plot.scale("projection")

docs/features/plots.md

@@ -313,7 +313,7 @@ const color = plot.scale("color"); // get the color scale
 console.log(color.range); // inspect the scale’s range
 ```
 
-Returns the [scale object](./scales.md#scale-options) for the scale with the specified *name* (such as *x* or *color*) on the given *plot*, where *plot* is a rendered plot element returned by [plot](#plot). If the associated *plot* has no scale with the given *name*, returns undefined.
+Given a rendered *plot* element returned by [plot](#plot), returns the *plot*’s [scale object](./scales.md#scale-options) for the scale with the specified *name* (such as *x* or *color*), or the [projection](./projections.md) if the *name* is *projection*. If the associated *plot* has no scale (or projection) with the given *name*, returns undefined.
 
 ## *plot*.legend(*name*, *options*) {#plot_legend}
 

docs/features/projections.md

@@ -274,3 +274,19 @@ The following projection clipping methods are supported for **clip**:
 * null or false - do not clip
 
 Whereas the **clip** [mark option](./marks.md#mark-options) is implemented using SVG clipping, the **clip** projection option affects the generated geometry and typically produces smaller SVG output.
+
+## Materialized projection
+
+After rendering, you can retrieve the materialized projection from a plot using [*plot*.scale](./plots.md#plot_scale):
+
+```js
+const plot = Plot.plot({projection: "mercator", marks: [Plot.graticule()]});
+const projection = plot.scale("projection");
+```
+
+The returned object exposes a *projection*.stream method (see d3-geo) that can be used to project geometry, as well as *projection*.apply(*point*) and (if supported) *projection*.invert(*point*). To reuse a projection across plots, pass the projection object as the **projection** option of another plot:
+
+```js
+const plot1 = Plot.plot({projection: "mercator", marks: [Plot.graticule()]});
+const plot2 = Plot.plot({projection: plot1.scale("projection"), marks: [Plot.geo(land)]});
+```

src/context.d.ts

@@ -1,5 +1,6 @@
-import type {GeoPath, GeoStreamWrapper} from "d3";
+import type {GeoPath} from "d3";
 import type {MarkOptions} from "./mark.js";
+import type {Projection} from "./projection.js";
 
 /** Additional rendering context provided to marks and initializers. */
 export interface Context {
@@ -16,7 +17,7 @@ export interface Context {
   className: string;
 
   /** The current projection, if any. */
-  projection?: GeoStreamWrapper;
+  projection?: Projection;
 
   /** A function to draw GeoJSON with the current projection, if any, otherwise with the x and y scales. */
   path: () => GeoPath;

src/plot.d.ts

@@ -2,6 +2,7 @@ import type {ChannelValue} from "./channel.js";
 import type {ColorLegendOptions, LegendOptions, OpacityLegendOptions, SymbolLegendOptions} from "./legends.js";
 import type {Data, MarkOptions, Markish} from "./mark.js";
 import type {ProjectionFactory, ProjectionImplementation, ProjectionName, ProjectionOptions} from "./projection.js";
+import type {Projection} from "./projection.js";
 import type {Scale, ScaleDefaults, ScaleName, ScaleOptions} from "./scales.js";
 
 export interface PlotOptions extends ScaleDefaults {
@@ -406,6 +407,12 @@ export interface Plot {
    */
   scale(name: ScaleName): Scale | undefined;
 
+  /**
+   * Returns this plot’s projection, or undefined if this plot does not use a
+   * projection.
+   */
+  scale(name: "projection"): Projection | undefined;
+
   /**
    * Generates a legend for the scale with the specified *name* and the given
    * *options*, returning either an SVG or HTML element depending on the scale

src/plot.js

@@ -340,7 +340,7 @@ export function plot(options = {}) {
     if ("value" in svg) (figure.value = svg.value), delete svg.value;
   }
 
-  figure.scale = exposeScales(scales.scales);
+  figure.scale = exposeScales(scales.scales, context);
   figure.legend = exposeLegends(scaleDescriptors, context, options);
 
   const w = consumeWarnings();

src/projection.d.ts

@@ -112,3 +112,12 @@ export interface ProjectionOptions extends InsetOptions {
    */
   clip?: boolean | number | "frame" | null;
 }
+
+/** A materialized projection, as returned by plot.scale("projection"). */
+export interface Projection extends ProjectionImplementation {
+  /** Returns the projected [x, y] coordinates for the given [longitude, latitude], if possible. */
+  apply(point: [longitude: number, latitude: number]): [x: number, y: number] | null;
+
+  /** Returns the the unprojected [longitude, latitude] for the given [x, y] coordinates, if possible. */
+  invert?(point: [x: number, y: number]): [longitude: number, latitude: number] | null;
+}

src/projection.js

@@ -38,7 +38,7 @@ export function createProjection(
   dimensions
 ) {
   if (projection == null) return;
-  if (typeof projection.stream === "function") return projection; // d3 projection
+  if (typeof projection.stream === "function") return exposeProjection(projection); // projection implementation
   let options;
   let domain;
   let clip = "frame";
@@ -80,34 +80,48 @@ export function createProjection(
   let tx = marginLeft + insetLeft;
   let ty = marginTop + insetTop;
   let transform;
+  let k = 1;
 
   // If a domain is specified, fit the projection to the frame.
   if (domain != null) {
     const [[x0, y0], [x1, y1]] = geoPath(projection).bounds(domain);
-    const k = Math.min(dx / (x1 - x0), dy / (y1 - y0));
+    k = Math.min(dx / (x1 - x0), dy / (y1 - y0));
     if (k > 0) {
       tx -= (k * (x0 + x1) - dx) / 2;
       ty -= (k * (y0 + y1) - dy) / 2;
-      transform = geoTransform({
-        point(x, y) {
-          this.stream.point(x * k + tx, y * k + ty);
-        }
-      });
+      transform = scaleAndTranslate(k, tx, ty);
     } else {
       warn(`Warning: the projection could not be fit to the specified domain; using the default scale.`);
     }
   }
 
-  transform ??=
-    tx === 0 && ty === 0
-      ? identity()
-      : geoTransform({
-          point(x, y) {
-            this.stream.point(x + tx, y + ty);
-          }
-        });
+  transform ??= translate(tx, ty);
 
-  return {stream: (s) => projection.stream(transform.stream(clip(s)))};
+  return {
+    stream(s) {
+      return projection.stream(transform.stream(clip(s)));
+    },
+    apply(p) {
+      let result = null;
+      this.stream({point: (...p) => (result = p)}).point(...p);
+      return result;
+    },
+    ...(projection.invert && {
+      invert(p) {
+        return projection.invert(transform.invert(p));
+      }
+    })
+  };
+}
+
+function exposeProjection(projection) {
+  return typeof projection === "function"
+    ? {
+        stream: (s) => projection.stream(s),
+        apply: (p) => projection(p),
+        ...(projection.invert && {invert: (p) => projection.invert(p)})
+      }
+    : projection;
 }
 
 function namedProjection(projection) {
@@ -195,15 +209,45 @@ function conicProjection(createProjection, kx, ky) {
   };
 }
 
-const identity = constant({stream: (stream) => stream});
+const identity = constant({
+  stream: (stream) => stream,
+  invert: (point) => point
+});
 
-const reflectY = constant(
-  geoTransform({
+const reflectY = constant({
+  ...geoTransform({
     point(x, y) {
       this.stream.point(x, -y);
     }
-  })
-);
+  }),
+  invert: ([x, y]) => [x, -y]
+});
+
+function translate(tx, ty) {
+  return tx === 0 && ty === 0
+    ? identity()
+    : {
+        ...geoTransform({
+          point(x, y) {
+            this.stream.point(x + tx, y + ty);
+          }
+        }),
+        invert: ([x, y]) => [x - tx, y - ty]
+      };
+}
+
+function scaleAndTranslate(k, tx, ty) {
+  return k === 1
+    ? translate(tx, ty)
+    : {
+        ...geoTransform({
+          point(x, y) {
+            this.stream.point(x * k + tx, y * k + ty);
+          }
+        }),
+        invert: ([x, y]) => [(x - tx) / k, (y - ty) / k]
+      };
+}
 
 // Applies a point-wise projection to the given paired x and y channels.
 // Note: mutates values!

src/scales.js

@@ -532,10 +532,10 @@ export function scale(options = {}) {
   return scale;
 }
 
-export function exposeScales(scales) {
+export function exposeScales(scales, context) {
   return (key) => {
     if (!registry.has((key = `${key}`))) throw new Error(`unknown scale: ${key}`);
-    return scales[key];
+    return (key === "projection" ? context : scales)[key];
   };
 }
 

test/assert.js

@@ -58,10 +58,25 @@ async function doesNotWarnAsync(run) {
   return result;
 }
 
+function allCloseTo(actual, expected, delta = 1e-6) {
+  delta = Number(delta);
+  actual = [...actual].map(Number);
+  expected = [...expected].map(Number);
+  assert(
+    actual.length === expected.length && actual.every((a, i) => Math.abs(expected[i] - a) <= delta),
+    `expected ${formatNumbers(actual)} to be close to ${formatNumbers(expected)} ±${delta}`
+  );
+}
+
+function formatNumbers(numbers) {
+  return `[${numbers.map((n) => n.toFixed(6)).join(", ")}]`;
+}
+
 export default {
   ...assert,
   warns,
   warnsAsync,
   doesNotWarn,
-  doesNotWarnAsync
+  doesNotWarnAsync,
+  allCloseTo
 };

test/scales/scales-test.js

@@ -1,7 +1,7 @@
 import * as Plot from "@observablehq/plot";
 import * as d3 from "d3";
 import assert from "../assert.js";
-import {it} from "vitest";
+import {describe, it} from "vitest";
 
 // TODO Expose as d3.schemeObservable10, or Plot.scheme("observable10")?
 const schemeObservable10 = [
@@ -2309,3 +2309,113 @@ function scaleApply(x, pairs) {
     assert.strictEqual(+x.invert(output).toFixed(10), input);
   }
 }
+
+describe("plot(…).scale('projection')", () => {
+  it("returns undefined when no projection is used", () => {
+    const plot = Plot.frame().plot();
+    assert.strictEqual(plot.scale("projection"), undefined);
+  });
+
+  it("returns the projection for a named projection", () => {
+    const plot = Plot.plot({projection: "mercator", marks: [Plot.graticule()]});
+    const projection = plot.scale("projection");
+    assert.strictEqual(d3.geoPath(projection)({type: "Point", coordinates: [-1.55, 47.22]}), "M316.749,224.179m0,4.5a4.5,4.5 0 1,1 0,-9a4.5,4.5 0 1,1 0,9z"); // prettier-ignore
+    assert.allCloseTo(projection.apply([-1.55, 47.22]), [316.74875, 224.179291]);
+    assert.allCloseTo(projection.invert([316.74875, 224.179291]), [-1.55, 47.22]);
+  });
+
+  it("returns the projection for a projection implementation", () => {
+    const plot = Plot.plot({projection: d3.geoMercator(), marks: [Plot.graticule()]});
+    const projection = plot.scale("projection");
+    assert.strictEqual(d3.geoPath(projection)({type: "Point", coordinates: [-1.55, 47.22]}), "M475.862,106.646m0,4.5a4.5,4.5 0 1,1 0,-9a4.5,4.5 0 1,1 0,9z"); // prettier-ignore
+    assert.allCloseTo(projection.apply([-1.55, 47.22]), [475.862361, 106.646008]);
+    assert.allCloseTo(projection.invert([475.862361, 106.646008]), [-1.55, 47.22]);
+  });
+
+  it("is the same for 'mercator' and {type: 'mercator'}", () => {
+    const projection1 = Plot.plot({projection: "mercator", marks: [Plot.graticule()]}).scale("projection");
+    const projection2 = Plot.plot({projection: {type: "mercator"}, marks: [Plot.graticule()]}).scale("projection");
+    assert.allCloseTo(projection1.apply([-1.55, 47.22]), projection2.apply([-1.55, 47.22]));
+    assert.allCloseTo(projection1.invert([316.74875, 224.179291]), projection2.invert([316.74875, 224.179291]));
+  });
+
+  it("exposes apply and invert for identity", () => {
+    const domain = {
+      type: "Polygon",
+      coordinates: [
+        [
+          [0, 0],
+          [200, 0],
+          [200, 100],
+          [0, 100],
+          [0, 0]
+        ]
+      ]
+    };
+    const plot = Plot.plot({
+      width: 400,
+      height: 200,
+      margin: 0,
+      projection: {type: "identity", domain},
+      marks: [Plot.frame()]
+    });
+    const p = plot.scale("projection");
+    assert.allCloseTo(p.apply([0, 0]), [0, 0]);
+    assert.allCloseTo(p.apply([200, 100]), [400, 200]);
+    assert.allCloseTo(p.apply([100, 50]), [200, 100]);
+    assert.allCloseTo(p.invert([0, 0]), [0, 0]);
+    assert.allCloseTo(p.invert([400, 200]), [200, 100]);
+    assert.allCloseTo(p.invert([200, 100]), [100, 50]);
+  });
+
+  it("exposes apply and invert for reflect-y", () => {
+    const domain = {
+      type: "Polygon",
+      coordinates: [
+        [
+          [0, 0],
+          [200, 0],
+          [200, 100],
+          [0, 100],
+          [0, 0]
+        ]
+      ]
+    };
+    const plot = Plot.plot({
+      width: 400,
+      height: 200,
+      margin: 0,
+      projection: {type: "reflect-y", domain},
+      marks: [Plot.frame()]
+    });
+    const p = plot.scale("projection");
+    assert.allCloseTo(p.apply([0, 0]), [0, 200]);
+    assert.allCloseTo(p.apply([200, 100]), [400, 0]);
+    assert.allCloseTo(p.apply([100, 50]), [200, 100]);
+    assert.allCloseTo(p.invert([0, 200]), [0, 0]);
+    assert.allCloseTo(p.invert([400, 0]), [200, 100]);
+    assert.allCloseTo(p.invert([200, 100]), [100, 50]);
+  });
+
+  it("round-trips to a second plot", () => {
+    const plot1 = Plot.plot({projection: "mercator", marks: [Plot.graticule()]});
+    const p1 = plot1.scale("projection");
+    const plot2 = Plot.plot({projection: p1, marks: [Plot.graticule()]});
+    const p2 = plot2.scale("projection");
+    // Same dimensions, so pixel coordinates match
+    const point = [-1.55, 47.22];
+    assert.allCloseTo(p1.apply(point), p2.apply(point));
+  });
+
+  it("round-trips with different dimensions", () => {
+    const plot1 = Plot.plot({width: 640, projection: "mercator", marks: [Plot.graticule()]});
+    const projection1 = plot1.scale("projection");
+    const plot2 = Plot.plot({width: 300, projection: projection1, marks: [Plot.graticule()]});
+    const projection2 = plot2.scale("projection");
+    // Different dimensions, but pixel coordinates still match
+    assert.allCloseTo(projection1.apply([-1.55, 47.22]), [316.74875, 224.179291]);
+    assert.allCloseTo(projection2.apply([-1.55, 47.22]), [316.74875, 224.179291]);
+    // But invert still round-trips
+    assert.allCloseTo(projection2.invert(projection2.apply([-1.55, 47.22])), [-1.55, 47.22]);
+  });
+});