remove halley in computeMaxSaturation

tychota · Nov 24, 2023 · eef941d · eef941d
1 parent d5eaa52
commit eef941d
Showing 1 changed file with 17 additions and 60 deletions.
diff --git a/src/gamut/rgb/oklab.ts b/src/gamut/rgb/oklab.ts
@@ -113,76 +113,33 @@ export abstract class OkLabInterpolateGamutMapping extends OkLabGamutMapping {
     // 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
-    let k0: number, k1: number, k2: number, k3: number, k4: number, wl: number, wm: number, ws: number;
+    let k0: number, k1: number, k2: number, k3: number, k4: number;
 
     if (-1.8817030993265862 * a - 0.8093650129914288 * b > 1) {
       // Red component goes under zero first
-      k0 = +1.4324033467840624;
-      k1 = +2.2781278435823524;
-      k2 = +0.7618497882679983;
-      k3 = +1.0260341945433478;
-      k4 = +0.7617909881094428;
-      wl = +4.0767416360759592;
-      wm = -3.3077115392580625;
-      ws = +0.2309699031821046;
+      k0 = +0.94190725;
+      k1 = +1.25611386;
+      k2 = +0.41951247;
+      k3 = +0.49514579;
+      k4 = +0.36308792;
     } else if (1.8144407988011 * a - 1.1944526678052367 * b > 1) {
       // Green component goes under zero first
-      k0 = +0.7379402524434013;
-      k1 = -0.4573974268862046;
-      k2 = +0.0815143817557270;
-      k3 = +0.1248577516844205;
-      k4 = -0.1434403763698065;
-      wl = -1.2684379732850315;
-      wm = +2.6097573492876882;
-      ws = -0.3413193760026572;
+      k0 = +0.73601075;
+      k1 = -0.44740025;
+      k2 = +0.08048903;
+      k3 = +0.11651011;
+      k4 = -0.14055292;
     } else {
       // Blue component goes under zero first
-      k0 = +1.3195478056858045;
-      k1 = -0.0002163824563852;
-      k2 = -1.1134545687345891;
-      k3 = -0.4851285430136246;
-      k4 = -0.0035353711153529;
-      wl = -0.0041960761386755;
-      wm = -0.7034186179359361;
-      ws = +1.7076146940746113;
+      k0 = +1.2373596;
+      k1 = -0.00419136;
+      k2 = -1.03212593;
+      k3 = -0.4339162;
+      k4 = +0.00108953;
     }
 
     // Approximate max saturation using a polynomial
-    let maxSaturation = 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
-
-    let k_l = +0.3963377773761749 * a + 0.2158037573099136 * b;
-    let k_m = -0.1055613458156586 * a - 0.0638541728258133 * b;
-    let k_s = -0.0894841775298119 * a - 1.2914855480194092 * b;
-
-    const halleyStep = () => {
-      let l_ = 1 + maxSaturation * k_l;
-      let m_ = 1 + maxSaturation * k_m;
-      let s_ = 1 + maxSaturation * k_s;
-
-      let l = l_ ** 3;
-      let m = m_ ** 3;
-      let s = s_ ** 3;
-
-      let l_dS = 3 * k_l * l_ * l_;
-      let m_dS = 3 * k_m * m_ * m_;
-      let s_dS = 3 * k_s * s_ * s_;
-
-      let l_dS2 = 6 * k_l * k_l * l_;
-      let m_dS2 = 6 * k_m * k_m * m_;
-      let s_dS2 = 6 * k_s * k_s * s_;
-
-      let f = wl * l + wm * m + ws * s;
-      let f_dS = wl * l_dS + wm * m_dS + ws * s_dS;
-      let f_dS2 = wl * l_dS2 + wm * m_dS2 + ws * s_dS2;
-
-      maxSaturation = maxSaturation - (f * f_dS) / (f_dS * f_dS - 0.5 * f * f_dS2);
-    };
-
-    repeat(halleyStep, OkLabInterpolateGamutMapping.HALLEY_STEPS_NB);
+    const maxSaturation = k0 + k1 * a + k2 * b + k3 * a * a + k4 * a * b;
 
     return maxSaturation;
   }