Module: Abachrome::Spectral

Defined in:
lib/abachrome/spectral.rb

Constant Summary collapse

SIZE =

Number of wavelength samples in spectral curves

38
GAMMA =

Gamma value for sRGB companding

2.4
BASE_SPECTRA =

Base spectral reflectance curves for White, Cyan, Magenta, Yellow, Red, Green, Blue These are the fundamental building blocks for converting RGB to spectral data

{
  W: [
    1.00116072718764, 1.00116065159728, 1.00116031922747, 1.00115867270789, 1.00115259844552, 1.00113252528998, 1.00108500663327, 1.00099687889453, 1.00086525152274,
    1.0006962900094, 1.00050496114888, 1.00030808187992, 1.00011966602013, 0.999952765968407, 0.999821836899297, 0.999738609557593, 0.999709551639612, 0.999731930210627,
    0.999799436346195, 0.999900330316671, 1.00002040652611, 1.00014478793658, 1.00025997903412, 1.00035579697089, 1.00042753780269, 1.00047623344888, 1.00050720967508,
    1.00052519156373, 1.00053509606896, 1.00054022097482, 1.00054272816784, 1.00054389569087, 1.00054448212151, 1.00054476959992, 1.00054489887762, 1.00054496254689,
    1.00054498927058, 1.000544996993
  ].freeze,
  C: [
    0.970585001322962, 0.970592498143425, 0.970625348729891, 0.970786806119017, 0.971368673228248, 0.973163230621252, 0.976740223158765, 0.981587605491377, 0.986280265652949,
    0.989949147689134, 0.99249270153842, 0.994145680405256, 0.995183975033212, 0.995756750110818, 0.99591281828671, 0.995606157834528, 0.994597600961854, 0.99221571549237,
    0.986236452783249, 0.967943337264541, 0.891285004244943, 0.536202477862053, 0.154108119001878, 0.0574575093228929, 0.0315349873107007, 0.0222633920086335, 0.0182022841492439,
    0.016299055973264, 0.0153656239334613, 0.0149111568733976, 0.0146954339898235, 0.0145964146717719, 0.0145470156699655, 0.0145228771899495, 0.0145120341118965,
    0.0145066940939832, 0.0145044507314479, 0.0145038009464639
  ].freeze,
  M: [
    0.990673557319988, 0.990671524961979, 0.990662582353421, 0.990618107644795, 0.99045148087871, 0.989871081400204, 0.98828660875964, 0.984290692797504, 0.973934905625306,
    0.941817838460145, 0.817390326195156, 0.432472805065729, 0.13845397825887, 0.0537347216940033, 0.0292174996673231, 0.021313651750859, 0.0201349530181136, 0.0241323096280662,
    0.0372236145223627, 0.0760506552706601, 0.205375471942399, 0.541268903460439, 0.815841685086486, 0.912817704123976, 0.946339830166962, 0.959927696331991, 0.966260595230312,
    0.969325970058424, 0.970854536721399, 0.971605066528128, 0.971962769757392, 0.972127272274509, 0.972209417745812, 0.972249577678424, 0.972267621998742, 0.97227650946215,
    0.972280243306874, 0.97228132482656
  ].freeze,
  Y: [
    0.0210523371789306, 0.0210564627517414, 0.0210746178695038, 0.0211649058448753, 0.0215027957272504, 0.0226738799041561, 0.0258235649693629, 0.0334879385639851,
    0.0519069663740307, 0.100749014833473, 0.239129899706847, 0.534804312272748, 0.79780757864303, 0.911449894067384, 0.953797963004507, 0.971241615465429, 0.979303123807588,
    0.983380119507575, 0.985461246567755, 0.986435046976605, 0.986738250670141, 0.986617882445032, 0.986277776758643, 0.985860592444056, 0.98547492767621, 0.985176934765558,
    0.984971574014181, 0.984846303415712, 0.984775351811199, 0.984738066625265, 0.984719648311765, 0.984711023391939, 0.984706683300676, 0.984704554393091, 0.98470359630937,
    0.984703124077552, 0.98470292561509, 0.984702868122795
  ].freeze,
  R: [
    0.0315605737777207, 0.0315520718330149, 0.0315148215513658, 0.0313318044982702, 0.0306729857725527, 0.0286480476989607, 0.0246450407045709, 0.0192960753663651,
    0.0142066612220556, 0.0102942608878609, 0.0076191460521811, 0.005898041083542, 0.0048233247781713, 0.0042298748350633, 0.0040599171299341, 0.0043533695594676,
    0.0053434425970201, 0.0076917201010463, 0.0135969795736536, 0.0316975442661115, 0.107861196355249, 0.463812603168704, 0.847055405272011, 0.943185409393918, 0.968862150696558,
    0.978030667473603, 0.982043643854306, 0.983923623718707, 0.984845484154382, 0.985294275814596, 0.985507295219825, 0.985605071539837, 0.985653849933578, 0.985677685033883,
    0.985688391806122, 0.985693664690031, 0.985695879848205, 0.985696521463762
  ].freeze,
  G: [
    0.0095560747554212, 0.0095581580120851, 0.0095673245444588, 0.0096129126297349, 0.0097837090401843, 0.010378622705871, 0.0120026452378567, 0.0160977721473922,
    0.026706190223168, 0.0595555440185881, 0.186039826532826, 0.570579820116159, 0.861467768400292, 0.945879089767658, 0.970465486474305, 0.97841363028445, 0.979589031411224,
    0.975533536908632, 0.962288755397813, 0.92312157451312, 0.793434018943111, 0.459270135902429, 0.185574103666303, 0.0881774959955372, 0.05436302287667, 0.0406288447060719,
    0.034221520431697, 0.0311185790956966, 0.0295708898336134, 0.0288108739348928, 0.0284486271324597, 0.0282820301724731, 0.0281988376490237, 0.0281581655342037,
    0.0281398910216386, 0.0281308901665811, 0.0281271086805816, 0.0281260133612096
  ].freeze,
  B: [
    0.979404752502014, 0.97940070684313, 0.979382903470261, 0.979294364945594, 0.97896301460857, 0.977814466694043, 0.974724321133836, 0.967198482343973, 0.949079657530575,
    0.900850128940977, 0.76315044546224, 0.465922171649319, 0.201263280451005, 0.0877524413419623, 0.0457176793291679, 0.0284706050521843, 0.020527176756985, 0.0165302792310211,
    0.0145135107212858, 0.0136003508637687, 0.0133604258769571, 0.013548894314568, 0.0139594356366992, 0.014443425575357, 0.0148854440621406, 0.0152254296999746,
    0.0154592848180209, 0.0156018026485961, 0.0156824871281936, 0.0157248764360615, 0.0157458108784121, 0.0157556123350225, 0.0157605443964911, 0.0157629637515278,
    0.0157640525629106, 0.015764589232951, 0.0157648147772649, 0.0157648801149616
  ].freeze
}.freeze
CMF =

CIE 1931 Color Matching Functions weighted by D65 Standard Illuminant Used to convert spectral reflectance to XYZ tristimulus values

[
  [
    0.0000646919989576, 0.0002194098998132, 0.0011205743509343, 0.0037666134117111, 0.011880553603799, 0.0232864424191771, 0.0345594181969747, 0.0372237901162006,
    0.0324183761091486, 0.021233205609381, 0.0104909907685421, 0.0032958375797931, 0.0005070351633801, 0.0009486742057141, 0.0062737180998318, 0.0168646241897775,
    0.028689649025981, 0.0426748124691731, 0.0562547481311377, 0.0694703972677158, 0.0830531516998291, 0.0861260963002257, 0.0904661376847769, 0.0850038650591277,
    0.0709066691074488, 0.0506288916373645, 0.035473961885264, 0.0214682102597065, 0.0125164567619117, 0.0068045816390165, 0.0034645657946526, 0.0014976097506959,
    0.000769700480928, 0.0004073680581315, 0.0001690104031614, 0.0000952245150365, 0.0000490309872958, 0.0000199961492222
  ].freeze,
  [
    0.000001844289444, 0.0000062053235865, 0.0000310096046799, 0.0001047483849269, 0.0003536405299538, 0.0009514714056444, 0.0022822631748318, 0.004207329043473,
    0.0066887983719014, 0.0098883960193565, 0.0152494514496311, 0.0214183109449723, 0.0334229301575068, 0.0513100134918512, 0.070402083939949, 0.0878387072603517,
    0.0942490536184085, 0.0979566702718931, 0.0941521856862608, 0.0867810237486753, 0.0788565338632013, 0.0635267026203555, 0.05374141675682, 0.042646064357412,
    0.0316173492792708, 0.020885205921391, 0.0138601101360152, 0.0081026402038399, 0.004630102258803, 0.0024913800051319, 0.0012593033677378, 0.000541646522168,
    0.0002779528920067, 0.0001471080673854, 0.0000610327472927, 0.0000343873229523, 0.0000177059860053, 0.000007220974913
  ].freeze,
  [
    0.000305017147638, 0.0010368066663574, 0.0053131363323992, 0.0179543925899536, 0.0570775815345485, 0.113651618936287, 0.17335872618355, 0.196206575558657,
    0.186082370706296, 0.139950475383207, 0.0891745294268649, 0.0478962113517075, 0.0281456253957952, 0.0161376622950514, 0.0077591019215214, 0.0042961483736618,
    0.0020055092122156, 0.0008614711098802, 0.0003690387177652, 0.0001914287288574, 0.0001495555858975, 0.0000923109285104, 0.0000681349182337, 0.0000288263655696,
    0.0000157671820553, 0.0000039406041027, 0.000001584012587, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
  ].freeze
].freeze
RGB_TO_XYZ =

sRGB to XYZ transformation matrix (D65 illuminant)

[
  [0.41239079926595934, 0.357584339383878, 0.1804807884018343],
  [0.21263900587151027, 0.715168678767756, 0.07219231536073371],
  [0.01933081871559182, 0.11919477979462598, 0.9505321522496607]
].freeze
XYZ_TO_RGB =

XYZ to sRGB transformation matrix (D65 illuminant)

[
  [3.2409699419045226, -1.537383177570094, -0.4986107602930034],
  [-0.9692436362808796, 1.8759675015077202, 0.04155505740717559],
  [0.05563007969699366, -0.20397695888897652, 1.0569715142428786]
].freeze

Class Method Summary collapse

Class Method Details

.compand(x) ⇒ Object

Companding: linear RGB to sRGB



129
130
131
132
 
# File 'lib/abachrome/spectral.rb', line 129

def compand(x)
  x = x.to_f
  x > 0.0031308 ? (1.055 * (x**(1.0 / GAMMA))) - 0.055 : x * 12.92
end

.ks_from_reflectance(r) ⇒ Object

Kubelka-Munk absorption/scattering parameter Converts reflectance R to absorption/scattering coefficient KS



204
205
206
 
# File 'lib/abachrome/spectral.rb', line 204

def ks_from_reflectance(r)
  ((1.0 - r)**2) / (2.0 * r)
end

.lrgb_to_reflectance(lrgb) ⇒ Object

Convert linear RGB to spectral reflectance curve Uses the seven primary spectral curves (W, C, M, Y, R, G, B)



153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
 
# File 'lib/abachrome/spectral.rb', line 153

def lrgb_to_reflectance(lrgb)
  r, g, b = lrgb

  # Extract white component
  w = [r, g, b].min
  r -= w
  g -= w
  b -= w

  # Extract CMY components
  c = [g, b].min
  m = [r, b].min
  y = [r, g].min

  # Extract pure RGB components
  r_pure = [0, [r - b, r - g].min].max
  g_pure = [0, [g - b, g - r].min].max
  b_pure = [0, [b - g, b - r].min].max

  # Combine spectral curves
  Array.new(SIZE) do |i|
    [
      Float::EPSILON,
      (w * BASE_SPECTRA[:W][i]) +
        (c * BASE_SPECTRA[:C][i]) +
        (m * BASE_SPECTRA[:M][i]) +
        (y * BASE_SPECTRA[:Y][i]) +
        (r_pure * BASE_SPECTRA[:R][i]) +
        (g_pure * BASE_SPECTRA[:G][i]) +
        (b_pure * BASE_SPECTRA[:B][i])
    ].max
  end
end

.lrgb_to_srgb(lrgb) ⇒ Object

Convert linear RGB to sRGB [0-1]



140
141
142
 
# File 'lib/abachrome/spectral.rb', line 140

def lrgb_to_srgb(lrgb)
  lrgb.map { |x| compand(x) }
end

.lrgb_to_xyz(lrgb) ⇒ Object

Convert linear RGB to XYZ



198
199
200
 
# File 'lib/abachrome/spectral.rb', line 198

def lrgb_to_xyz(lrgb)
  mul_mat_vec(RGB_TO_XYZ, lrgb)
end

.luminance_from_xyz(xyz) ⇒ Object

Calculate luminance from XYZ (Y component)



215
216
217
 
# File 'lib/abachrome/spectral.rb', line 215

def luminance_from_xyz(xyz)
  [Float::EPSILON, xyz[1]].max
end

.mix(colors, tinting_strengths: {}) ⇒ Abachrome::Color

Mix colors using Kubelka-Munk theory

Examples:

red = Abachrome.from_rgb(1, 0, 0)
blue = Abachrome.from_rgb(0, 0, 1)
mixed = Abachrome::Spectral.mix([{color: red, weight: 1}, {color: blue, weight: 1}])

Parameters:

  • colors (Array<Hash>) —

    Array of hashes with :color (Abachrome::Color) and :weight (Numeric)

  • tinting_strengths (Hash) (defaults to: {}) —

    Optional hash mapping colors to tinting strengths (default: 1.0)

Returns:



229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
 
# File 'lib/abachrome/spectral.rb', line 229

def mix(colors, tinting_strengths: {})
  # Convert colors to linear RGB and then to spectral reflectance
  spectral_data = colors.map do |data|
    color = data[:color]
    weight = data[:weight].to_f
    tinting_strength = tinting_strengths[color] || 1.0

    # Convert to linear RGB
    lrgb_color = color.to_color_space(:lrgb)
    lrgb = lrgb_color.coordinates.map(&:to_f)

    # Get spectral reflectance and KS values
    reflectance = lrgb_to_reflectance(lrgb)
    ks_values = reflectance.map { |r| ks_from_reflectance(r) }

    # Calculate XYZ for luminance
    xyz = reflectance_to_xyz(reflectance)
    luminance = luminance_from_xyz(xyz)

    # Calculate effective concentration
    # Note: weight is already normalized (sums to 1), so we don't square it
    # spectral.js squares 'factor' because it uses unnormalized values
    concentration = weight * (tinting_strength**2) * luminance

    {
      ks_values: ks_values,
      concentration: concentration
    }
  end

  # Mix KS values using weighted average
  total_concentration = spectral_data.sum { |d| d[:concentration] }

  mixed_reflectance = Array.new(SIZE) do |i|
    ks_mix = spectral_data.sum { |d| d[:ks_values][i] * d[:concentration] }
    ks_mix /= total_concentration
    reflectance_from_ks(ks_mix)
  end

  # Convert back to RGB
  xyz = reflectance_to_xyz(mixed_reflectance)
  lrgb = xyz_to_lrgb(xyz)
  srgb = lrgb_to_srgb(lrgb)

  # Return as Color object
  Abachrome::Color.from_rgb(*srgb)
end

.mul_mat_vec(matrix, vector) ⇒ Object

Matrix-vector multiplication



145
146
147
148
149
 
# File 'lib/abachrome/spectral.rb', line 145

def mul_mat_vec(matrix, vector)
  matrix.map do |row|
    row.zip(vector).map { |a, b| a * b }.sum
  end
end

.reflectance_from_ks(ks) ⇒ Object

Inverse Kubelka-Munk function Converts KS back to reflectance



210
211
212
 
# File 'lib/abachrome/spectral.rb', line 210

def reflectance_from_ks(ks)
  1.0 + ks - Math.sqrt((ks**2) + (2.0 * ks))
end

.reflectance_to_xyz(reflectance) ⇒ Object

Convert spectral reflectance to XYZ using CIE color matching functions



188
189
190
 
# File 'lib/abachrome/spectral.rb', line 188

def reflectance_to_xyz(reflectance)
  mul_mat_vec(CMF, reflectance)
end

.srgb_to_lrgb(srgb) ⇒ Object

Convert sRGB [0-1] to linear RGB



135
136
137
 
# File 'lib/abachrome/spectral.rb', line 135

def srgb_to_lrgb(srgb)
  srgb.map { |x| uncompand(x) }
end

.uncompand(x) ⇒ Object

Inverse companding: sRGB to linear RGB



123
124
125
126
 
# File 'lib/abachrome/spectral.rb', line 123

def uncompand(x)
  x = x.to_f
  x > 0.04045 ? ((x + 0.055) / 1.055)**GAMMA : x / 12.92
end

.xyz_to_lrgb(xyz) ⇒ Object

Convert XYZ to linear RGB



193
194
195
 
# File 'lib/abachrome/spectral.rb', line 193

def xyz_to_lrgb(xyz)
  mul_mat_vec(XYZ_TO_RGB, xyz)
end