r2/spatial: add Box methods

spatial/r2/box.go

@@ -0,0 +1,111 @@
+// Copyright ©2022 The Gonum 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 r2
+
+import "math"
+
+// Box is a 2D bounding box. Well formed Boxes have
+// Min components smaller than Max components.
+type Box struct {
+	Min, Max Vec
+}
+
+// NewBox is shorthand for Box{Min:Vec{x0,y0}, Max:Vec{x1,y1}}.
+// The sides are swapped so that the resulting Box is well formed.
+func NewBox(x0, y0, x1, y1 float64) Box {
+	return Box{
+		Min: Vec{X: math.Min(x0, x1), Y: math.Min(y0, y1)},
+		Max: Vec{X: math.Max(x0, x1), Y: math.Max(y0, y1)},
+	}
+}
+
+// Size returns the size of the Box.
+func (a Box) Size() Vec {
+	return Sub(a.Max, a.Min)
+}
+
+// Center returns the center of the Box.
+func (a Box) Center() Vec {
+	return Scale(0.5, Add(a.Min, a.Max))
+}
+
+// IsEmpty returns true if a Box's volume is zero
+// or if a Min component is greater than its Max component.
+func (a Box) Empty() bool {
+	return a.Min.X >= a.Max.X || a.Min.Y >= a.Max.Y
+}
+
+// Vertices returns a slice of the 4 vertices
+// corresponding to each of the Box's corners.
+//
+// The order of the vertices is CCW in the XY plane starting at the box minimum.
+// If viewing box from +Z position the ordering is as follows:
+//  1. Bottom left.
+//  2. Bottom right.
+//  3. Top right.
+//  4. Top left.
+func (a Box) Vertices() []Vec {
+	return []Vec{
+		0: a.Min,
+		1: {a.Max.X, a.Min.Y},
+		2: a.Max,
+		3: {a.Min.X, a.Max.Y},
+	}
+}
+
+// Union returns a box enclosing both the receiver and argument Boxes.
+func (a Box) Union(b Box) Box {
+	if a.Empty() {
+		return b
+	}
+	if b.Empty() {
+		return a
+	}
+	return Box{
+		Min: minElem(a.Min, b.Min),
+		Max: maxElem(a.Max, b.Max),
+	}
+}
+
+// Add adds v to the bounding box components.
+// It is the equivalent of translating the Box by v.
+func (a Box) Add(v Vec) Box {
+	return Box{Add(a.Min, v), Add(a.Max, v)}
+}
+
+// Scale returns a new Box scaled by a size vector around its center.
+// The scaling is done element wise, which is to say the Box's X size is
+// scaled by v.X. Negative components of v are interpreted as zero.
+func (a Box) Scale(v Vec) Box {
+	v = maxElem(v, Vec{})
+	// TODO(soypat): Probably a better way to do this.
+	return centeredBox(a.Center(), mulElem(v, a.Size()))
+}
+
+// centeredBox creates a Box with a given center and size. Size's negative
+// components are interpreted as zero so that resulting box is well formed.
+func centeredBox(center, size Vec) Box {
+	size = maxElem(size, Vec{})
+	half := Scale(0.5, absElem(size))
+	return Box{Min: Sub(center, half), Max: Add(center, half)}
+}
+
+// Contains returns true if v is contained within the bounds of the Box.
+func (a Box) Contains(v Vec) bool {
+	if a.Empty() {
+		return v == a.Min && v == a.Max
+	}
+	return a.Min.X <= v.X && v.X <= a.Max.X &&
+		a.Min.Y <= v.Y && v.Y <= a.Max.Y
+}
+
+// Canon returns the canonical version of b. The returned Box has minimum
+// and maximum coordinates swapped if necessary so that it is well-formed.
+func (b Box) Canon() Box {
+	return Box{
+		Min: minElem(b.Min, b.Max),
+		Max: maxElem(b.Min, b.Max),
+	}
+}