image: fix Rectangle.Overlaps and Rectangle.Union for empty rectangles.

Fixes #9895.

Change-Id: I37d78ced9ff8196e32d299504908a1c41ad4592d
Reviewed-on: https://go-review.googlesource.com/4990Reviewed-by: Rob Pike <r@golang.org>

src/image/geom.go

@@ -164,6 +164,12 @@ func (r Rectangle) Intersect(s Rectangle) Rectangle {
 
 // Union returns the smallest rectangle that contains both r and s.
 func (r Rectangle) Union(s Rectangle) Rectangle {
+	if r.Empty() {
+		return s
+	}
+	if s.Empty() {
+		return r
+	}
 	if r.Min.X > s.Min.X {
 		r.Min.X = s.Min.X
 	}
@@ -192,7 +198,8 @@ func (r Rectangle) Eq(s Rectangle) bool {
 
 // Overlaps reports whether r and s have a non-empty intersection.
 func (r Rectangle) Overlaps(s Rectangle) bool {
-	return r.Min.X < s.Max.X && s.Min.X < r.Max.X &&
+	return !r.Empty() && !s.Empty() &&
+		r.Min.X < s.Max.X && s.Min.X < r.Max.X &&
 		r.Min.Y < s.Max.Y && s.Min.Y < r.Max.Y
 }
 

src/image/geom_test.go

+// Copyright 2015 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package image
+
+import (
+	"fmt"
+	"testing"
+)
+
+func TestRectangle(t *testing.T) {
+	// in checks that every point in f is in g.
+	in := func(f, g Rectangle) error {
+		if !f.In(g) {
+			return fmt.Errorf("f=%s, f.In(%s): got false, want true", f, g)
+		}
+		for y := f.Min.Y; y < f.Max.Y; y++ {
+			for x := f.Min.X; x < f.Max.X; x++ {
+				p := Point{x, y}
+				if !p.In(g) {
+					return fmt.Errorf("p=%s, p.In(%s): got false, want true", p, g)
+				}
+			}
+		}
+		return nil
+	}
+
+	rects := []Rectangle{
+		Rect(0, 0, 10, 10),
+		Rect(1, 2, 3, 4),
+		Rect(4, 6, 10, 10),
+		Rect(2, 3, 12, 5),
+		Rect(-1, -2, 0, 0),
+		Rect(-1, -2, 4, 6),
+		Rect(-10, -20, 30, 40),
+		Rect(8, 8, 8, 8),
+		Rect(88, 88, 88, 88),
+		Rect(6, 5, 4, 3),
+	}
+
+	// The intersection should be the largest rectangle a such that every point
+	// in a is both in r and in s.
+	for _, r := range rects {
+		for _, s := range rects {
+			a := r.Intersect(s)
+			if err := in(a, r); err != nil {
+				t.Errorf("Intersect: r=%s, s=%s, a=%s, a not in r: %v", r, s, a, err)
+			}
+			if err := in(a, s); err != nil {
+				t.Errorf("Intersect: r=%s, s=%s, a=%s, a not in s: %v", r, s, a, err)
+			}
+			if a.Empty() == r.Overlaps(s) {
+				t.Errorf("Intersect: r=%s, s=%s, a=%s: empty=%t same as overlaps=%t",
+					r, s, a, a.Empty(), r.Overlaps(s))
+			}
+			largerThanA := [4]Rectangle{a, a, a, a}
+			largerThanA[0].Min.X--
+			largerThanA[1].Min.Y--
+			largerThanA[2].Max.X++
+			largerThanA[3].Max.Y++
+			for i, b := range largerThanA {
+				if b.Empty() {
+					// b isn't actually larger than a.
+					continue
+				}
+				if in(b, r) == nil && in(b, s) == nil {
+					t.Errorf("Intersect: r=%s, s=%s, a=%s, b=%s, i=%d: intersection could be larger",
+						r, s, a, b, i)
+				}
+			}
+		}
+	}
+
+	// The union should be the smallest rectangle a such that every point in r
+	// is in a and every point in s is in a.
+	for _, r := range rects {
+		for _, s := range rects {
+			a := r.Union(s)
+			if err := in(r, a); err != nil {
+				t.Errorf("Union: r=%s, s=%s, a=%s, r not in a: %v", r, s, a, err)
+			}
+			if err := in(s, a); err != nil {
+				t.Errorf("Union: r=%s, s=%s, a=%s, s not in a: %v", r, s, a, err)
+			}
+			if a.Empty() {
+				// You can't get any smaller than a.
+				continue
+			}
+			smallerThanA := [4]Rectangle{a, a, a, a}
+			smallerThanA[0].Min.X++
+			smallerThanA[1].Min.Y++
+			smallerThanA[2].Max.X--
+			smallerThanA[3].Max.Y--
+			for i, b := range smallerThanA {
+				if in(r, b) == nil && in(s, b) == nil {
+					t.Errorf("Union: r=%s, s=%s, a=%s, b=%s, i=%d: union could be smaller",
+						r, s, a, b, i)
+				}
+			}
+		}
+	}
+}