Merge branch 'zoom-rho' into two

README.md

@@ -133,6 +133,10 @@ Returns an interpolator between the two views *a* and *b* of a two-dimensional p
 
 The returned interpolator exposes a *duration* property which encodes the recommended transition duration in milliseconds. This duration is based on the path length of the curved trajectory through *x,y* space. If you want a slower or faster transition, multiply this by an arbitrary scale factor (<i>V</i> as described in the original paper).
 
+<a name="interpolate_rho" href="#interpolate_rho">#</a> *interpolateZoom*.<b>rho</b>(<i>rho</i>) · [Source](https://github.com/d3/d3-interpolate/blob/master/src/zoom.js)<!-- , [Examples](https://observablehq.com/@d3/interpolatezoom-rho) -->
+
+Given a [zoom interpolator](#interpolateZoom), returns a new zoom interpolator using the specified curvature *rho*. When *rho* is close to 0, the interpolator is almost linear. The default curvature is sqrt(2).
+
 <a name="interpolateDiscrete" href="#interpolateDiscrete">#</a> d3.<b>interpolateDiscrete</b>(<i>values</i>) · [Source](https://github.com/d3/d3-interpolate/blob/master/src/discrete.js), [Examples](https://observablehq.com/@d3/d3-interpolatediscrete)
 
 Returns a discrete interpolator for the given array of *values*. The returned interpolator maps *t* in [0, 1 / *n*) to *values*[0], *t* in [1 / *n*, 2 / *n*) to *values*[1], and so on, where *n* = *values*.length. In effect, this is a lightweight [quantize scale](https://github.com/d3/d3-scale/blob/master/README.md#quantize-scales) with a fixed domain of [0, 1].

src/zoom.js

@@ -1,7 +1,4 @@
-var rho = Math.SQRT2,
-    rho2 = 2,
-    rho4 = 4,
-    epsilon2 = 1e-12;
+var epsilon2 = 1e-12;
 
 function cosh(x) {
   return ((x = Math.exp(x)) + 1 / x) / 2;
@@ -15,50 +12,60 @@ function tanh(x) {
   return ((x = Math.exp(2 * x)) - 1) / (x + 1);
 }
 
-// p0 = [ux0, uy0, w0]
-// p1 = [ux1, uy1, w1]
-export default function(p0, p1) {
-  var ux0 = p0[0], uy0 = p0[1], w0 = p0[2],
-      ux1 = p1[0], uy1 = p1[1], w1 = p1[2],
-      dx = ux1 - ux0,
-      dy = uy1 - uy0,
-      d2 = dx * dx + dy * dy,
-      i,
-      S;
+export default (function zoomRho(rho, rho2, rho4) {
 
-  // Special case for u0 ≅ u1.
-  if (d2 < epsilon2) {
-    S = Math.log(w1 / w0) / rho;
-    i = function(t) {
-      return [
-        ux0 + t * dx,
-        uy0 + t * dy,
-        w0 * Math.exp(rho * t * S)
-      ];
+  // p0 = [ux0, uy0, w0]
+  // p1 = [ux1, uy1, w1]
+  function zoom(p0, p1) {
+    var ux0 = p0[0], uy0 = p0[1], w0 = p0[2],
+        ux1 = p1[0], uy1 = p1[1], w1 = p1[2],
+        dx = ux1 - ux0,
+        dy = uy1 - uy0,
+        d2 = dx * dx + dy * dy,
+        i,
+        S;
+
+    // Special case for u0 ≅ u1.
+    if (d2 < epsilon2) {
+      S = Math.log(w1 / w0) / rho;
+      i = function(t) {
+        return [
+          ux0 + t * dx,
+          uy0 + t * dy,
+          w0 * Math.exp(rho * t * S)
+        ];
+      }
     }
-  }
 
-  // General case.
-  else {
-    var d1 = Math.sqrt(d2),
-        b0 = (w1 * w1 - w0 * w0 + rho4 * d2) / (2 * w0 * rho2 * d1),
-        b1 = (w1 * w1 - w0 * w0 - rho4 * d2) / (2 * w1 * rho2 * d1),
-        r0 = Math.log(Math.sqrt(b0 * b0 + 1) - b0),
-        r1 = Math.log(Math.sqrt(b1 * b1 + 1) - b1);
-    S = (r1 - r0) / rho;
-    i = function(t) {
-      var s = t * S,
-          coshr0 = cosh(r0),
-          u = w0 / (rho2 * d1) * (coshr0 * tanh(rho * s + r0) - sinh(r0));
-      return [
-        ux0 + u * dx,
-        uy0 + u * dy,
-        w0 * coshr0 / cosh(rho * s + r0)
-      ];
+    // General case.
+    else {
+      var d1 = Math.sqrt(d2),
+          b0 = (w1 * w1 - w0 * w0 + rho4 * d2) / (2 * w0 * rho2 * d1),
+          b1 = (w1 * w1 - w0 * w0 - rho4 * d2) / (2 * w1 * rho2 * d1),
+          r0 = Math.log(Math.sqrt(b0 * b0 + 1) - b0),
+          r1 = Math.log(Math.sqrt(b1 * b1 + 1) - b1);
+      S = (r1 - r0) / rho;
+      i = function(t) {
+        var s = t * S,
+            coshr0 = cosh(r0),
+            u = w0 / (rho2 * d1) * (coshr0 * tanh(rho * s + r0) - sinh(r0));
+        return [
+          ux0 + u * dx,
+          uy0 + u * dy,
+          w0 * coshr0 / cosh(rho * s + r0)
+        ];
+      }
     }
+
+    i.duration = S * 1000 * rho / Math.SQRT2;
+
+    return i;
   }
 
-  i.duration = S * 1000;
+  zoom.rho = function(_) {
+    var _1 = Math.max(1e-3, +_), _2 = _1 * _1, _4 = _2 * _2;
+    return zoomRho(_1, _2, _4);
+  };
 
-  return i;
-}
+  return zoom;
+})(Math.SQRT2, 2, 4);

test/inDelta.js

@@ -1,10 +1,26 @@
 var tape = require("tape");
 
-tape.Test.prototype.inDelta = function(actual, expected) {
-  this._assert(expected - 1e-6 < actual && actual < expected + 1e-6, {
-    message: "should be in delta",
+tape.Test.prototype.inDelta = function(actual, expected, delta) {
+  delta = delta || 1e-6;
+  this._assert(inDelta(actual, expected, delta), {
+    message: "should be in delta " + delta,
     operator: "inDelta",
     actual: actual,
     expected: expected
   });
 };
+
+function inDelta(actual, expected, delta) {
+  return (Array.isArray(expected) ? inDeltaArray : inDeltaNumber)(actual, expected, delta);
+}
+
+function inDeltaArray(actual, expected, delta) {
+  var n = expected.length, i = -1;
+  if (actual.length !== n) return false;
+  while (++i < n) if (!inDelta(actual[i], expected[i], delta)) return false;
+  return true;
+}
+
+function inDeltaNumber(actual, expected, delta) {
+  return actual >= expected - delta && actual <= expected + delta;
+}

test/zoom-test.js

@@ -5,3 +5,32 @@ tape("interpolateZoom(a, b) handles nearly-coincident points", function(test) {
   test.deepEqual(interpolate.interpolateZoom([324.68721096803614, 59.43501602433761, 1.8827137399562621], [324.6872108946794, 59.43501601062763, 7.399052110984391])(0.5), [324.68721093135775, 59.43501601748262, 3.7323313186268305]);
   test.end();
 });
+
+tape("interpolateZoom returns the expected duration", function(test) {
+  test.inDelta(interpolate.interpolateZoom([0, 0, 1], [0, 0, 1.1]).duration, 67, 1);
+  test.inDelta(interpolate.interpolateZoom([0, 0, 1], [0, 0, 2]).duration, 490, 1);
+  test.inDelta(interpolate.interpolateZoom([0, 0, 1], [10, 0, 8]).duration, 2872.5, 1);
+  test.end();
+});
+
+tape("interpolateZoom parameter rho() defaults to sqrt(2)", function(test) {
+  test.inDelta(
+    interpolate.interpolateZoom([0,0,1], [10, 10, 5])(0.5),
+    interpolate.interpolateZoom.rho(Math.sqrt(2))([0,0,1], [10, 10, 5])(0.5),
+  );
+  test.end();
+});
+
+tape("interpolateZoom.rho(0) is (almost) linear", function(test) {
+  const interp = interpolate.interpolateZoom.rho(0)([0, 0, 1], [10, 0, 8]);
+  test.inDelta(interp(0.5), [1.111, 0, Math.sqrt(8)], 1e-3);
+  test.equal(Math.round(interp.duration), 1470);
+  test.end();
+});
+
+tape("interpolateZoom parameter rho(2) has a high curvature and takes more time", function(test) {
+  const interp = interpolate.interpolateZoom.rho(2)([0, 0, 1], [10, 0, 8]);
+  test.inDelta(interp(0.5), [1.111, 0, 12.885], 1e-3);
+  test.equal(Math.round(interp.duration), 3775);
+  test.end();
+});