symmetric diverging scales by domain extension (#563)

Author: mbostock

src/scales/diverging.js

@@ -51,10 +51,11 @@ function ScaleD(key, scale, transform, channels, {
 
   // Normalize the interpolator for symmetric difference around the pivot.
   if (symmetric) {
-    const mindelta = Math.abs(transform(min) - transform(pivot));
-    const maxdelta = Math.abs(transform(max) - transform(pivot));
-    if (mindelta < maxdelta) interpolate = truncateLower(interpolate, mindelta / maxdelta);
-    else if (mindelta > maxdelta) interpolate = truncateUpper(interpolate, maxdelta / mindelta);
+    const mid = transform.apply(pivot);
+    const mindelta = mid - transform.apply(min);
+    const maxdelta = transform.apply(max) - mid;
+    if (mindelta < maxdelta) min = transform.invert(mid - maxdelta);
+    else if (mindelta > maxdelta) max = transform.invert(mid + mindelta);
   }
 
   scale.domain([min, pivot, max]).unknown(unknown).interpolator(interpolate);
@@ -64,37 +65,66 @@ function ScaleD(key, scale, transform, channels, {
 }
 
 export function ScaleDiverging(key, channels, options) {
-  return ScaleD(key, scaleDiverging(), x => x, channels, options);
+  return ScaleD(key, scaleDiverging(), transformIdentity, channels, options);
 }
 
 export function ScaleDivergingSqrt(key, channels, options) {
   return ScaleDivergingPow(key, channels, {...options, exponent: 0.5});
 }
 
 export function ScaleDivergingPow(key, channels, {exponent = 1, ...options}) {
-  return ScaleD(key, scaleDivergingPow().exponent(exponent), transformPow(exponent), channels, {...options, type: "diverging-pow"});
+  return ScaleD(key, scaleDivergingPow().exponent(exponent = +exponent), transformPow(exponent), channels, {...options, type: "diverging-pow"});
 }
 
 export function ScaleDivergingLog(key, channels, {base = 10, pivot = 1, domain = inferDomain(channels, pivot < 0 ? negative : positive), ...options}) {
-  return ScaleD(key, scaleDivergingLog().base(base), Math.log, channels, {domain, pivot, ...options});
+  return ScaleD(key, scaleDivergingLog().base(base = +base), transformLog, channels, {domain, pivot, ...options});
 }
 
 export function ScaleDivergingSymlog(key, channels, {constant = 1, ...options}) {
-  return ScaleD(key, scaleDivergingSymlog().constant(constant), transformSymlog(constant), channels, options);
+  return ScaleD(key, scaleDivergingSymlog().constant(constant = +constant), transformSymlog(constant), channels, options);
 }
 
-function truncateLower(interpolate, k) {
-  return t => interpolate(t < 0.5 ? t * k + (1 - k) / 2 : t);
-}
+const transformIdentity = {
+  apply(x) {
+    return x;
+  },
+  invert(x) {
+    return x;
+  }
+};
 
-function truncateUpper(interpolate, k) {
-  return t => interpolate(t > 0.5 ? t * k + (1 - k) / 2 : t);
-}
+const transformLog = {
+  apply: Math.log,
+  invert: Math.exp
+};
+
+const transformSqrt = {
+  apply(x) {
+    return Math.sign(x) * Math.sqrt(Math.abs(x));
+  },
+  invert(x) {
+    return Math.sign(x) * (x * x);
+  }
+};
 
 function transformPow(exponent) {
-  return exponent === 0.5 ? Math.sqrt : x => Math.sign(x) * Math.pow(Math.abs(x), exponent);
+  return exponent === 0.5 ? transformSqrt : {
+    apply(x) {
+      return Math.sign(x) * Math.pow(Math.abs(x), exponent);
+    },
+    invert(x) {
+      return Math.sign(x) * Math.pow(Math.abs(x), 1 / exponent);
+    }
+  };
 }
 
 function transformSymlog(constant) {
-  return x => Math.sign(x) * Math.log1p(Math.abs(x / constant));
+  return {
+    apply(x) {
+      return Math.sign(x) * Math.log1p(Math.abs(x / constant));
+    },
+    invert(x) {
+      return Math.sign(x) * Math.expm1(Math.abs(x)) * constant;
+    }
+  };
 }

test/scales/scales-test.js

@@ -393,18 +393,14 @@ it("plot(…).scale('color') can return an asymmetric diverging scale", async ()
 it("plot(…).scale('color') can return a symmetric diverging scale", async () => {
   const gistemp = await d3.csv("data/gistemp.csv", d3.autoType);
   const plot = Plot.dot(gistemp, {x: "Date", stroke: "Anomaly"}).plot({color: {type: "diverging"}});
-  const {interpolate, ...color} = plot.scale("color");
-  assert.deepStrictEqual(color, {
+  assert.deepStrictEqual(plot.scale("color"), {
     type: "diverging",
-    domain: [-0.78, 1.35],
+    domain: [-1.35, 1.35],
+    interpolate: d3.interpolateRdBu,
     pivot: 0,
     clamp: false,
     label: "Anomaly"
   });
-  const k = 0.78 / 1.35;
-  for (const t of d3.ticks(0, 1, 100)) {
-    assert.strictEqual(interpolate(t), d3.interpolateRdBu(t < 0.5 ? t * k + (1 - k) / 2: t));
-  }
 });
 
 it("plot(…).scale('color') can return a diverging scale with an explicit range", async () => {
@@ -455,6 +451,21 @@ it("plot(…).scale('color') can return a transformed diverging scale", async ()
   });
 });
 
+it("plot(…).scale('color') can return a transformed symmetric diverging scale", async () => {
+  const transform = d => d * 100;
+  const gistemp = await d3.csv("data/gistemp.csv", d3.autoType);
+  const plot = Plot.dot(gistemp, {x: "Date", stroke: "Anomaly"}).plot({color: {type: "diverging", transform}});
+  assert.deepStrictEqual(plot.scale("color"), {
+    type: "diverging",
+    domain: [-135, 135],
+    pivot: 0,
+    transform,
+    interpolate: d3.interpolateRdBu,
+    clamp: false,
+    label: "Anomaly"
+  });
+});
+
 it("plot(…).scale('color') can return an asymmetric diverging pow scale with an explicit scheme", async () => {
   const gistemp = await d3.csv("data/gistemp.csv", d3.autoType);
   const plot = Plot.dot(gistemp, {x: "Date", stroke: "Anomaly"}).plot({color: {type: "diverging-sqrt", symmetric: false, scheme: "piyg"}});