Detect coincident points when drawing arcs with rounding.

When rounding is used, it's possible for `arc()` to generate empty arcs
in the case where the start and end points are almost coincident, and
become coincident after rounding is applied.

This adds a check for coincident points after rounding is applied, and
splits the arc into two if coincident points are detected.

Fixes d3#38.

src/path.js

@@ -23,12 +23,33 @@ function appendRound(digits) {
   };
 }
 
+function round(digits) {
+  const k = 10 ** digits;
+  return function(value) {
+    return Math.round(value * k) / k;
+  };
+}
+
+function equal(x0, y0, x1, y1) {
+  return x0 === x1 && y0 === y1;
+}
+
+function equalRound(digits) {
+  let d = Math.floor(digits);
+  if (d > 15) return equal;
+  const r = round(digits);
+  return function(x0, y0, x1, y1) {
+    return r(x0) === r(x1) && r(y0) === r(y1);
+  };
+}
+
 export class Path {
   constructor(digits) {
     this._x0 = this._y0 = // start of current subpath
     this._x1 = this._y1 = null; // end of current subpath
     this._ = "";
     this._append = digits == null ? append : appendRound(digits);
+    this._equal = digits === null ? equal : equalRound(digits);
   }
   moveTo(x, y) {
     this._append`M${this._x0 = this._x1 = +x},${this._y0 = this._y1 = +y}`;
@@ -133,7 +154,15 @@ export class Path {
 
     // Is this arc non-empty? Draw an arc!
     else if (da > epsilon) {
-      this._append`A${r},${r},0,${+(da >= pi)},${cw},${this._x1 = x + r * Math.cos(a1)},${this._y1 = y + r * Math.sin(a1)}`;
+      // If the start and end points are coincident after rounding, we need to draw two arcs.
+      const x1 = x + r * Math.cos(a1);
+      const y1 = y + r * Math.sin(a1);
+      if (this._equal(x0, y0, x1, y1)) {
+        da /= 2;
+        let a00 = a0 + da;
+        this._append`A${r},${r},0,${+(da >= pi)},${cw},${x + r * Math.cos(a00)},${y + r * Math.sin(a00)}`;
+      }
+      this._append`A${r},${r},0,${+(da >= pi)},${cw},${this._x1 = x1},${this._y1 = y1}`;
     }
   }
   rect(x, y, w, h) {

test/pathRound-test.js

@@ -50,6 +50,17 @@ it("pathRound.arc(x, y, r, a0, a1, ccw) limits the precision", () => {
   assert.strictEqual(p + "", precision(p0 + "", 1));
 });
 
+it("pathRound.arc(x, y, r, a0, a1, ccw) draws two arcs for near-circular arcs with rounding", () => {
+  const p0 = path(), p = pathRound(1);
+  const a0 = -1.5707963267948966;
+  const a1 = 4.712383653719071;
+  const a00 = a0 + (a1 - a0) / 2;
+  p0.arc(0, 0, 75, a0, a00, false);
+  p0.arc(0, 0, 75, a00, a1, false);
+  p.arc(0, 0, 75, a0, a1, false);
+  assert.strictEqual(p + "", precision(p0 + "", 1));
+});
+
 it("pathRound.arcTo(x1, y1, x2, y2, r) limits the precision", () => {
   const p0 = path(), p = pathRound(1);
   p0.arcTo(10.0001, 10.0001, 123.456, 456.789, 12345.6789);
@@ -79,5 +90,5 @@ it("pathRound.rect(x, y, w, h) limits the precision", () => {
 });
 
 function precision(str, precision) {
-  return str.replace(/\d+\.\d+/g, s => +parseFloat(s).toFixed(precision));
+  return str.replace(/-?\d+\.\d+(e-?\d+)?/g, s => +parseFloat(s).toFixed(precision));
 }