 	l = 1.16*fy - 0.16
 	a = 5.0 * (lab_f(x/wref[0]) - fy)
 	b = 2.0 * (fy - lab_f(z/wref[2]))
 	return
 }
 
 func lab_finv(t float64) float64 {
 	if t > 6.0/29.0 {
 		return t * t * t
 	}
 	return 3.0 * 6.0 / 29.0 * 6.0 / 29.0 * (t - 4.0/29.0)
 }
 
 func LabToXyz(l, a, b float64) (x, y, z float64) {
 	// D65 white (see above).
 	return LabToXyzWhiteRef(l, a, b, D65)
 }
 
 func LabToXyzWhiteRef(l, a, b float64, wref [3]float64) (x, y, z float64) {
 	l2 := (l + 0.16) / 1.16
 	x = wref[0] * lab_finv(l2+a/5.0)
 	y = wref[1] * lab_finv(l2)
 	z = wref[2] * lab_finv(l2-b/2.0)
 	return
 }
 
 // Converts the given color to CIE L*a*b* space using D65 as reference white.
 func (col Color) Lab() (l, a, b float64) {
 	return XyzToLab(col.Xyz())
 }
 
 // Converts the given color to CIE L*a*b* space, taking into account
 // a given reference white. (i.e. the monitor's white)
 func (col Color) LabWhiteRef(wref [3]float64) (l, a, b float64) {
 	x, y, z := col.Xyz()
 	return XyzToLabWhiteRef(x, y, z, wref)
 }
 
 // Generates a color by using data given in CIE L*a*b* space using D65 as reference white.
 // WARNING: many combinations of `l`, `a`, and `b` values do not have corresponding
 // valid RGB values, check the FAQ in the README if you're unsure.
 func Lab(l, a, b float64) Color {
 	return Xyz(LabToXyz(l, a, b))
 }
 
 // Generates a color by using data given in CIE L*a*b* space, taking
 // into account a given reference white. (i.e. the monitor's white)
 func LabWhiteRef(l, a, b float64, wref [3]float64) Color {
 	return Xyz(LabToXyzWhiteRef(l, a, b, wref))
 }
 
 // DistanceLab is a good measure of visual similarity between two colors!
 // A result of 0 would mean identical colors, while a result of 1 or higher
 // means the colors differ a lot.
 func (c1 Color) DistanceLab(c2 Color) float64 {
 	l1, a1, b1 := c1.Lab()
 	l2, a2, b2 := c2.Lab()
 	return math.Sqrt(sq(l1-l2) + sq(a1-a2) + sq(b1-b2))
 }
 
 // DistanceCIE76 is the same as DistanceLab.
 func (c1 Color) DistanceCIE76(c2 Color) float64 {
 	return c1.DistanceLab(c2)
 }
 
 // Uses the CIE94 formula to calculate color distance. More accurate than
 // DistanceLab, but also more work.
 func (cl Color) DistanceCIE94(cr Color) float64 {
 	l1, a1, b1 := cl.Lab()
 	l2, a2, b2 := cr.Lab()
 
 	// NOTE: Since all those formulas expect L,a,b values 100x larger than we
 	//       have them in this library, we either need to adjust all constants
 	//       in the formula, or convert the ranges of L,a,b before, and then
 	//       scale the distances down again. The latter is less error-prone.
 	l1, a1, b1 = l1*100.0, a1*100.0, b1*100.0
 	l2, a2, b2 = l2*100.0, a2*100.0, b2*100.0
 
 	kl := 1.0 // 2.0 for textiles
 	kc := 1.0
 	kh := 1.0
 	k1 := 0.045 // 0.048 for textiles
 	k2 := 0.015 // 0.014 for textiles.
 
 	deltaL := l1 - l2
 	c1 := math.Sqrt(sq(a1) + sq(b1))
 	c2 := math.Sqrt(sq(a2) + sq(b2))
 	deltaCab := c1 - c2
 
 	// Not taking Sqrt here for stability, and it's unnecessary.
 	deltaHab2 := sq(a1-a2) + sq(b1-b2) - sq(deltaCab)
 	sl := 1.0
 	sc := 1.0 + k1*c1
 	sh := 1.0 + k2*c1
 
 	vL2 := sq(deltaL / (kl * sl))
 	vC2 := sq(deltaCab / (kc * sc))
 	vH2 := deltaHab2 / sq(kh*sh)
 
 	return math.Sqrt(vL2+vC2+vH2) * 0.01 // See above.
 }
 
 // DistanceCIEDE2000 uses the Delta E 2000 formula to calculate color
 // distance. It is more expensive but more accurate than both DistanceLab
 // and DistanceCIE94.
 func (cl Color) DistanceCIEDE2000(cr Color) float64 {
 	return cl.DistanceCIEDE2000klch(cr, 1.0, 1.0, 1.0)
 }
 
 // DistanceCIEDE2000klch uses the Delta E 2000 formula with custom values
 // for the weighting factors kL, kC, and kH.
 func (cl Color) DistanceCIEDE2000klch(cr Color, kl, kc, kh float64) float64 {
 	l1, a1, b1 := cl.Lab()
 	l2, a2, b2 := cr.Lab()
 
 	// As with CIE94, we scale up the ranges of L,a,b beforehand and scale
 	// them down again afterwards.
 	l1, a1, b1 = l1*100.0, a1*100.0, b1*100.0
 	l2, a2, b2 = l2*100.0, a2*100.0, b2*100.0
 
 	cab1 := math.Sqrt(sq(a1) + sq(b1))
 	cab2 := math.Sqrt(sq(a2) + sq(b2))
 	cabmean := (cab1 + cab2) / 2
 
 	g := 0.5 * (1 - math.Sqrt(math.Pow(cabmean, 7)/(math.Pow(cabmean, 7)+math.Pow(25, 7))))
 	ap1 := (1 + g) * a1
 	ap2 := (1 + g) * a2
 	cp1 := math.Sqrt(sq(ap1) + sq(b1))
 	cp2 := math.Sqrt(sq(ap2) + sq(b2))
 
 	hp1 := 0.0
 	if b1 != ap1 || ap1 != 0 {
 		hp1 = math.Atan2(b1, ap1)
 		if hp1 < 0 {
 			hp1 += math.Pi * 2
 		}
 		hp1 *= 180 / math.Pi
 	}
 	hp2 := 0.0
 	if b2 != ap2 || ap2 != 0 {
 		hp2 = math.Atan2(b2, ap2)
 		if hp2 < 0 {
 			hp2 += math.Pi * 2
 		}
 		hp2 *= 180 / math.Pi
 	}
 
 	deltaLp := l2 - l1
 	deltaCp := cp2 - cp1
 	dhp := 0.0
 	cpProduct := cp1 * cp2
 	if cpProduct != 0 {
 		dhp = hp2 - hp1
 		if dhp > 180 {
 			dhp -= 360
 		} else if dhp < -180 {
 			dhp += 360
 		}
 	}
 	deltaHp := 2 * math.Sqrt(cpProduct) * math.Sin(dhp/2*math.Pi/180)
 
 	lpmean := (l1 + l2) / 2
 	cpmean := (cp1 + cp2) / 2
 	hpmean := hp1 + hp2
 	if cpProduct != 0 {
 		hpmean /= 2
 		if math.Abs(hp1-hp2) > 180 {
 			if hp1+hp2 < 360 {
 				hpmean += 180
 			} else {
 				hpmean -= 180
 			}
 		}
 	}
 
 	t := 1 - 0.17*math.Cos((hpmean-30)*math.Pi/180) + 0.24*math.Cos(2*hpmean*math.Pi/180) + 0.32*math.Cos((3*hpmean+6)*math.Pi/180) - 0.2*math.Cos((4*hpmean-63)*math.Pi/180)
 	deltaTheta := 30 * math.Exp(-sq((hpmean-275)/25))
 	rc := 2 * math.Sqrt(math.Pow(cpmean, 7)/(math.Pow(cpmean, 7)+math.Pow(25, 7)))
 	sl := 1 + (0.015*sq(lpmean-50))/math.Sqrt(20+sq(lpmean-50))
 	sc := 1 + 0.045*cpmean
 	sh := 1 + 0.015*cpmean*t
 	rt := -math.Sin(2*deltaTheta*math.Pi/180) * rc
 
 	return math.Sqrt(sq(deltaLp/(kl*sl))+sq(deltaCp/(kc*sc))+sq(deltaHp/(kh*sh))+rt*(deltaCp/(kc*sc))*(deltaHp/(kh*sh))) * 0.01
 }
 
 // BlendLab blends two colors in the L*a*b* color-space, which should result in a smoother blend.
 // t == 0 results in c1, t == 1 results in c2
 func (c1 Color) BlendLab(c2 Color, t float64) Color {
 	l1, a1, b1 := c1.Lab()
 	l2, a2, b2 := c2.Lab()
 	return Lab(l1+t*(l2-l1),
 		a1+t*(a2-a1),
 		b1+t*(b2-b1))
 }
 
 /// L*u*v* ///
 //////////////
 // http://en.wikipedia.org/wiki/CIELUV#XYZ_.E2.86.92_CIELUV_and_CIELUV_.E2.86.92_XYZ_conversions
 // For L*u*v*, we need to L*u*v*<->XYZ<->RGB and the first one is device dependent.
 
 func XyzToLuv(x, y, z float64) (l, a, b float64) {
 	// Use D65 white as reference point by default.
 	// http://www.fredmiranda.com/forum/topic/1035332
 	// http://en.wikipedia.org/wiki/Standard_illuminant
 	return XyzToLuvWhiteRef(x, y, z, D65)
 }
 
 func XyzToLuvWhiteRef(x, y, z float64, wref [3]float64) (l, u, v float64) {
 	if y/wref[1] <= 6.0/29.0*6.0/29.0*6.0/29.0 {
 		l = y / wref[1] * (29.0 / 3.0 * 29.0 / 3.0 * 29.0 / 3.0) / 100.0
 	} else {
 		l = 1.16*math.Cbrt(y/wref[1]) - 0.16
 	}
 	ubis, vbis := xyz_to_uv(x, y, z)
 	un, vn := xyz_to_uv(wref[0], wref[1], wref[2])
 	u = 13.0 * l * (ubis - un)
 	v = 13.0 * l * (vbis - vn)
 	return
 }
 
 // For this part, we do as R's graphics.hcl does, not as wikipedia does.
 // Or is it the same?
 func xyz_to_uv(x, y, z float64) (u, v float64) {
 	denom := x + 15.0*y + 3.0*z
 	if denom == 0.0 {
 		u, v = 0.0, 0.0
 	} else {
 		u = 4.0 * x / denom
 		v = 9.0 * y / denom
 	}
 	return
 }
 
 func LuvToXyz(l, u, v float64) (x, y, z float64) {
 	// D65 white (see above).
 	return LuvToXyzWhiteRef(l, u, v, D65)
 }
 
 func LuvToXyzWhiteRef(l, u, v float64, wref [3]float64) (x, y, z float64) {
 	//y = wref[1] * lab_finv((l + 0.16) / 1.16)
 	if l <= 0.08 {
 		y = wref[1] * l * 100.0 * 3.0 / 29.0 * 3.0 / 29.0 * 3.0 / 29.0
 	} else {
 		y = wref[1] * cub((l+0.16)/1.16)
 	}
 	un, vn := xyz_to_uv(wref[0], wref[1], wref[2])
 	if l != 0.0 {
 		ubis := u/(13.0*l) + un
 		vbis := v/(13.0*l) + vn
 		x = y * 9.0 * ubis / (4.0 * vbis)
 		z = y * (12.0 - 3.0*ubis - 20.0*vbis) / (4.0 * vbis)
 	} else {
 		x, y = 0.0, 0.0
 	}
 	return
 }
 
 // Converts the given color to CIE L*u*v* space using D65 as reference white.
 // L* is in [0..1] and both u* and v* are in about [-1..1]
 func (col Color) Luv() (l, u, v float64) {
 	return XyzToLuv(col.Xyz())
 }
 
 // Converts the given color to CIE L*u*v* space, taking into account
 // a given reference white. (i.e. the monitor's white)
 // L* is in [0..1] and both u* and v* are in about [-1..1]
 func (col Color) LuvWhiteRef(wref [3]float64) (l, u, v float64) {
 	x, y, z := col.Xyz()
 	return XyzToLuvWhiteRef(x, y, z, wref)
 }
 
 // Generates a color by using data given in CIE L*u*v* space using D65 as reference white.
 // L* is in [0..1] and both u* and v* are in about [-1..1]
 // WARNING: many combinations of `l`, `u`, and `v` values do not have corresponding
 // valid RGB values, check the FAQ in the README if you're unsure.
 func Luv(l, u, v float64) Color {
 	return Xyz(LuvToXyz(l, u, v))
 }
 
 // Generates a color by using data given in CIE L*u*v* space, taking
 // into account a given reference white. (i.e. the monitor's white)
 // L* is in [0..1] and both u* and v* are in about [-1..1]
 func LuvWhiteRef(l, u, v float64, wref [3]float64) Color {
 	return Xyz(LuvToXyzWhiteRef(l, u, v, wref))
 }
 
 // DistanceLuv is a good measure of visual similarity between two colors!
 // A result of 0 would mean identical colors, while a result of 1 or higher
 // means the colors differ a lot.
 func (c1 Color) DistanceLuv(c2 Color) float64 {
 	l1, u1, v1 := c1.Luv()
 	l2, u2, v2 := c2.Luv()
 	return math.Sqrt(sq(l1-l2) + sq(u1-u2) + sq(v1-v2))
 }
 
 // BlendLuv blends two colors in the CIE-L*u*v* color-space, which should result in a smoother blend.
 // t == 0 results in c1, t == 1 results in c2
 func (c1 Color) BlendLuv(c2 Color, t float64) Color {
 	l1, u1, v1 := c1.Luv()
 	l2, u2, v2 := c2.Luv()
 	return Luv(l1+t*(l2-l1),
 		u1+t*(u2-u1),
 		v1+t*(v2-v1))
 }
 
 /// HCL ///
 ///////////
 // HCL is nothing else than L*a*b* in cylindrical coordinates!
 // (this was wrong on English wikipedia, I fixed it, let's hope the fix stays.)
 // But it is widely popular since it is a "correct HSV"
 // http://www.hunterlab.com/appnotes/an09_96a.pdf
 
 // Converts the given color to HCL space using D65 as reference white.
 // H values are in [0..360], C and L values are in [0..1] although C can overshoot 1.0
 func (col Color) Hcl() (h, c, l float64) {
 	return col.HclWhiteRef(D65)
 }
 
 func LabToHcl(L, a, b float64) (h, c, l float64) {
 	// Oops, floating point workaround necessary if a ~= b and both are very small (i.e. almost zero).
 	if math.Abs(b-a) > 1e-4 && math.Abs(a) > 1e-4 {
 		h = math.Mod(57.29577951308232087721*math.Atan2(b, a)+360.0, 360.0) // Rad2Deg
 	} else {
 		h = 0.0
 	}
 	c = math.Sqrt(sq(a) + sq(b))
 	l = L
 	return
 }
 
 // Converts the given color to HCL space, taking into account
 // a given reference white. (i.e. the monitor's white)
 // H values are in [0..360], C and L values are in [0..1]
 func (col Color) HclWhiteRef(wref [3]float64) (h, c, l float64) {
 	L, a, b := col.LabWhiteRef(wref)
 	return LabToHcl(L, a, b)
 }
 
 // Generates a color by using data given in HCL space using D65 as reference white.
 // H values are in [0..360], C and L values are in [0..1]
 // WARNING: many combinations of `h`, `c`, and `l` values do not have corresponding
 // valid RGB values, check the FAQ in the README if you're unsure.
 func Hcl(h, c, l float64) Color {
 	return HclWhiteRef(h, c, l, D65)
 }
 
 func HclToLab(h, c, l float64) (L, a, b float64) {
 	H := 0.01745329251994329576 * h // Deg2Rad
 	a = c * math.Cos(H)
 	b = c * math.Sin(H)
 	L = l
 	return
 }
 
 // Generates a color by using data given in HCL space, taking
 // into account a given reference white. (i.e. the monitor's white)
 // H values are in [0..360], C and L values are in [0..1]
 func HclWhiteRef(h, c, l float64, wref [3]float64) Color {
 	L, a, b := HclToLab(h, c, l)
 	return LabWhiteRef(L, a, b, wref)
 }
 
 // BlendHcl blends two colors in the CIE-L*C*h° color-space, which should result in a smoother blend.
 // t == 0 results in c1, t == 1 results in c2
 func (col1 Color) BlendHcl(col2 Color, t float64) Color {
 	h1, c1, l1 := col1.Hcl()
 	h2, c2, l2 := col2.Hcl()
 
 	// We know that h are both in [0..360]
 	return Hcl(interp_angle(h1, h2, t), c1+t*(c2-c1), l1+t*(l2-l1)).Clamped()
 }
 
 // LuvLch
 
 // Converts the given color to LuvLCh space using D65 as reference white.
 // h values are in [0..360], C and L values are in [0..1] although C can overshoot 1.0
 func (col Color) LuvLCh() (l, c, h float64) {
 	return col.LuvLChWhiteRef(D65)
 }
 
 func LuvToLuvLCh(L, u, v float64) (l, c, h float64) {
 	// Oops, floating point workaround necessary if u ~= v and both are very small (i.e. almost zero).
 	if math.Abs(v-u) > 1e-4 && math.Abs(u) > 1e-4 {
 		h = math.Mod(57.29577951308232087721*math.Atan2(v, u)+360.0, 360.0) // Rad2Deg
 	} else {
 		h = 0.0
 	}
 	l = L
 	c = math.Sqrt(sq(u) + sq(v))
 	return
 }
 
 // Converts the given color to LuvLCh space, taking into account
 // a given reference white. (i.e. the monitor's white)
 // h values are in [0..360], c and l values are in [0..1]
 func (col Color) LuvLChWhiteRef(wref [3]float64) (l, c, h float64) {
 	return LuvToLuvLCh(col.LuvWhiteRef(wref))
 }
 
 // Generates a color by using data given in LuvLCh space using D65 as reference white.
 // h values are in [0..360], C and L values are in [0..1]
 // WARNING: many combinations of `l`, `c`, and `h` values do not have corresponding
 // valid RGB values, check the FAQ in the README if you're unsure.
 func LuvLCh(l, c, h float64) Color {
 	return LuvLChWhiteRef(l, c, h, D65)
 }
 
 func LuvLChToLuv(l, c, h float64) (L, u, v float64) {
 	H := 0.01745329251994329576 * h // Deg2Rad
 	u = c * math.Cos(H)
 	v = c * math.Sin(H)
 	L = l
 	return
 }
 
 // Generates a color by using data given in LuvLCh space, taking
 // into account a given reference white. (i.e. the monitor's white)
 // h values are in [0..360], C and L values are in [0..1]
 func LuvLChWhiteRef(l, c, h float64, wref [3]float64) Color {
 	L, u, v := LuvLChToLuv(l, c, h)
 	return LuvWhiteRef(L, u, v, wref)
 }
 
 // BlendLuvLCh blends two colors in the cylindrical CIELUV color space.
 // t == 0 results in c1, t == 1 results in c2
 func (col1 Color) BlendLuvLCh(col2 Color, t float64) Color {
 	l1, c1, h1 := col1.LuvLCh()
 	l2, c2, h2 := col2.LuvLCh()
 
 	// We know that h are both in [0..360]
 	return LuvLCh(l1+t*(l2-l1), c1+t*(c2-c1), interp_angle(h1, h2, t))
 }