exp/draw: clip destination rectangle to the image bounds.

image: introduce Intersect and Union rectangle methods.

R=r, rog, nigeltao
CC=golang-dev
https://golang.org/cl/2115043

src/pkg/exp/draw/draw.go

@@ -60,9 +60,10 @@ func DrawMask(dst Image, r image.Rectangle, src image.Image, sp image.Point, mas
 	if r.Dy() > dy {
 		r.Max.Y = r.Min.Y + dy
 	}
-
-	// TODO(nigeltao): Clip r to dst's bounding box, and handle the case when sp or mp has negative X or Y.
-	// TODO(nigeltao): Ensure that r is well formed, i.e. r.Max.X >= r.Min.X and likewise for Y.
+	r = r.Intersect(dst.Bounds())
+	if r.Empty() {
+		return
+	}
 
 	// Fast paths for special cases. If none of them apply, then we fall back to a general but slow implementation.
 	if dst0, ok := dst.(*image.RGBA); ok {

src/pkg/image/geom.go

@@ -37,6 +37,9 @@ func Pt(X, Y int) Point {
 }
 
 // A Rectangle contains the points with Min.X <= X < Max.X, Min.Y <= Y < Max.Y.
+// It is well-formed if Min.X <= Max.X and likewise for Y. Points are always
+// well-formed. A rectangle's methods always return well-formed outputs for
+// well-formed inputs.
 type Rectangle struct {
 	Min, Max Point
 }
@@ -72,12 +75,63 @@ func (r Rectangle) Sub(p Point) Rectangle {
 	}
 }
 
-// Inset returns the rectangle r inset by n, which may be negative.
+// Inset returns the rectangle r inset by n, which may be negative. If either
+// of r's dimensions is less than 2*n then an empty rectangle near the center
+// of r will be returned.
 func (r Rectangle) Inset(n int) Rectangle {
-	return Rectangle{
-		Point{r.Min.X + n, r.Min.Y + n},
-		Point{r.Max.X - n, r.Max.Y - n},
+	if r.Dx() < 2*n {
+		r.Min.X = (r.Min.X + r.Max.X) / 2
+		r.Max.X = r.Min.X
+	} else {
+		r.Min.X += n
+		r.Max.X -= n
 	}
+	if r.Dy() < 2*n {
+		r.Min.Y = (r.Min.Y + r.Max.Y) / 2
+		r.Max.Y = r.Min.Y
+	} else {
+		r.Min.Y += n
+		r.Max.Y -= n
+	}
+	return r
+}
+
+// Intersect returns the largest rectangle contained by both r and s. If the
+// two rectangles do not overlap then the zero rectangle will be returned.
+func (r Rectangle) Intersect(s Rectangle) Rectangle {
+	if r.Min.X < s.Min.X {
+		r.Min.X = s.Min.X
+	}
+	if r.Min.Y < s.Min.Y {
+		r.Min.Y = s.Min.Y
+	}
+	if r.Max.X > s.Max.X {
+		r.Max.X = s.Max.X
+	}
+	if r.Max.Y > s.Max.Y {
+		r.Max.Y = s.Max.Y
+	}
+	if r.Min.X > r.Max.X || r.Min.Y > r.Max.Y {
+		return ZR
+	}
+	return r
+}
+
+// Union returns the smallest rectangle that contains both r and s.
+func (r Rectangle) Union(s Rectangle) Rectangle {
+	if r.Min.X > s.Min.X {
+		r.Min.X = s.Min.X
+	}
+	if r.Min.Y > s.Min.Y {
+		r.Min.Y = s.Min.Y
+	}
+	if r.Max.X < s.Max.X {
+		r.Max.X = s.Max.X
+	}
+	if r.Max.Y < s.Max.Y {
+		r.Max.Y = s.Max.Y
+	}
+	return r
 }
 
 // Empty returns whether the rectangle contains no points.
@@ -103,9 +157,8 @@ func (r Rectangle) Contains(p Point) bool {
 		p.Y >= r.Min.Y && p.Y < r.Max.Y
 }
 
-// Canon returns the canonical version of r. The returned rectangle has
-// minimum and maximum coordinates swapped if necessary so that Min.X <= Max.X
-// and Min.Y <= Max.Y.
+// Canon returns the canonical version of r. The returned rectangle has minimum
+// and maximum coordinates swapped if necessary so that it is well-formed.
 func (r Rectangle) Canon() Rectangle {
 	if r.Max.X < r.Min.X {
 		r.Min.X, r.Max.X = r.Max.X, r.Min.X