Initial commit

vendor/golang.org/x/image/LICENSE

@@ -0,0 +1,27 @@
+Copyright (c) 2009 The Go Authors. All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+   * Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+   * Redistributions in binary form must reproduce the above
+copyright notice, this list of conditions and the following disclaimer
+in the documentation and/or other materials provided with the
+distribution.
+   * Neither the name of Google Inc. nor the names of its
+contributors may be used to endorse or promote products derived from
+this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

vendor/golang.org/x/image/PATENTS

@@ -0,0 +1,22 @@
+Additional IP Rights Grant (Patents)
+
+"This implementation" means the copyrightable works distributed by
+Google as part of the Go project.
+
+Google hereby grants to You a perpetual, worldwide, non-exclusive,
+no-charge, royalty-free, irrevocable (except as stated in this section)
+patent license to make, have made, use, offer to sell, sell, import,
+transfer and otherwise run, modify and propagate the contents of this
+implementation of Go, where such license applies only to those patent
+claims, both currently owned or controlled by Google and acquired in
+the future, licensable by Google that are necessarily infringed by this
+implementation of Go.  This grant does not include claims that would be
+infringed only as a consequence of further modification of this
+implementation.  If you or your agent or exclusive licensee institute or
+order or agree to the institution of patent litigation against any
+entity (including a cross-claim or counterclaim in a lawsuit) alleging
+that this implementation of Go or any code incorporated within this
+implementation of Go constitutes direct or contributory patent
+infringement, or inducement of patent infringement, then any patent
+rights granted to you under this License for this implementation of Go
+shall terminate as of the date such litigation is filed.

vendor/golang.org/x/image/font/BUILD.bazel

@@ -0,0 +1,24 @@
+load("@io_bazel_rules_go//go:def.bzl", "go_library")
+
+go_library(
+    name = "go_default_library",
+    srcs = ["font.go"],
+    importmap = "go-common/vendor/golang.org/x/image/font",
+    importpath = "golang.org/x/image/font",
+    visibility = ["//visibility:public"],
+    deps = ["//vendor/golang.org/x/image/math/fixed:go_default_library"],
+)
+
+filegroup(
+    name = "package-srcs",
+    srcs = glob(["**"]),
+    tags = ["automanaged"],
+    visibility = ["//visibility:private"],
+)
+
+filegroup(
+    name = "all-srcs",
+    srcs = [":package-srcs"],
+    tags = ["automanaged"],
+    visibility = ["//visibility:public"],
+)

vendor/golang.org/x/image/font/font.go

@@ -0,0 +1,359 @@
+// 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 font defines an interface for font faces, for drawing text on an
+// image.
+//
+// Other packages provide font face implementations. For example, a truetype
+// package would provide one based on .ttf font files.
+package font // import "golang.org/x/image/font"
+
+import (
+	"image"
+	"image/draw"
+	"io"
+	"unicode/utf8"
+
+	"golang.org/x/image/math/fixed"
+)
+
+// TODO: who is responsible for caches (glyph images, glyph indices, kerns)?
+// The Drawer or the Face?
+
+// Face is a font face. Its glyphs are often derived from a font file, such as
+// "Comic_Sans_MS.ttf", but a face has a specific size, style, weight and
+// hinting. For example, the 12pt and 18pt versions of Comic Sans are two
+// different faces, even if derived from the same font file.
+//
+// A Face is not safe for concurrent use by multiple goroutines, as its methods
+// may re-use implementation-specific caches and mask image buffers.
+//
+// To create a Face, look to other packages that implement specific font file
+// formats.
+type Face interface {
+	io.Closer
+
+	// Glyph returns the draw.DrawMask parameters (dr, mask, maskp) to draw r's
+	// glyph at the sub-pixel destination location dot, and that glyph's
+	// advance width.
+	//
+	// It returns !ok if the face does not contain a glyph for r.
+	//
+	// The contents of the mask image returned by one Glyph call may change
+	// after the next Glyph call. Callers that want to cache the mask must make
+	// a copy.
+	Glyph(dot fixed.Point26_6, r rune) (
+		dr image.Rectangle, mask image.Image, maskp image.Point, advance fixed.Int26_6, ok bool)
+
+	// GlyphBounds returns the bounding box of r's glyph, drawn at a dot equal
+	// to the origin, and that glyph's advance width.
+	//
+	// It returns !ok if the face does not contain a glyph for r.
+	//
+	// The glyph's ascent and descent equal -bounds.Min.Y and +bounds.Max.Y. A
+	// visual depiction of what these metrics are is at
+	// https://developer.apple.com/library/mac/documentation/TextFonts/Conceptual/CocoaTextArchitecture/Art/glyph_metrics_2x.png
+	GlyphBounds(r rune) (bounds fixed.Rectangle26_6, advance fixed.Int26_6, ok bool)
+
+	// GlyphAdvance returns the advance width of r's glyph.
+	//
+	// It returns !ok if the face does not contain a glyph for r.
+	GlyphAdvance(r rune) (advance fixed.Int26_6, ok bool)
+
+	// Kern returns the horizontal adjustment for the kerning pair (r0, r1). A
+	// positive kern means to move the glyphs further apart.
+	Kern(r0, r1 rune) fixed.Int26_6
+
+	// Metrics returns the metrics for this Face.
+	Metrics() Metrics
+
+	// TODO: ColoredGlyph for various emoji?
+	// TODO: Ligatures? Shaping?
+}
+
+// Metrics holds the metrics for a Face. A visual depiction is at
+// https://developer.apple.com/library/mac/documentation/TextFonts/Conceptual/CocoaTextArchitecture/Art/glyph_metrics_2x.png
+type Metrics struct {
+	// Height is the recommended amount of vertical space between two lines of
+	// text.
+	Height fixed.Int26_6
+
+	// Ascent is the distance from the top of a line to its baseline.
+	Ascent fixed.Int26_6
+
+	// Descent is the distance from the bottom of a line to its baseline. The
+	// value is typically positive, even though a descender goes below the
+	// baseline.
+	Descent fixed.Int26_6
+}
+
+// Drawer draws text on a destination image.
+//
+// A Drawer is not safe for concurrent use by multiple goroutines, since its
+// Face is not.
+type Drawer struct {
+	// Dst is the destination image.
+	Dst draw.Image
+	// Src is the source image.
+	Src image.Image
+	// Face provides the glyph mask images.
+	Face Face
+	// Dot is the baseline location to draw the next glyph. The majority of the
+	// affected pixels will be above and to the right of the dot, but some may
+	// be below or to the left. For example, drawing a 'j' in an italic face
+	// may affect pixels below and to the left of the dot.
+	Dot fixed.Point26_6
+
+	// TODO: Clip image.Image?
+	// TODO: SrcP image.Point for Src images other than *image.Uniform? How
+	// does it get updated during DrawString?
+}
+
+// TODO: should DrawString return the last rune drawn, so the next DrawString
+// call can kern beforehand? Or should that be the responsibility of the caller
+// if they really want to do that, since they have to explicitly shift d.Dot
+// anyway? What if ligatures span more than two runes? What if grapheme
+// clusters span multiple runes?
+//
+// TODO: do we assume that the input is in any particular Unicode Normalization
+// Form?
+//
+// TODO: have DrawRunes(s []rune)? DrawRuneReader(io.RuneReader)?? If we take
+// io.RuneReader, we can't assume that we can rewind the stream.
+//
+// TODO: how does this work with line breaking: drawing text up until a
+// vertical line? Should DrawString return the number of runes drawn?
+
+// DrawBytes draws s at the dot and advances the dot's location.
+//
+// It is equivalent to DrawString(string(s)) but may be more efficient.
+func (d *Drawer) DrawBytes(s []byte) {
+	prevC := rune(-1)
+	for len(s) > 0 {
+		c, size := utf8.DecodeRune(s)
+		s = s[size:]
+		if prevC >= 0 {
+			d.Dot.X += d.Face.Kern(prevC, c)
+		}
+		dr, mask, maskp, advance, ok := d.Face.Glyph(d.Dot, c)
+		if !ok {
+			// TODO: is falling back on the U+FFFD glyph the responsibility of
+			// the Drawer or the Face?
+			// TODO: set prevC = '\ufffd'?
+			continue
+		}
+		draw.DrawMask(d.Dst, dr, d.Src, image.Point{}, mask, maskp, draw.Over)
+		d.Dot.X += advance
+		prevC = c
+	}
+}
+
+// DrawString draws s at the dot and advances the dot's location.
+func (d *Drawer) DrawString(s string) {
+	prevC := rune(-1)
+	for _, c := range s {
+		if prevC >= 0 {
+			d.Dot.X += d.Face.Kern(prevC, c)
+		}
+		dr, mask, maskp, advance, ok := d.Face.Glyph(d.Dot, c)
+		if !ok {
+			// TODO: is falling back on the U+FFFD glyph the responsibility of
+			// the Drawer or the Face?
+			// TODO: set prevC = '\ufffd'?
+			continue
+		}
+		draw.DrawMask(d.Dst, dr, d.Src, image.Point{}, mask, maskp, draw.Over)
+		d.Dot.X += advance
+		prevC = c
+	}
+}
+
+// BoundBytes returns the bounding box of s, drawn at the drawer dot, as well as
+// the advance.
+//
+// It is equivalent to BoundBytes(string(s)) but may be more efficient.
+func (d *Drawer) BoundBytes(s []byte) (bounds fixed.Rectangle26_6, advance fixed.Int26_6) {
+	bounds, advance = BoundBytes(d.Face, s)
+	bounds.Min = bounds.Min.Add(d.Dot)
+	bounds.Max = bounds.Max.Add(d.Dot)
+	return
+}
+
+// BoundString returns the bounding box of s, drawn at the drawer dot, as well
+// as the advance.
+func (d *Drawer) BoundString(s string) (bounds fixed.Rectangle26_6, advance fixed.Int26_6) {
+	bounds, advance = BoundString(d.Face, s)
+	bounds.Min = bounds.Min.Add(d.Dot)
+	bounds.Max = bounds.Max.Add(d.Dot)
+	return
+}
+
+// MeasureBytes returns how far dot would advance by drawing s.
+//
+// It is equivalent to MeasureString(string(s)) but may be more efficient.
+func (d *Drawer) MeasureBytes(s []byte) (advance fixed.Int26_6) {
+	return MeasureBytes(d.Face, s)
+}
+
+// MeasureString returns how far dot would advance by drawing s.
+func (d *Drawer) MeasureString(s string) (advance fixed.Int26_6) {
+	return MeasureString(d.Face, s)
+}
+
+// BoundBytes returns the bounding box of s with f, drawn at a dot equal to the
+// origin, as well as the advance.
+//
+// It is equivalent to BoundString(string(s)) but may be more efficient.
+func BoundBytes(f Face, s []byte) (bounds fixed.Rectangle26_6, advance fixed.Int26_6) {
+	prevC := rune(-1)
+	for len(s) > 0 {
+		c, size := utf8.DecodeRune(s)
+		s = s[size:]
+		if prevC >= 0 {
+			advance += f.Kern(prevC, c)
+		}
+		b, a, ok := f.GlyphBounds(c)
+		if !ok {
+			// TODO: is falling back on the U+FFFD glyph the responsibility of
+			// the Drawer or the Face?
+			// TODO: set prevC = '\ufffd'?
+			continue
+		}
+		b.Min.X += advance
+		b.Max.X += advance
+		bounds = bounds.Union(b)
+		advance += a
+		prevC = c
+	}
+	return
+}
+
+// BoundString returns the bounding box of s with f, drawn at a dot equal to the
+// origin, as well as the advance.
+func BoundString(f Face, s string) (bounds fixed.Rectangle26_6, advance fixed.Int26_6) {
+	prevC := rune(-1)
+	for _, c := range s {
+		if prevC >= 0 {
+			advance += f.Kern(prevC, c)
+		}
+		b, a, ok := f.GlyphBounds(c)
+		if !ok {
+			// TODO: is falling back on the U+FFFD glyph the responsibility of
+			// the Drawer or the Face?
+			// TODO: set prevC = '\ufffd'?
+			continue
+		}
+		b.Min.X += advance
+		b.Max.X += advance
+		bounds = bounds.Union(b)
+		advance += a
+		prevC = c
+	}
+	return
+}
+
+// MeasureBytes returns how far dot would advance by drawing s with f.
+//
+// It is equivalent to MeasureString(string(s)) but may be more efficient.
+func MeasureBytes(f Face, s []byte) (advance fixed.Int26_6) {
+	prevC := rune(-1)
+	for len(s) > 0 {
+		c, size := utf8.DecodeRune(s)
+		s = s[size:]
+		if prevC >= 0 {
+			advance += f.Kern(prevC, c)
+		}
+		a, ok := f.GlyphAdvance(c)
+		if !ok {
+			// TODO: is falling back on the U+FFFD glyph the responsibility of
+			// the Drawer or the Face?
+			// TODO: set prevC = '\ufffd'?
+			continue
+		}
+		advance += a
+		prevC = c
+	}
+	return advance
+}
+
+// MeasureString returns how far dot would advance by drawing s with f.
+func MeasureString(f Face, s string) (advance fixed.Int26_6) {
+	prevC := rune(-1)
+	for _, c := range s {
+		if prevC >= 0 {
+			advance += f.Kern(prevC, c)
+		}
+		a, ok := f.GlyphAdvance(c)
+		if !ok {
+			// TODO: is falling back on the U+FFFD glyph the responsibility of
+			// the Drawer or the Face?
+			// TODO: set prevC = '\ufffd'?
+			continue
+		}
+		advance += a
+		prevC = c
+	}
+	return advance
+}
+
+// Hinting selects how to quantize a vector font's glyph nodes.
+//
+// Not all fonts support hinting.
+type Hinting int
+
+const (
+	HintingNone Hinting = iota
+	HintingVertical
+	HintingFull
+)
+
+// Stretch selects a normal, condensed, or expanded face.
+//
+// Not all fonts support stretches.
+type Stretch int
+
+const (
+	StretchUltraCondensed Stretch = -4
+	StretchExtraCondensed Stretch = -3
+	StretchCondensed      Stretch = -2
+	StretchSemiCondensed  Stretch = -1
+	StretchNormal         Stretch = +0
+	StretchSemiExpanded   Stretch = +1
+	StretchExpanded       Stretch = +2
+	StretchExtraExpanded  Stretch = +3
+	StretchUltraExpanded  Stretch = +4
+)
+
+// Style selects a normal, italic, or oblique face.
+//
+// Not all fonts support styles.
+type Style int
+
+const (
+	StyleNormal Style = iota
+	StyleItalic
+	StyleOblique
+)
+
+// Weight selects a normal, light or bold face.
+//
+// Not all fonts support weights.
+//
+// The named Weight constants (e.g. WeightBold) correspond to CSS' common
+// weight names (e.g. "Bold"), but the numerical values differ, so that in Go,
+// the zero value means to use a normal weight. For the CSS names and values,
+// see https://developer.mozilla.org/en/docs/Web/CSS/font-weight
+type Weight int
+
+const (
+	WeightThin       Weight = -3 // CSS font-weight value 100.
+	WeightExtraLight Weight = -2 // CSS font-weight value 200.
+	WeightLight      Weight = -1 // CSS font-weight value 300.
+	WeightNormal     Weight = +0 // CSS font-weight value 400.
+	WeightMedium     Weight = +1 // CSS font-weight value 500.
+	WeightSemiBold   Weight = +2 // CSS font-weight value 600.
+	WeightBold       Weight = +3 // CSS font-weight value 700.
+	WeightExtraBold  Weight = +4 // CSS font-weight value 800.
+	WeightBlack      Weight = +5 // CSS font-weight value 900.
+)

vendor/golang.org/x/image/math/fixed/BUILD.bazel

@@ -0,0 +1,23 @@
+load("@io_bazel_rules_go//go:def.bzl", "go_library")
+
+go_library(
+    name = "go_default_library",
+    srcs = ["fixed.go"],
+    importmap = "go-common/vendor/golang.org/x/image/math/fixed",
+    importpath = "golang.org/x/image/math/fixed",
+    visibility = ["//visibility:public"],
+)
+
+filegroup(
+    name = "package-srcs",
+    srcs = glob(["**"]),
+    tags = ["automanaged"],
+    visibility = ["//visibility:private"],
+)
+
+filegroup(
+    name = "all-srcs",
+    srcs = [":package-srcs"],
+    tags = ["automanaged"],
+    visibility = ["//visibility:public"],
+)

vendor/golang.org/x/image/math/fixed/fixed.go

@@ -0,0 +1,410 @@
+// 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 fixed implements fixed-point integer types.
+package fixed // import "golang.org/x/image/math/fixed"
+
+import (
+	"fmt"
+)
+
+// TODO: implement fmt.Formatter for %f and %g.
+
+// I returns the integer value i as an Int26_6.
+//
+// For example, passing the integer value 2 yields Int26_6(128).
+func I(i int) Int26_6 {
+	return Int26_6(i << 6)
+}
+
+// Int26_6 is a signed 26.6 fixed-point number.
+//
+// The integer part ranges from -33554432 to 33554431, inclusive. The
+// fractional part has 6 bits of precision.
+//
+// For example, the number one-and-a-quarter is Int26_6(1<<6 + 1<<4).
+type Int26_6 int32
+
+// String returns a human-readable representation of a 26.6 fixed-point number.
+//
+// For example, the number one-and-a-quarter becomes "1:16".
+func (x Int26_6) String() string {
+	const shift, mask = 6, 1<<6 - 1
+	if x >= 0 {
+		return fmt.Sprintf("%d:%02d", int32(x>>shift), int32(x&mask))
+	}
+	x = -x
+	if x >= 0 {
+		return fmt.Sprintf("-%d:%02d", int32(x>>shift), int32(x&mask))
+	}
+	return "-33554432:00" // The minimum value is -(1<<25).
+}
+
+// Floor returns the greatest integer value less than or equal to x.
+//
+// Its return type is int, not Int26_6.
+func (x Int26_6) Floor() int { return int((x + 0x00) >> 6) }
+
+// Round returns the nearest integer value to x. Ties are rounded up.
+//
+// Its return type is int, not Int26_6.
+func (x Int26_6) Round() int { return int((x + 0x20) >> 6) }
+
+// Ceil returns the least integer value greater than or equal to x.
+//
+// Its return type is int, not Int26_6.
+func (x Int26_6) Ceil() int { return int((x + 0x3f) >> 6) }
+
+// Mul returns x*y in 26.6 fixed-point arithmetic.
+func (x Int26_6) Mul(y Int26_6) Int26_6 {
+	return Int26_6((int64(x)*int64(y) + 1<<5) >> 6)
+}
+
+// Int52_12 is a signed 52.12 fixed-point number.
+//
+// The integer part ranges from -2251799813685248 to 2251799813685247,
+// inclusive. The fractional part has 12 bits of precision.
+//
+// For example, the number one-and-a-quarter is Int52_12(1<<12 + 1<<10).
+type Int52_12 int64
+
+// String returns a human-readable representation of a 52.12 fixed-point
+// number.
+//
+// For example, the number one-and-a-quarter becomes "1:1024".
+func (x Int52_12) String() string {
+	const shift, mask = 12, 1<<12 - 1
+	if x >= 0 {
+		return fmt.Sprintf("%d:%04d", int64(x>>shift), int64(x&mask))
+	}
+	x = -x
+	if x >= 0 {
+		return fmt.Sprintf("-%d:%04d", int64(x>>shift), int64(x&mask))
+	}
+	return "-2251799813685248:0000" // The minimum value is -(1<<51).
+}
+
+// Floor returns the greatest integer value less than or equal to x.
+//
+// Its return type is int, not Int52_12.
+func (x Int52_12) Floor() int { return int((x + 0x000) >> 12) }
+
+// Round returns the nearest integer value to x. Ties are rounded up.
+//
+// Its return type is int, not Int52_12.
+func (x Int52_12) Round() int { return int((x + 0x800) >> 12) }
+
+// Ceil returns the least integer value greater than or equal to x.
+//
+// Its return type is int, not Int52_12.
+func (x Int52_12) Ceil() int { return int((x + 0xfff) >> 12) }
+
+// Mul returns x*y in 52.12 fixed-point arithmetic.
+func (x Int52_12) Mul(y Int52_12) Int52_12 {
+	const M, N = 52, 12
+	lo, hi := muli64(int64(x), int64(y))
+	ret := Int52_12(hi<<M | lo>>N)
+	ret += Int52_12((lo >> (N - 1)) & 1) // Round to nearest, instead of rounding down.
+	return ret
+}
+
+// muli64 multiplies two int64 values, returning the 128-bit signed integer
+// result as two uint64 values.
+//
+// This implementation is similar to $GOROOT/src/runtime/softfloat64.go's mullu
+// function, which is in turn adapted from Hacker's Delight.
+func muli64(u, v int64) (lo, hi uint64) {
+	const (
+		s    = 32
+		mask = 1<<s - 1
+	)
+
+	u1 := uint64(u >> s)
+	u0 := uint64(u & mask)
+	v1 := uint64(v >> s)
+	v0 := uint64(v & mask)
+
+	w0 := u0 * v0
+	t := u1*v0 + w0>>s
+	w1 := t & mask
+	w2 := uint64(int64(t) >> s)
+	w1 += u0 * v1
+	return uint64(u) * uint64(v), u1*v1 + w2 + uint64(int64(w1)>>s)
+}
+
+// P returns the integer values x and y as a Point26_6.
+//
+// For example, passing the integer values (2, -3) yields Point26_6{128, -192}.
+func P(x, y int) Point26_6 {
+	return Point26_6{Int26_6(x << 6), Int26_6(y << 6)}
+}
+
+// Point26_6 is a 26.6 fixed-point coordinate pair.
+//
+// It is analogous to the image.Point type in the standard library.
+type Point26_6 struct {
+	X, Y Int26_6
+}
+
+// Add returns the vector p+q.
+func (p Point26_6) Add(q Point26_6) Point26_6 {
+	return Point26_6{p.X + q.X, p.Y + q.Y}
+}
+
+// Sub returns the vector p-q.
+func (p Point26_6) Sub(q Point26_6) Point26_6 {
+	return Point26_6{p.X - q.X, p.Y - q.Y}
+}
+
+// Mul returns the vector p*k.
+func (p Point26_6) Mul(k Int26_6) Point26_6 {
+	return Point26_6{p.X * k / 64, p.Y * k / 64}
+}
+
+// Div returns the vector p/k.
+func (p Point26_6) Div(k Int26_6) Point26_6 {
+	return Point26_6{p.X * 64 / k, p.Y * 64 / k}
+}
+
+// In returns whether p is in r.
+func (p Point26_6) In(r Rectangle26_6) bool {
+	return r.Min.X <= p.X && p.X < r.Max.X && r.Min.Y <= p.Y && p.Y < r.Max.Y
+}
+
+// Point52_12 is a 52.12 fixed-point coordinate pair.
+//
+// It is analogous to the image.Point type in the standard library.
+type Point52_12 struct {
+	X, Y Int52_12
+}
+
+// Add returns the vector p+q.
+func (p Point52_12) Add(q Point52_12) Point52_12 {
+	return Point52_12{p.X + q.X, p.Y + q.Y}
+}
+
+// Sub returns the vector p-q.
+func (p Point52_12) Sub(q Point52_12) Point52_12 {
+	return Point52_12{p.X - q.X, p.Y - q.Y}
+}
+
+// Mul returns the vector p*k.
+func (p Point52_12) Mul(k Int52_12) Point52_12 {
+	return Point52_12{p.X * k / 4096, p.Y * k / 4096}
+}
+
+// Div returns the vector p/k.
+func (p Point52_12) Div(k Int52_12) Point52_12 {
+	return Point52_12{p.X * 4096 / k, p.Y * 4096 / k}
+}
+
+// In returns whether p is in r.
+func (p Point52_12) In(r Rectangle52_12) bool {
+	return r.Min.X <= p.X && p.X < r.Max.X && r.Min.Y <= p.Y && p.Y < r.Max.Y
+}
+
+// R returns the integer values minX, minY, maxX, maxY as a Rectangle26_6.
+//
+// For example, passing the integer values (0, 1, 2, 3) yields
+// Rectangle26_6{Point26_6{0, 64}, Point26_6{128, 192}}.
+//
+// Like the image.Rect function in the standard library, the returned rectangle
+// has minimum and maximum coordinates swapped if necessary so that it is
+// well-formed.
+func R(minX, minY, maxX, maxY int) Rectangle26_6 {
+	if minX > maxX {
+		minX, maxX = maxX, minX
+	}
+	if minY > maxY {
+		minY, maxY = maxY, minY
+	}
+	return Rectangle26_6{
+		Point26_6{
+			Int26_6(minX << 6),
+			Int26_6(minY << 6),
+		},
+		Point26_6{
+			Int26_6(maxX << 6),
+			Int26_6(maxY << 6),
+		},
+	}
+}
+
+// Rectangle26_6 is a 26.6 fixed-point coordinate rectangle. The Min bound is
+// inclusive and the Max bound is exclusive. It is well-formed if Min.X <=
+// Max.X and likewise for Y.
+//
+// It is analogous to the image.Rectangle type in the standard library.
+type Rectangle26_6 struct {
+	Min, Max Point26_6
+}
+
+// Add returns the rectangle r translated by p.
+func (r Rectangle26_6) Add(p Point26_6) Rectangle26_6 {
+	return Rectangle26_6{
+		Point26_6{r.Min.X + p.X, r.Min.Y + p.Y},
+		Point26_6{r.Max.X + p.X, r.Max.Y + p.Y},
+	}
+}
+
+// Sub returns the rectangle r translated by -p.
+func (r Rectangle26_6) Sub(p Point26_6) Rectangle26_6 {
+	return Rectangle26_6{
+		Point26_6{r.Min.X - p.X, r.Min.Y - p.Y},
+		Point26_6{r.Max.X - p.X, r.Max.Y - p.Y},
+	}
+}
+
+// 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 Rectangle26_6) Intersect(s Rectangle26_6) Rectangle26_6 {
+	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
+	}
+	// Letting r0 and s0 be the values of r and s at the time that the method
+	// is called, this next line is equivalent to:
+	//
+	// if max(r0.Min.X, s0.Min.X) >= min(r0.Max.X, s0.Max.X) || likewiseForY { etc }
+	if r.Empty() {
+		return Rectangle26_6{}
+	}
+	return r
+}
+
+// Union returns the smallest rectangle that contains both r and s.
+func (r Rectangle26_6) Union(s Rectangle26_6) Rectangle26_6 {
+	if r.Empty() {
+		return s
+	}
+	if s.Empty() {
+		return r
+	}
+	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.
+func (r Rectangle26_6) Empty() bool {
+	return r.Min.X >= r.Max.X || r.Min.Y >= r.Max.Y
+}
+
+// In returns whether every point in r is in s.
+func (r Rectangle26_6) In(s Rectangle26_6) bool {
+	if r.Empty() {
+		return true
+	}
+	// Note that r.Max is an exclusive bound for r, so that r.In(s)
+	// does not require that r.Max.In(s).
+	return s.Min.X <= r.Min.X && r.Max.X <= s.Max.X &&
+		s.Min.Y <= r.Min.Y && r.Max.Y <= s.Max.Y
+}
+
+// Rectangle52_12 is a 52.12 fixed-point coordinate rectangle. The Min bound is
+// inclusive and the Max bound is exclusive. It is well-formed if Min.X <=
+// Max.X and likewise for Y.
+//
+// It is analogous to the image.Rectangle type in the standard library.
+type Rectangle52_12 struct {
+	Min, Max Point52_12
+}
+
+// Add returns the rectangle r translated by p.
+func (r Rectangle52_12) Add(p Point52_12) Rectangle52_12 {
+	return Rectangle52_12{
+		Point52_12{r.Min.X + p.X, r.Min.Y + p.Y},
+		Point52_12{r.Max.X + p.X, r.Max.Y + p.Y},
+	}
+}
+
+// Sub returns the rectangle r translated by -p.
+func (r Rectangle52_12) Sub(p Point52_12) Rectangle52_12 {
+	return Rectangle52_12{
+		Point52_12{r.Min.X - p.X, r.Min.Y - p.Y},
+		Point52_12{r.Max.X - p.X, r.Max.Y - p.Y},
+	}
+}
+
+// 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 Rectangle52_12) Intersect(s Rectangle52_12) Rectangle52_12 {
+	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
+	}
+	// Letting r0 and s0 be the values of r and s at the time that the method
+	// is called, this next line is equivalent to:
+	//
+	// if max(r0.Min.X, s0.Min.X) >= min(r0.Max.X, s0.Max.X) || likewiseForY { etc }
+	if r.Empty() {
+		return Rectangle52_12{}
+	}
+	return r
+}
+
+// Union returns the smallest rectangle that contains both r and s.
+func (r Rectangle52_12) Union(s Rectangle52_12) Rectangle52_12 {
+	if r.Empty() {
+		return s
+	}
+	if s.Empty() {
+		return r
+	}
+	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.
+func (r Rectangle52_12) Empty() bool {
+	return r.Min.X >= r.Max.X || r.Min.Y >= r.Max.Y
+}
+
+// In returns whether every point in r is in s.
+func (r Rectangle52_12) In(s Rectangle52_12) bool {
+	if r.Empty() {
+		return true
+	}
+	// Note that r.Max is an exclusive bound for r, so that r.In(s)
+	// does not require that r.Max.In(s).
+	return s.Min.X <= r.Min.X && r.Max.X <= s.Max.X &&
+		s.Min.Y <= r.Min.Y && r.Max.Y <= s.Max.Y
+}