feat(r1): Interval.approxEqual, Interval.directedHausdorffDistance

missinglink · Jul 19, 2024 · 3422fe8 · 3422fe8
1 parent c21d906
commit 3422fe8
Show file tree

Hide file tree

Showing 2 changed files with 62 additions and 0 deletions.
diff --git a/r1/Interval.ts b/r1/Interval.ts
@@ -137,6 +137,26 @@ export class Interval {
     return new Interval(this.lo - margin, this.hi + margin)
   }
 
+  /**
+   * Reports whether the interval can be transformed into the given interval by moving each endpoint a small distance.
+   * The empty interval is considered to be positioned arbitrarily on the real line, so any interval with a small enough length will match the empty interval.
+   */
+  approxEqual(oi: Interval): boolean {
+    if (this.isEmpty()) return oi.length() <= 2 * 1e-15
+    if (oi.isEmpty()) return this.length() <= 2 * 1e-15
+    return Math.abs(oi.lo - this.lo) <= 1e-15 && Math.abs(oi.hi - this.hi) <= 1e-15
+  }
+
+  /**
+   * Returns the Hausdorff distance to the given interval. For two intervals x and y, this distance is defined as:
+   * h(x, y) = max_{p in x} min_{q in y} d(p, q).
+   */
+  directedHausdorffDistance(oi: Interval): number {
+    if (this.isEmpty()) return 0
+    if (oi.isEmpty()) return Infinity
+    return Math.max(0, Math.max(this.hi - oi.hi, oi.lo - this.lo))
+  }
+
   /**
    * Truncates {lo, hi} floats to n digits of precision.
    */

diff --git a/r1/Interval_test.ts b/r1/Interval_test.ts
@@ -120,6 +120,48 @@ test('expanded', t => {
   ok(UNIT.expanded(-0.51).equal(EMPTY))
 })
 
+test('approxEqual', t => {
+  // Choose two values lo and hi such that it's okay to shift an endpoint by
+  // kLo (i.e., the resulting interval is equivalent) but not by kHi.
+  const lo = 4 * 2.220446049250313e-16 // < max_error default
+  const hi = 6 * 2.220446049250313e-16 // > max_error default
+
+  // Empty intervals.
+  ok(EMPTY.approxEqual(EMPTY))
+  ok(new Interval(0, 0).approxEqual(EMPTY))
+  ok(EMPTY.approxEqual(new Interval(0, 0)))
+  ok(new Interval(1, 1).approxEqual(EMPTY))
+  ok(EMPTY.approxEqual(new Interval(1, 1)))
+  ok(!EMPTY.approxEqual(new Interval(0, 1)))
+  ok(EMPTY.approxEqual(new Interval(1, 1 + 2 * lo)))
+  ok(!EMPTY.approxEqual(new Interval(1, 1 + 2 * hi)))
+
+  // Singleton intervals.
+  ok(new Interval(1, 1).approxEqual(new Interval(1, 1)))
+  ok(new Interval(1, 1).approxEqual(new Interval(1 - lo, 1 - lo)))
+  ok(new Interval(1, 1).approxEqual(new Interval(1 + lo, 1 + lo)))
+  ok(!new Interval(1, 1).approxEqual(new Interval(1 - hi, 1)))
+  ok(!new Interval(1, 1).approxEqual(new Interval(1, 1 + hi)))
+  ok(new Interval(1, 1).approxEqual(new Interval(1 - lo, 1 + lo)))
+  ok(!new Interval(0, 0).approxEqual(new Interval(1, 1)))
+
+  // Other intervals.
+  ok(new Interval(1 - lo, 2 + lo).approxEqual(new Interval(1, 2)))
+  ok(new Interval(1 + lo, 2 - lo).approxEqual(new Interval(1, 2)))
+  ok(!new Interval(1 - hi, 2 + lo).approxEqual(new Interval(1, 2)))
+  ok(!new Interval(1 + hi, 2 - lo).approxEqual(new Interval(1, 2)))
+  ok(!new Interval(1 - lo, 2 + hi).approxEqual(new Interval(1, 2)))
+  ok(!new Interval(1 + lo, 2 - hi).approxEqual(new Interval(1, 2)))
+})
+
+test('directedHausdorffDistance', t => {
+  equal(EMPTY.directedHausdorffDistance(EMPTY), 0)
+  equal(UNIT.directedHausdorffDistance(EMPTY), Infinity)
+  equal(new Interval(1, 1).directedHausdorffDistance(new Interval(1, 1)), 0)
+  equal(new Interval(1, 3).directedHausdorffDistance(new Interval(1, 1)), 2)
+  equal(new Interval(1, 1).directedHausdorffDistance(new Interval(3, 5)), 2)
+})
+
 test('toString', t => {
   equal(new Interval(2, 4.5).toString(), '[2.0000000, 4.5000000]')
 })