// Copyright(c) 2021 Björn Ottosson // // Permission is hereby granted, free of charge, to any person obtaining a copy of // this software and associated documentation files(the "Software"), to deal in // the Software without restriction, including without limitation the rights to // use, copy, modify, merge, publish, distribute, sublicense, and /or sell copies // of the Software, and to permit persons to whom the Software is furnished to do // so, subject to the following conditions : // The above copyright notice and this permission notice shall be included in all // copies or substantial portions of the Software. // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR // IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, // FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.IN NO EVENT SHALL THE // AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER // LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, // OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE // SOFTWARE. #ifndef OK_COLOR_H #define OK_COLOR_H #include <cmath> #include <cfloat> class ok_color { public: struct Lab { float L; float a; float b; }; struct RGB { float r; float g; float b; }; struct HSV { float h; float s; float v; }; struct HSL { float h; float s; float l; }; struct LC { float L; float C; }; // Alternative representation of (L_cusp, C_cusp) // Encoded so S = C_cusp/L_cusp and T = C_cusp/(1-L_cusp) // The maximum value for C in the triangle is then found as fmin(S*L, T*(1-L)), for a given L struct ST { float S; float T; }; static constexpr float pi = 3.1415926535897932384626433832795028841971693993751058209749445923078164062f; float clamp(float x, float min, float max) { if (x < min) return min; if (x > max) return max; return x; } float sgn(float x) { return (float)(0.f < x) - (float)(x < 0.f); } float srgb_transfer_function(float a) { return .0031308f >= a ? 12.92f * a : 1.055f * powf(a, .4166666666666667f) - .055f; } float srgb_transfer_function_inv(float a) { return .04045f < a ? powf((a + .055f) / 1.055f, 2.4f) : a / 12.92f; } Lab linear_srgb_to_oklab(RGB c) { float l = 0.4122214708f * c.r + 0.5363325363f * c.g + 0.0514459929f * c.b; float m = 0.2119034982f * c.r + 0.6806995451f * c.g + 0.1073969566f * c.b; float s = 0.0883024619f * c.r + 0.2817188376f * c.g + 0.6299787005f * c.b; float l_ = cbrtf(l); float m_ = cbrtf(m); float s_ = cbrtf(s); return { 0.2104542553f * l_ + 0.7936177850f * m_ - 0.0040720468f * s_, 1.9779984951f * l_ - 2.4285922050f * m_ + 0.4505937099f * s_, 0.0259040371f * l_ + 0.7827717662f * m_ - 0.8086757660f * s_, }; } RGB oklab_to_linear_srgb(Lab c) { float l_ = c.L + 0.3963377774f * c.a + 0.2158037573f * c.b; float m_ = c.L - 0.1055613458f * c.a - 0.0638541728f * c.b; float s_ = c.L - 0.0894841775f * c.a - 1.2914855480f * c.b; float l = l_ * l_ * l_; float m = m_ * m_ * m_; float s = s_ * s_ * s_; return { +4.0767416621f * l - 3.3077115913f * m + 0.2309699292f * s, -1.2684380046f * l + 2.6097574011f * m - 0.3413193965f * s, -0.0041960863f * l - 0.7034186147f * m + 1.7076147010f * s, }; } // Finds the maximum saturation possible for a given hue that fits in sRGB // Saturation here is defined as S = C/L // a and b must be normalized so a^2 + b^2 == 1 float compute_max_saturation(float a, float b) { // Max saturation will be when one of r, g or b goes below zero. // Select different coefficients depending on which component goes below zero first float k0, k1, k2, k3, k4, wl, wm, ws; if (-1.88170328f * a - 0.80936493f * b > 1) { // Red component k0 = +1.19086277f; k1 = +1.76576728f; k2 = +0.59662641f; k3 = +0.75515197f; k4 = +0.56771245f; wl = +4.0767416621f; wm = -3.3077115913f; ws = +0.2309699292f; } else if (1.81444104f * a - 1.19445276f * b > 1) { // Green component k0 = +0.73956515f; k1 = -0.45954404f; k2 = +0.08285427f; k3 = +0.12541070f; k4 = +0.14503204f; wl = -1.2684380046f; wm = +2.6097574011f; ws = -0.3413193965f; } else { // Blue component k0 = +1.35733652f; k1 = -0.00915799f; k2 = -1.15130210f; k3 = -0.50559606f; k4 = +0.00692167f; wl = -0.0041960863f; wm = -0.7034186147f; ws = +1.7076147010f; } // Approximate max saturation using a polynomial: float S = k0 + k1 * a + k2 * b + k3 * a * a + k4 * a * b; // Do one step Halley's method to get closer // this gives an error less than 10e6, except for some blue hues where the dS/dh is close to infinite // this should be sufficient for most applications, otherwise do two/three steps float k_l = +0.3963377774f * a + 0.2158037573f * b; float k_m = -0.1055613458f * a - 0.0638541728f * b; float k_s = -0.0894841775f * a - 1.2914855480f * b; { float l_ = 1.f + S * k_l; float m_ = 1.f + S * k_m; float s_ = 1.f + S * k_s; float l = l_ * l_ * l_; float m = m_ * m_ * m_; float s = s_ * s_ * s_; float l_dS = 3.f * k_l * l_ * l_; float m_dS = 3.f * k_m * m_ * m_; float s_dS = 3.f * k_s * s_ * s_; float l_dS2 = 6.f * k_l * k_l * l_; float m_dS2 = 6.f * k_m * k_m * m_; float s_dS2 = 6.f * k_s * k_s * s_; float f = wl * l + wm * m + ws * s; float f1 = wl * l_dS + wm * m_dS + ws * s_dS; float f2 = wl * l_dS2 + wm * m_dS2 + ws * s_dS2; S = S - f * f1 / (f1 * f1 - 0.5f * f * f2); } return S; } // finds L_cusp and C_cusp for a given hue // a and b must be normalized so a^2 + b^2 == 1 LC find_cusp(float a, float b) { // First, find the maximum saturation (saturation S = C/L) float S_cusp = compute_max_saturation(a, b); // Convert to linear sRGB to find the first point where at least one of r,g or b >= 1: RGB rgb_at_max = oklab_to_linear_srgb({ 1, S_cusp * a, S_cusp * b }); float L_cusp = cbrtf(1.f / fmax(fmax(rgb_at_max.r, rgb_at_max.g), rgb_at_max.b)); float C_cusp = L_cusp * S_cusp; return { L_cusp , C_cusp }; } // Finds intersection of the line defined by // L = L0 * (1 - t) + t * L1; // C = t * C1; // a and b must be normalized so a^2 + b^2 == 1 float find_gamut_intersection(float a, float b, float L1, float C1, float L0, LC cusp) { // Find the intersection for upper and lower half seprately float t; if (((L1 - L0) * cusp.C - (cusp.L - L0) * C1) <= 0.f) { // Lower half t = cusp.C * L0 / (C1 * cusp.L + cusp.C * (L0 - L1)); } else { // Upper half // First intersect with triangle t = cusp.C * (L0 - 1.f) / (C1 * (cusp.L - 1.f) + cusp.C * (L0 - L1)); // Then one step Halley's method { float dL = L1 - L0; float dC = C1; float k_l = +0.3963377774f * a + 0.2158037573f * b; float k_m = -0.1055613458f * a - 0.0638541728f * b; float k_s = -0.0894841775f * a - 1.2914855480f * b; float l_dt = dL + dC * k_l; float m_dt = dL + dC * k_m; float s_dt = dL + dC * k_s; // If higher accuracy is required, 2 or 3 iterations of the following block can be used: { float L = L0 * (1.f - t) + t * L1; float C = t * C1; float l_ = L + C * k_l; float m_ = L + C * k_m; float s_ = L + C * k_s; float l = l_ * l_ * l_; float m = m_ * m_ * m_; float s = s_ * s_ * s_; float ldt = 3 * l_dt * l_ * l_; float mdt = 3 * m_dt * m_ * m_; float sdt = 3 * s_dt * s_ * s_; float ldt2 = 6 * l_dt * l_dt * l_; float mdt2 = 6 * m_dt * m_dt * m_; float sdt2 = 6 * s_dt * s_dt * s_; float r = 4.0767416621f * l - 3.3077115913f * m + 0.2309699292f * s - 1; float r1 = 4.0767416621f * ldt - 3.3077115913f * mdt + 0.2309699292f * sdt; float r2 = 4.0767416621f * ldt2 - 3.3077115913f * mdt2 + 0.2309699292f * sdt2; float u_r = r1 / (r1 * r1 - 0.5f * r * r2); float t_r = -r * u_r; float g = -1.2684380046f * l + 2.6097574011f * m - 0.3413193965f * s - 1; float g1 = -1.2684380046f * ldt + 2.6097574011f * mdt - 0.3413193965f * sdt; float g2 = -1.2684380046f * ldt2 + 2.6097574011f * mdt2 - 0.3413193965f * sdt2; float u_g = g1 / (g1 * g1 - 0.5f * g * g2); float t_g = -g * u_g; b = -0.0041960863f * l - 0.7034186147f * m + 1.7076147010f * s - 1; float b1 = -0.0041960863f * ldt - 0.7034186147f * mdt + 1.7076147010f * sdt; float b2 = -0.0041960863f * ldt2 - 0.7034186147f * mdt2 + 1.7076147010f * sdt2; float u_b = b1 / (b1 * b1 - 0.5f * b * b2); float t_b = -b * u_b; t_r = u_r >= 0.f ? t_r : FLT_MAX; t_g = u_g >= 0.f ? t_g : FLT_MAX; t_b = u_b >= 0.f ? t_b : FLT_MAX; t += fmin(t_r, fmin(t_g, t_b)); } } } return t; } float find_gamut_intersection(float a, float b, float L1, float C1, float L0) { // Find the cusp of the gamut triangle LC cusp = find_cusp(a, b); return find_gamut_intersection(a, b, L1, C1, L0, cusp); } RGB gamut_clip_preserve_chroma(RGB rgb) { if (rgb.r < 1 && rgb.g < 1 && rgb.b < 1 && rgb.r > 0 && rgb.g > 0 && rgb.b > 0) return rgb; Lab lab = linear_srgb_to_oklab(rgb); float L = lab.L; float eps = 0.00001f; float C = fmax(eps, sqrtf(lab.a * lab.a + lab.b * lab.b)); float a_ = lab.a / C; float b_ = lab.b / C; float L0 = clamp(L, 0, 1); float t = find_gamut_intersection(a_, b_, L, C, L0); float L_clipped = L0 * (1 - t) + t * L; float C_clipped = t * C; return oklab_to_linear_srgb({ L_clipped, C_clipped * a_, C_clipped * b_ }); } RGB gamut_clip_project_to_0_5(RGB rgb) { if (rgb.r < 1 && rgb.g < 1 && rgb.b < 1 && rgb.r > 0 && rgb.g > 0 && rgb.b > 0) return rgb; Lab lab = linear_srgb_to_oklab(rgb); float L = lab.L; float eps = 0.00001f; float C = fmax(eps, sqrtf(lab.a * lab.a + lab.b * lab.b)); float a_ = lab.a / C; float b_ = lab.b / C; float L0 = 0.5; float t = find_gamut_intersection(a_, b_, L, C, L0); float L_clipped = L0 * (1 - t) + t * L; float C_clipped = t * C; return oklab_to_linear_srgb({ L_clipped, C_clipped * a_, C_clipped * b_ }); } RGB gamut_clip_project_to_L_cusp(RGB rgb) { if (rgb.r < 1 && rgb.g < 1 && rgb.b < 1 && rgb.r > 0 && rgb.g > 0 && rgb.b > 0) return rgb; Lab lab = linear_srgb_to_oklab(rgb); float L = lab.L; float eps = 0.00001f; float C = fmax(eps, sqrtf(lab.a * lab.a + lab.b * lab.b)); float a_ = lab.a / C; float b_ = lab.b / C; // The cusp is computed here and in find_gamut_intersection, an optimized solution would only compute it once. LC cusp = find_cusp(a_, b_); float L0 = cusp.L; float t = find_gamut_intersection(a_, b_, L, C, L0); float L_clipped = L0 * (1 - t) + t * L; float C_clipped = t * C; return oklab_to_linear_srgb({ L_clipped, C_clipped * a_, C_clipped * b_ }); } RGB gamut_clip_adaptive_L0_0_5(RGB rgb, float alpha = 0.05f) { if (rgb.r < 1 && rgb.g < 1 && rgb.b < 1 && rgb.r > 0 && rgb.g > 0 && rgb.b > 0) return rgb; Lab lab = linear_srgb_to_oklab(rgb); float L = lab.L; float eps = 0.00001f; float C = fmax(eps, sqrtf(lab.a * lab.a + lab.b * lab.b)); float a_ = lab.a / C; float b_ = lab.b / C; float Ld = L - 0.5f; float e1 = 0.5f + fabs(Ld) + alpha * C; float L0 = 0.5f * (1.f + sgn(Ld) * (e1 - sqrtf(e1 * e1 - 2.f * fabs(Ld)))); float t = find_gamut_intersection(a_, b_, L, C, L0); float L_clipped = L0 * (1.f - t) + t * L; float C_clipped = t * C; return oklab_to_linear_srgb({ L_clipped, C_clipped * a_, C_clipped * b_ }); } RGB gamut_clip_adaptive_L0_L_cusp(RGB rgb, float alpha = 0.05f) { if (rgb.r < 1 && rgb.g < 1 && rgb.b < 1 && rgb.r > 0 && rgb.g > 0 && rgb.b > 0) return rgb; Lab lab = linear_srgb_to_oklab(rgb); float L = lab.L; float eps = 0.00001f; float C = fmax(eps, sqrtf(lab.a * lab.a + lab.b * lab.b)); float a_ = lab.a / C; float b_ = lab.b / C; // The cusp is computed here and in find_gamut_intersection, an optimized solution would only compute it once. LC cusp = find_cusp(a_, b_); float Ld = L - cusp.L; float k = 2.f * (Ld > 0 ? 1.f - cusp.L : cusp.L); float e1 = 0.5f * k + fabs(Ld) + alpha * C / k; float L0 = cusp.L + 0.5f * (sgn(Ld) * (e1 - sqrtf(e1 * e1 - 2.f * k * fabs(Ld)))); float t = find_gamut_intersection(a_, b_, L, C, L0); float L_clipped = L0 * (1.f - t) + t * L; float C_clipped = t * C; return oklab_to_linear_srgb({ L_clipped, C_clipped * a_, C_clipped * b_ }); } float toe(float x) { constexpr float k_1 = 0.206f; constexpr float k_2 = 0.03f; constexpr float k_3 = (1.f + k_1) / (1.f + k_2); return 0.5f * (k_3 * x - k_1 + sqrtf((k_3 * x - k_1) * (k_3 * x - k_1) + 4 * k_2 * k_3 * x)); } float toe_inv(float x) { constexpr float k_1 = 0.206f; constexpr float k_2 = 0.03f; constexpr float k_3 = (1.f + k_1) / (1.f + k_2); return (x * x + k_1 * x) / (k_3 * (x + k_2)); } ST to_ST(LC cusp) { float L = cusp.L; float C = cusp.C; return { C / L, C / (1 - L) }; } // Returns a smooth approximation of the location of the cusp // This polynomial was created by an optimization process // It has been designed so that S_mid < S_max and T_mid < T_max ST get_ST_mid(float a_, float b_) { float S = 0.11516993f + 1.f / ( +7.44778970f + 4.15901240f * b_ + a_ * (-2.19557347f + 1.75198401f * b_ + a_ * (-2.13704948f - 10.02301043f * b_ + a_ * (-4.24894561f + 5.38770819f * b_ + 4.69891013f * a_ ))) ); float T = 0.11239642f + 1.f / ( +1.61320320f - 0.68124379f * b_ + a_ * (+0.40370612f + 0.90148123f * b_ + a_ * (-0.27087943f + 0.61223990f * b_ + a_ * (+0.00299215f - 0.45399568f * b_ - 0.14661872f * a_ ))) ); return { S, T }; } struct Cs { float C_0; float C_mid; float C_max; }; Cs get_Cs(float L, float a_, float b_) { LC cusp = find_cusp(a_, b_); float C_max = find_gamut_intersection(a_, b_, L, 1, L, cusp); ST ST_max = to_ST(cusp); // Scale factor to compensate for the curved part of gamut shape: float k = C_max / fmin((L * ST_max.S), (1 - L) * ST_max.T); float C_mid; { ST ST_mid = get_ST_mid(a_, b_); // Use a soft minimum function, instead of a sharp triangle shape to get a smooth value for chroma. float C_a = L * ST_mid.S; float C_b = (1.f - L) * ST_mid.T; C_mid = 0.9f * k * sqrtf(sqrtf(1.f / (1.f / (C_a * C_a * C_a * C_a) + 1.f / (C_b * C_b * C_b * C_b)))); } float C_0; { // for C_0, the shape is independent of hue, so ST are constant. Values picked to roughly be the average values of ST. float C_a = L * 0.4f; float C_b = (1.f - L) * 0.8f; // Use a soft minimum function, instead of a sharp triangle shape to get a smooth value for chroma. C_0 = sqrtf(1.f / (1.f / (C_a * C_a) + 1.f / (C_b * C_b))); } return { C_0, C_mid, C_max }; } RGB okhsl_to_srgb(HSL hsl) { float h = hsl.h; float s = hsl.s; float l = hsl.l; if (l == 1.0f) { return { 1.f, 1.f, 1.f }; } else if (l == 0.f) { return { 0.f, 0.f, 0.f }; } float a_ = cosf(2.f * pi * h); float b_ = sinf(2.f * pi * h); float L = toe_inv(l); Cs cs = get_Cs(L, a_, b_); float C_0 = cs.C_0; float C_mid = cs.C_mid; float C_max = cs.C_max; float mid = 0.8f; float mid_inv = 1.25f; float C, t, k_0, k_1, k_2; if (s < mid) { t = mid_inv * s; k_1 = mid * C_0; k_2 = (1.f - k_1 / C_mid); C = t * k_1 / (1.f - k_2 * t); } else { t = (s - mid)/ (1 - mid); k_0 = C_mid; k_1 = (1.f - mid) * C_mid * C_mid * mid_inv * mid_inv / C_0; k_2 = (1.f - (k_1) / (C_max - C_mid)); C = k_0 + t * k_1 / (1.f - k_2 * t); } RGB rgb = oklab_to_linear_srgb({ L, C * a_, C * b_ }); return { srgb_transfer_function(rgb.r), srgb_transfer_function(rgb.g), srgb_transfer_function(rgb.b), }; } HSL srgb_to_okhsl(RGB rgb) { Lab lab = linear_srgb_to_oklab({ srgb_transfer_function_inv(rgb.r), srgb_transfer_function_inv(rgb.g), srgb_transfer_function_inv(rgb.b) }); float C = sqrtf(lab.a * lab.a + lab.b * lab.b); float a_ = lab.a / C; float b_ = lab.b / C; float L = lab.L; float h = 0.5f + 0.5f * atan2f(-lab.b, -lab.a) / pi; Cs cs = get_Cs(L, a_, b_); float C_0 = cs.C_0; float C_mid = cs.C_mid; float C_max = cs.C_max; // Inverse of the interpolation in okhsl_to_srgb: float mid = 0.8f; float mid_inv = 1.25f; float s; if (C < C_mid) { float k_1 = mid * C_0; float k_2 = (1.f - k_1 / C_mid); float t = C / (k_1 + k_2 * C); s = t * mid; } else { float k_0 = C_mid; float k_1 = (1.f - mid) * C_mid * C_mid * mid_inv * mid_inv / C_0; float k_2 = (1.f - (k_1) / (C_max - C_mid)); float t = (C - k_0) / (k_1 + k_2 * (C - k_0)); s = mid + (1.f - mid) * t; } float l = toe(L); return { h, s, l }; } RGB okhsv_to_srgb(HSV hsv) { float h = hsv.h; float s = hsv.s; float v = hsv.v; float a_ = cosf(2.f * pi * h); float b_ = sinf(2.f * pi * h); LC cusp = find_cusp(a_, b_); ST ST_max = to_ST(cusp); float S_max = ST_max.S; float T_max = ST_max.T; float S_0 = 0.5f; float k = 1 - S_0 / S_max; // first we compute L and V as if the gamut is a perfect triangle: // L, C when v==1: float L_v = 1 - s * S_0 / (S_0 + T_max - T_max * k * s); float C_v = s * T_max * S_0 / (S_0 + T_max - T_max * k * s); float L = v * L_v; float C = v * C_v; // then we compensate for both toe and the curved top part of the triangle: float L_vt = toe_inv(L_v); float C_vt = C_v * L_vt / L_v; float L_new = toe_inv(L); C = C * L_new / L; L = L_new; RGB rgb_scale = oklab_to_linear_srgb({ L_vt, a_ * C_vt, b_ * C_vt }); float scale_L = cbrtf(1.f / fmax(fmax(rgb_scale.r, rgb_scale.g), fmax(rgb_scale.b, 0.f))); L = L * scale_L; C = C * scale_L; RGB rgb = oklab_to_linear_srgb({ L, C * a_, C * b_ }); return { srgb_transfer_function(rgb.r), srgb_transfer_function(rgb.g), srgb_transfer_function(rgb.b), }; } HSV srgb_to_okhsv(RGB rgb) { Lab lab = linear_srgb_to_oklab({ srgb_transfer_function_inv(rgb.r), srgb_transfer_function_inv(rgb.g), srgb_transfer_function_inv(rgb.b) }); float C = sqrtf(lab.a * lab.a + lab.b * lab.b); float a_ = lab.a / C; float b_ = lab.b / C; float L = lab.L; float h = 0.5f + 0.5f * atan2f(-lab.b, -lab.a) / pi; LC cusp = find_cusp(a_, b_); ST ST_max = to_ST(cusp); float S_max = ST_max.S; float T_max = ST_max.T; float S_0 = 0.5f; float k = 1 - S_0 / S_max; // first we find L_v, C_v, L_vt and C_vt float t = T_max / (C + L * T_max); float L_v = t * L; float C_v = t * C; float L_vt = toe_inv(L_v); float C_vt = C_v * L_vt / L_v; // we can then use these to invert the step that compensates for the toe and the curved top part of the triangle: RGB rgb_scale = oklab_to_linear_srgb({ L_vt, a_ * C_vt, b_ * C_vt }); float scale_L = cbrtf(1.f / fmax(fmax(rgb_scale.r, rgb_scale.g), fmax(rgb_scale.b, 0.f))); L = L / scale_L; C = C / scale_L; C = C * toe(L) / L; L = toe(L); // we can now compute v and s: float v = L / L_v; float s = (S_0 + T_max) * C_v / ((T_max * S_0) + T_max * k * C_v); return { h, s, v }; } }; #endif // OK_COLOR_H