Add response time badge and chart

vendor/github.com/golang/freetype/AUTHORS

@@ -0,0 +1,20 @@
+# This is the official list of Freetype-Go authors for copyright purposes.
+# This file is distinct from the CONTRIBUTORS files.
+# See the latter for an explanation.
+#
+# Freetype-Go is derived from Freetype, which is written in C. The latter
+# is copyright 1996-2010 David Turner, Robert Wilhelm, and Werner Lemberg.
+
+# Names should be added to this file as
+#	Name or Organization <email address>
+# The email address is not required for organizations.
+
+# Please keep the list sorted.
+
+Google Inc.
+Jeff R. Allen <jra@nella.org>
+Maksim Kochkin <maxxarts@gmail.com>
+Michael Fogleman <fogleman@gmail.com>
+Rémy Oudompheng <oudomphe@phare.normalesup.org>
+Roger Peppe <rogpeppe@gmail.com>
+Steven Edwards <steven@stephenwithav.com>

vendor/github.com/golang/freetype/CONTRIBUTORS

@@ -0,0 +1,38 @@
+# This is the official list of people who can contribute
+# (and typically have contributed) code to the Freetype-Go repository.
+# The AUTHORS file lists the copyright holders; this file
+# lists people.  For example, Google employees are listed here
+# but not in AUTHORS, because Google holds the copyright.
+#
+# The submission process automatically checks to make sure
+# that people submitting code are listed in this file (by email address).
+#
+# Names should be added to this file only after verifying that
+# the individual or the individual's organization has agreed to
+# the appropriate Contributor License Agreement, found here:
+#
+#     http://code.google.com/legal/individual-cla-v1.0.html
+#     http://code.google.com/legal/corporate-cla-v1.0.html
+#
+# The agreement for individuals can be filled out on the web.
+#
+# When adding J Random Contributor's name to this file,
+# either J's name or J's organization's name should be
+# added to the AUTHORS file, depending on whether the
+# individual or corporate CLA was used.
+
+# Names should be added to this file like so:
+#     Name <email address>
+
+# Please keep the list sorted.
+
+Andrew Gerrand <adg@golang.org>
+Jeff R. Allen <jra@nella.org> <jeff.allen@gmail.com>
+Maksim Kochkin <maxxarts@gmail.com>
+Michael Fogleman <fogleman@gmail.com>
+Nigel Tao <nigeltao@golang.org>
+Rémy Oudompheng <oudomphe@phare.normalesup.org> <remyoudompheng@gmail.com>
+Rob Pike <r@golang.org>
+Roger Peppe <rogpeppe@gmail.com>
+Russ Cox <rsc@golang.org>
+Steven Edwards <steven@stephenwithav.com>

vendor/github.com/golang/freetype/LICENSE

@@ -0,0 +1,12 @@
+Use of the Freetype-Go software is subject to your choice of exactly one of
+the following two licenses:
+  * The FreeType License, which is similar to the original BSD license with
+    an advertising clause, or
+  * The GNU General Public License (GPL), version 2 or later.
+
+The text of these licenses are available in the licenses/ftl.txt and the
+licenses/gpl.txt files respectively. They are also available at
+http://freetype.sourceforge.net/license.html
+
+The Luxi fonts in the testdata directory are licensed separately. See the
+testdata/COPYING file for details.

vendor/github.com/golang/freetype/raster/geom.go

@@ -0,0 +1,245 @@
+// Copyright 2010 The Freetype-Go Authors. All rights reserved.
+// Use of this source code is governed by your choice of either the
+// FreeType License or the GNU General Public License version 2 (or
+// any later version), both of which can be found in the LICENSE file.
+
+package raster
+
+import (
+	"fmt"
+	"math"
+
+	"golang.org/x/image/math/fixed"
+)
+
+// maxAbs returns the maximum of abs(a) and abs(b).
+func maxAbs(a, b fixed.Int26_6) fixed.Int26_6 {
+	if a < 0 {
+		a = -a
+	}
+	if b < 0 {
+		b = -b
+	}
+	if a < b {
+		return b
+	}
+	return a
+}
+
+// pNeg returns the vector -p, or equivalently p rotated by 180 degrees.
+func pNeg(p fixed.Point26_6) fixed.Point26_6 {
+	return fixed.Point26_6{-p.X, -p.Y}
+}
+
+// pDot returns the dot product p·q.
+func pDot(p fixed.Point26_6, q fixed.Point26_6) fixed.Int52_12 {
+	px, py := int64(p.X), int64(p.Y)
+	qx, qy := int64(q.X), int64(q.Y)
+	return fixed.Int52_12(px*qx + py*qy)
+}
+
+// pLen returns the length of the vector p.
+func pLen(p fixed.Point26_6) fixed.Int26_6 {
+	// TODO(nigeltao): use fixed point math.
+	x := float64(p.X)
+	y := float64(p.Y)
+	return fixed.Int26_6(math.Sqrt(x*x + y*y))
+}
+
+// pNorm returns the vector p normalized to the given length, or zero if p is
+// degenerate.
+func pNorm(p fixed.Point26_6, length fixed.Int26_6) fixed.Point26_6 {
+	d := pLen(p)
+	if d == 0 {
+		return fixed.Point26_6{}
+	}
+	s, t := int64(length), int64(d)
+	x := int64(p.X) * s / t
+	y := int64(p.Y) * s / t
+	return fixed.Point26_6{fixed.Int26_6(x), fixed.Int26_6(y)}
+}
+
+// pRot45CW returns the vector p rotated clockwise by 45 degrees.
+//
+// Note that the Y-axis grows downwards, so {1, 0}.Rot45CW is {1/√2, 1/√2}.
+func pRot45CW(p fixed.Point26_6) fixed.Point26_6 {
+	// 181/256 is approximately 1/√2, or sin(π/4).
+	px, py := int64(p.X), int64(p.Y)
+	qx := (+px - py) * 181 / 256
+	qy := (+px + py) * 181 / 256
+	return fixed.Point26_6{fixed.Int26_6(qx), fixed.Int26_6(qy)}
+}
+
+// pRot90CW returns the vector p rotated clockwise by 90 degrees.
+//
+// Note that the Y-axis grows downwards, so {1, 0}.Rot90CW is {0, 1}.
+func pRot90CW(p fixed.Point26_6) fixed.Point26_6 {
+	return fixed.Point26_6{-p.Y, p.X}
+}
+
+// pRot135CW returns the vector p rotated clockwise by 135 degrees.
+//
+// Note that the Y-axis grows downwards, so {1, 0}.Rot135CW is {-1/√2, 1/√2}.
+func pRot135CW(p fixed.Point26_6) fixed.Point26_6 {
+	// 181/256 is approximately 1/√2, or sin(π/4).
+	px, py := int64(p.X), int64(p.Y)
+	qx := (-px - py) * 181 / 256
+	qy := (+px - py) * 181 / 256
+	return fixed.Point26_6{fixed.Int26_6(qx), fixed.Int26_6(qy)}
+}
+
+// pRot45CCW returns the vector p rotated counter-clockwise by 45 degrees.
+//
+// Note that the Y-axis grows downwards, so {1, 0}.Rot45CCW is {1/√2, -1/√2}.
+func pRot45CCW(p fixed.Point26_6) fixed.Point26_6 {
+	// 181/256 is approximately 1/√2, or sin(π/4).
+	px, py := int64(p.X), int64(p.Y)
+	qx := (+px + py) * 181 / 256
+	qy := (-px + py) * 181 / 256
+	return fixed.Point26_6{fixed.Int26_6(qx), fixed.Int26_6(qy)}
+}
+
+// pRot90CCW returns the vector p rotated counter-clockwise by 90 degrees.
+//
+// Note that the Y-axis grows downwards, so {1, 0}.Rot90CCW is {0, -1}.
+func pRot90CCW(p fixed.Point26_6) fixed.Point26_6 {
+	return fixed.Point26_6{p.Y, -p.X}
+}
+
+// pRot135CCW returns the vector p rotated counter-clockwise by 135 degrees.
+//
+// Note that the Y-axis grows downwards, so {1, 0}.Rot135CCW is {-1/√2, -1/√2}.
+func pRot135CCW(p fixed.Point26_6) fixed.Point26_6 {
+	// 181/256 is approximately 1/√2, or sin(π/4).
+	px, py := int64(p.X), int64(p.Y)
+	qx := (-px + py) * 181 / 256
+	qy := (-px - py) * 181 / 256
+	return fixed.Point26_6{fixed.Int26_6(qx), fixed.Int26_6(qy)}
+}
+
+// An Adder accumulates points on a curve.
+type Adder interface {
+	// Start starts a new curve at the given point.
+	Start(a fixed.Point26_6)
+	// Add1 adds a linear segment to the current curve.
+	Add1(b fixed.Point26_6)
+	// Add2 adds a quadratic segment to the current curve.
+	Add2(b, c fixed.Point26_6)
+	// Add3 adds a cubic segment to the current curve.
+	Add3(b, c, d fixed.Point26_6)
+}
+
+// A Path is a sequence of curves, and a curve is a start point followed by a
+// sequence of linear, quadratic or cubic segments.
+type Path []fixed.Int26_6
+
+// String returns a human-readable representation of a Path.
+func (p Path) String() string {
+	s := ""
+	for i := 0; i < len(p); {
+		if i != 0 {
+			s += " "
+		}
+		switch p[i] {
+		case 0:
+			s += "S0" + fmt.Sprint([]fixed.Int26_6(p[i+1:i+3]))
+			i += 4
+		case 1:
+			s += "A1" + fmt.Sprint([]fixed.Int26_6(p[i+1:i+3]))
+			i += 4
+		case 2:
+			s += "A2" + fmt.Sprint([]fixed.Int26_6(p[i+1:i+5]))
+			i += 6
+		case 3:
+			s += "A3" + fmt.Sprint([]fixed.Int26_6(p[i+1:i+7]))
+			i += 8
+		default:
+			panic("freetype/raster: bad path")
+		}
+	}
+	return s
+}
+
+// Clear cancels any previous calls to p.Start or p.AddXxx.
+func (p *Path) Clear() {
+	*p = (*p)[:0]
+}
+
+// Start starts a new curve at the given point.
+func (p *Path) Start(a fixed.Point26_6) {
+	*p = append(*p, 0, a.X, a.Y, 0)
+}
+
+// Add1 adds a linear segment to the current curve.
+func (p *Path) Add1(b fixed.Point26_6) {
+	*p = append(*p, 1, b.X, b.Y, 1)
+}
+
+// Add2 adds a quadratic segment to the current curve.
+func (p *Path) Add2(b, c fixed.Point26_6) {
+	*p = append(*p, 2, b.X, b.Y, c.X, c.Y, 2)
+}
+
+// Add3 adds a cubic segment to the current curve.
+func (p *Path) Add3(b, c, d fixed.Point26_6) {
+	*p = append(*p, 3, b.X, b.Y, c.X, c.Y, d.X, d.Y, 3)
+}
+
+// AddPath adds the Path q to p.
+func (p *Path) AddPath(q Path) {
+	*p = append(*p, q...)
+}
+
+// AddStroke adds a stroked Path.
+func (p *Path) AddStroke(q Path, width fixed.Int26_6, cr Capper, jr Joiner) {
+	Stroke(p, q, width, cr, jr)
+}
+
+// firstPoint returns the first point in a non-empty Path.
+func (p Path) firstPoint() fixed.Point26_6 {
+	return fixed.Point26_6{p[1], p[2]}
+}
+
+// lastPoint returns the last point in a non-empty Path.
+func (p Path) lastPoint() fixed.Point26_6 {
+	return fixed.Point26_6{p[len(p)-3], p[len(p)-2]}
+}
+
+// addPathReversed adds q reversed to p.
+// For example, if q consists of a linear segment from A to B followed by a
+// quadratic segment from B to C to D, then the values of q looks like:
+// index: 01234567890123
+// value: 0AA01BB12CCDD2
+// So, when adding q backwards to p, we want to Add2(C, B) followed by Add1(A).
+func addPathReversed(p Adder, q Path) {
+	if len(q) == 0 {
+		return
+	}
+	i := len(q) - 1
+	for {
+		switch q[i] {
+		case 0:
+			return
+		case 1:
+			i -= 4
+			p.Add1(
+				fixed.Point26_6{q[i-2], q[i-1]},
+			)
+		case 2:
+			i -= 6
+			p.Add2(
+				fixed.Point26_6{q[i+2], q[i+3]},
+				fixed.Point26_6{q[i-2], q[i-1]},
+			)
+		case 3:
+			i -= 8
+			p.Add3(
+				fixed.Point26_6{q[i+4], q[i+5]},
+				fixed.Point26_6{q[i+2], q[i+3]},
+				fixed.Point26_6{q[i-2], q[i-1]},
+			)
+		default:
+			panic("freetype/raster: bad path")
+		}
+	}
+}

vendor/github.com/golang/freetype/raster/paint.go

@@ -0,0 +1,287 @@
+// Copyright 2010 The Freetype-Go Authors. All rights reserved.
+// Use of this source code is governed by your choice of either the
+// FreeType License or the GNU General Public License version 2 (or
+// any later version), both of which can be found in the LICENSE file.
+
+package raster
+
+import (
+	"image"
+	"image/color"
+	"image/draw"
+	"math"
+)
+
+// A Span is a horizontal segment of pixels with constant alpha. X0 is an
+// inclusive bound and X1 is exclusive, the same as for slices. A fully opaque
+// Span has Alpha == 0xffff.
+type Span struct {
+	Y, X0, X1 int
+	Alpha     uint32
+}
+
+// A Painter knows how to paint a batch of Spans. Rasterization may involve
+// Painting multiple batches, and done will be true for the final batch. The
+// Spans' Y values are monotonically increasing during a rasterization. Paint
+// may use all of ss as scratch space during the call.
+type Painter interface {
+	Paint(ss []Span, done bool)
+}
+
+// The PainterFunc type adapts an ordinary function to the Painter interface.
+type PainterFunc func(ss []Span, done bool)
+
+// Paint just delegates the call to f.
+func (f PainterFunc) Paint(ss []Span, done bool) { f(ss, done) }
+
+// An AlphaOverPainter is a Painter that paints Spans onto a *image.Alpha using
+// the Over Porter-Duff composition operator.
+type AlphaOverPainter struct {
+	Image *image.Alpha
+}
+
+// Paint satisfies the Painter interface.
+func (r AlphaOverPainter) Paint(ss []Span, done bool) {
+	b := r.Image.Bounds()
+	for _, s := range ss {
+		if s.Y < b.Min.Y {
+			continue
+		}
+		if s.Y >= b.Max.Y {
+			return
+		}
+		if s.X0 < b.Min.X {
+			s.X0 = b.Min.X
+		}
+		if s.X1 > b.Max.X {
+			s.X1 = b.Max.X
+		}
+		if s.X0 >= s.X1 {
+			continue
+		}
+		base := (s.Y-r.Image.Rect.Min.Y)*r.Image.Stride - r.Image.Rect.Min.X
+		p := r.Image.Pix[base+s.X0 : base+s.X1]
+		a := int(s.Alpha >> 8)
+		for i, c := range p {
+			v := int(c)
+			p[i] = uint8((v*255 + (255-v)*a) / 255)
+		}
+	}
+}
+
+// NewAlphaOverPainter creates a new AlphaOverPainter for the given image.
+func NewAlphaOverPainter(m *image.Alpha) AlphaOverPainter {
+	return AlphaOverPainter{m}
+}
+
+// An AlphaSrcPainter is a Painter that paints Spans onto a *image.Alpha using
+// the Src Porter-Duff composition operator.
+type AlphaSrcPainter struct {
+	Image *image.Alpha
+}
+
+// Paint satisfies the Painter interface.
+func (r AlphaSrcPainter) Paint(ss []Span, done bool) {
+	b := r.Image.Bounds()
+	for _, s := range ss {
+		if s.Y < b.Min.Y {
+			continue
+		}
+		if s.Y >= b.Max.Y {
+			return
+		}
+		if s.X0 < b.Min.X {
+			s.X0 = b.Min.X
+		}
+		if s.X1 > b.Max.X {
+			s.X1 = b.Max.X
+		}
+		if s.X0 >= s.X1 {
+			continue
+		}
+		base := (s.Y-r.Image.Rect.Min.Y)*r.Image.Stride - r.Image.Rect.Min.X
+		p := r.Image.Pix[base+s.X0 : base+s.X1]
+		color := uint8(s.Alpha >> 8)
+		for i := range p {
+			p[i] = color
+		}
+	}
+}
+
+// NewAlphaSrcPainter creates a new AlphaSrcPainter for the given image.
+func NewAlphaSrcPainter(m *image.Alpha) AlphaSrcPainter {
+	return AlphaSrcPainter{m}
+}
+
+// An RGBAPainter is a Painter that paints Spans onto a *image.RGBA.
+type RGBAPainter struct {
+	// Image is the image to compose onto.
+	Image *image.RGBA
+	// Op is the Porter-Duff composition operator.
+	Op draw.Op
+	// cr, cg, cb and ca are the 16-bit color to paint the spans.
+	cr, cg, cb, ca uint32
+}
+
+// Paint satisfies the Painter interface.
+func (r *RGBAPainter) Paint(ss []Span, done bool) {
+	b := r.Image.Bounds()
+	for _, s := range ss {
+		if s.Y < b.Min.Y {
+			continue
+		}
+		if s.Y >= b.Max.Y {
+			return
+		}
+		if s.X0 < b.Min.X {
+			s.X0 = b.Min.X
+		}
+		if s.X1 > b.Max.X {
+			s.X1 = b.Max.X
+		}
+		if s.X0 >= s.X1 {
+			continue
+		}
+		// This code mimics drawGlyphOver in $GOROOT/src/image/draw/draw.go.
+		ma := s.Alpha
+		const m = 1<<16 - 1
+		i0 := (s.Y-r.Image.Rect.Min.Y)*r.Image.Stride + (s.X0-r.Image.Rect.Min.X)*4
+		i1 := i0 + (s.X1-s.X0)*4
+		if r.Op == draw.Over {
+			for i := i0; i < i1; i += 4 {
+				dr := uint32(r.Image.Pix[i+0])
+				dg := uint32(r.Image.Pix[i+1])
+				db := uint32(r.Image.Pix[i+2])
+				da := uint32(r.Image.Pix[i+3])
+				a := (m - (r.ca * ma / m)) * 0x101
+				r.Image.Pix[i+0] = uint8((dr*a + r.cr*ma) / m >> 8)
+				r.Image.Pix[i+1] = uint8((dg*a + r.cg*ma) / m >> 8)
+				r.Image.Pix[i+2] = uint8((db*a + r.cb*ma) / m >> 8)
+				r.Image.Pix[i+3] = uint8((da*a + r.ca*ma) / m >> 8)
+			}
+		} else {
+			for i := i0; i < i1; i += 4 {
+				r.Image.Pix[i+0] = uint8(r.cr * ma / m >> 8)
+				r.Image.Pix[i+1] = uint8(r.cg * ma / m >> 8)
+				r.Image.Pix[i+2] = uint8(r.cb * ma / m >> 8)
+				r.Image.Pix[i+3] = uint8(r.ca * ma / m >> 8)
+			}
+		}
+	}
+}
+
+// SetColor sets the color to paint the spans.
+func (r *RGBAPainter) SetColor(c color.Color) {
+	r.cr, r.cg, r.cb, r.ca = c.RGBA()
+}
+
+// NewRGBAPainter creates a new RGBAPainter for the given image.
+func NewRGBAPainter(m *image.RGBA) *RGBAPainter {
+	return &RGBAPainter{Image: m}
+}
+
+// A MonochromePainter wraps another Painter, quantizing each Span's alpha to
+// be either fully opaque or fully transparent.
+type MonochromePainter struct {
+	Painter   Painter
+	y, x0, x1 int
+}
+
+// Paint delegates to the wrapped Painter after quantizing each Span's alpha
+// value and merging adjacent fully opaque Spans.
+func (m *MonochromePainter) Paint(ss []Span, done bool) {
+	// We compact the ss slice, discarding any Spans whose alpha quantizes to zero.
+	j := 0
+	for _, s := range ss {
+		if s.Alpha >= 0x8000 {
+			if m.y == s.Y && m.x1 == s.X0 {
+				m.x1 = s.X1
+			} else {
+				ss[j] = Span{m.y, m.x0, m.x1, 1<<16 - 1}
+				j++
+				m.y, m.x0, m.x1 = s.Y, s.X0, s.X1
+			}
+		}
+	}
+	if done {
+		// Flush the accumulated Span.
+		finalSpan := Span{m.y, m.x0, m.x1, 1<<16 - 1}
+		if j < len(ss) {
+			ss[j] = finalSpan
+			j++
+			m.Painter.Paint(ss[:j], true)
+		} else if j == len(ss) {
+			m.Painter.Paint(ss, false)
+			if cap(ss) > 0 {
+				ss = ss[:1]
+			} else {
+				ss = make([]Span, 1)
+			}
+			ss[0] = finalSpan
+			m.Painter.Paint(ss, true)
+		} else {
+			panic("unreachable")
+		}
+		// Reset the accumulator, so that this Painter can be re-used.
+		m.y, m.x0, m.x1 = 0, 0, 0
+	} else {
+		m.Painter.Paint(ss[:j], false)
+	}
+}
+
+// NewMonochromePainter creates a new MonochromePainter that wraps the given
+// Painter.
+func NewMonochromePainter(p Painter) *MonochromePainter {
+	return &MonochromePainter{Painter: p}
+}
+
+// A GammaCorrectionPainter wraps another Painter, performing gamma-correction
+// on each Span's alpha value.
+type GammaCorrectionPainter struct {
+	// Painter is the wrapped Painter.
+	Painter Painter
+	// a is the precomputed alpha values for linear interpolation, with fully
+	// opaque == 0xffff.
+	a [256]uint16
+	// gammaIsOne is whether gamma correction is a no-op.
+	gammaIsOne bool
+}
+
+// Paint delegates to the wrapped Painter after performing gamma-correction on
+// each Span.
+func (g *GammaCorrectionPainter) Paint(ss []Span, done bool) {
+	if !g.gammaIsOne {
+		const n = 0x101
+		for i, s := range ss {
+			if s.Alpha == 0 || s.Alpha == 0xffff {
+				continue
+			}
+			p, q := s.Alpha/n, s.Alpha%n
+			// The resultant alpha is a linear interpolation of g.a[p] and g.a[p+1].
+			a := uint32(g.a[p])*(n-q) + uint32(g.a[p+1])*q
+			ss[i].Alpha = (a + n/2) / n
+		}
+	}
+	g.Painter.Paint(ss, done)
+}
+
+// SetGamma sets the gamma value.
+func (g *GammaCorrectionPainter) SetGamma(gamma float64) {
+	g.gammaIsOne = gamma == 1
+	if g.gammaIsOne {
+		return
+	}
+	for i := 0; i < 256; i++ {
+		a := float64(i) / 0xff
+		a = math.Pow(a, gamma)
+		g.a[i] = uint16(0xffff * a)
+	}
+}
+
+// NewGammaCorrectionPainter creates a new GammaCorrectionPainter that wraps
+// the given Painter.
+func NewGammaCorrectionPainter(p Painter, gamma float64) *GammaCorrectionPainter {
+	g := &GammaCorrectionPainter{Painter: p}
+	g.SetGamma(gamma)
+	return g
+}

vendor/github.com/golang/freetype/raster/raster.go

@@ -0,0 +1,601 @@
+// Copyright 2010 The Freetype-Go Authors. All rights reserved.
+// Use of this source code is governed by your choice of either the
+// FreeType License or the GNU General Public License version 2 (or
+// any later version), both of which can be found in the LICENSE file.
+
+// Package raster provides an anti-aliasing 2-D rasterizer.
+//
+// It is part of the larger Freetype suite of font-related packages, but the
+// raster package is not specific to font rasterization, and can be used
+// standalone without any other Freetype package.
+//
+// Rasterization is done by the same area/coverage accumulation algorithm as
+// the Freetype "smooth" module, and the Anti-Grain Geometry library. A
+// description of the area/coverage algorithm is at
+// http://projects.tuxee.net/cl-vectors/section-the-cl-aa-algorithm
+package raster // import "github.com/golang/freetype/raster"
+
+import (
+	"strconv"
+
+	"golang.org/x/image/math/fixed"
+)
+
+// A cell is part of a linked list (for a given yi co-ordinate) of accumulated
+// area/coverage for the pixel at (xi, yi).
+type cell struct {
+	xi          int
+	area, cover int
+	next        int
+}
+
+type Rasterizer struct {
+	// If false, the default behavior is to use the even-odd winding fill
+	// rule during Rasterize.
+	UseNonZeroWinding bool
+	// An offset (in pixels) to the painted spans.
+	Dx, Dy int
+
+	// The width of the Rasterizer. The height is implicit in len(cellIndex).
+	width int
+	// splitScaleN is the scaling factor used to determine how many times
+	// to decompose a quadratic or cubic segment into a linear approximation.
+	splitScale2, splitScale3 int
+
+	// The current pen position.
+	a fixed.Point26_6
+	// The current cell and its area/coverage being accumulated.
+	xi, yi      int
+	area, cover int
+
+	// Saved cells.
+	cell []cell
+	// Linked list of cells, one per row.
+	cellIndex []int
+	// Buffers.
+	cellBuf      [256]cell
+	cellIndexBuf [64]int
+	spanBuf      [64]Span
+}
+
+// findCell returns the index in r.cell for the cell corresponding to
+// (r.xi, r.yi). The cell is created if necessary.
+func (r *Rasterizer) findCell() int {
+	if r.yi < 0 || r.yi >= len(r.cellIndex) {
+		return -1
+	}
+	xi := r.xi
+	if xi < 0 {
+		xi = -1
+	} else if xi > r.width {
+		xi = r.width
+	}
+	i, prev := r.cellIndex[r.yi], -1
+	for i != -1 && r.cell[i].xi <= xi {
+		if r.cell[i].xi == xi {
+			return i
+		}
+		i, prev = r.cell[i].next, i
+	}
+	c := len(r.cell)
+	if c == cap(r.cell) {
+		buf := make([]cell, c, 4*c)
+		copy(buf, r.cell)
+		r.cell = buf[0 : c+1]
+	} else {
+		r.cell = r.cell[0 : c+1]
+	}
+	r.cell[c] = cell{xi, 0, 0, i}
+	if prev == -1 {
+		r.cellIndex[r.yi] = c
+	} else {
+		r.cell[prev].next = c
+	}
+	return c
+}
+
+// saveCell saves any accumulated r.area/r.cover for (r.xi, r.yi).
+func (r *Rasterizer) saveCell() {
+	if r.area != 0 || r.cover != 0 {
+		i := r.findCell()
+		if i != -1 {
+			r.cell[i].area += r.area
+			r.cell[i].cover += r.cover
+		}
+		r.area = 0
+		r.cover = 0
+	}
+}
+
+// setCell sets the (xi, yi) cell that r is accumulating area/coverage for.
+func (r *Rasterizer) setCell(xi, yi int) {
+	if r.xi != xi || r.yi != yi {
+		r.saveCell()
+		r.xi, r.yi = xi, yi
+	}
+}
+
+// scan accumulates area/coverage for the yi'th scanline, going from
+// x0 to x1 in the horizontal direction (in 26.6 fixed point co-ordinates)
+// and from y0f to y1f fractional vertical units within that scanline.
+func (r *Rasterizer) scan(yi int, x0, y0f, x1, y1f fixed.Int26_6) {
+	// Break the 26.6 fixed point X co-ordinates into integral and fractional parts.
+	x0i := int(x0) / 64
+	x0f := x0 - fixed.Int26_6(64*x0i)
+	x1i := int(x1) / 64
+	x1f := x1 - fixed.Int26_6(64*x1i)
+
+	// A perfectly horizontal scan.
+	if y0f == y1f {
+		r.setCell(x1i, yi)
+		return
+	}
+	dx, dy := x1-x0, y1f-y0f
+	// A single cell scan.
+	if x0i == x1i {
+		r.area += int((x0f + x1f) * dy)
+		r.cover += int(dy)
+		return
+	}
+	// There are at least two cells. Apart from the first and last cells,
+	// all intermediate cells go through the full width of the cell,
+	// or 64 units in 26.6 fixed point format.
+	var (
+		p, q, edge0, edge1 fixed.Int26_6
+		xiDelta            int
+	)
+	if dx > 0 {
+		p, q = (64-x0f)*dy, dx
+		edge0, edge1, xiDelta = 0, 64, 1
+	} else {
+		p, q = x0f*dy, -dx
+		edge0, edge1, xiDelta = 64, 0, -1
+	}
+	yDelta, yRem := p/q, p%q
+	if yRem < 0 {
+		yDelta -= 1
+		yRem += q
+	}
+	// Do the first cell.
+	xi, y := x0i, y0f
+	r.area += int((x0f + edge1) * yDelta)
+	r.cover += int(yDelta)
+	xi, y = xi+xiDelta, y+yDelta
+	r.setCell(xi, yi)
+	if xi != x1i {
+		// Do all the intermediate cells.
+		p = 64 * (y1f - y + yDelta)
+		fullDelta, fullRem := p/q, p%q
+		if fullRem < 0 {
+			fullDelta -= 1
+			fullRem += q
+		}
+		yRem -= q
+		for xi != x1i {
+			yDelta = fullDelta
+			yRem += fullRem
+			if yRem >= 0 {
+				yDelta += 1
+				yRem -= q
+			}
+			r.area += int(64 * yDelta)
+			r.cover += int(yDelta)
+			xi, y = xi+xiDelta, y+yDelta
+			r.setCell(xi, yi)
+		}
+	}
+	// Do the last cell.
+	yDelta = y1f - y
+	r.area += int((edge0 + x1f) * yDelta)
+	r.cover += int(yDelta)
+}
+
+// Start starts a new curve at the given point.
+func (r *Rasterizer) Start(a fixed.Point26_6) {
+	r.setCell(int(a.X/64), int(a.Y/64))
+	r.a = a
+}
+
+// Add1 adds a linear segment to the current curve.
+func (r *Rasterizer) Add1(b fixed.Point26_6) {
+	x0, y0 := r.a.X, r.a.Y
+	x1, y1 := b.X, b.Y
+	dx, dy := x1-x0, y1-y0
+	// Break the 26.6 fixed point Y co-ordinates into integral and fractional
+	// parts.
+	y0i := int(y0) / 64
+	y0f := y0 - fixed.Int26_6(64*y0i)
+	y1i := int(y1) / 64
+	y1f := y1 - fixed.Int26_6(64*y1i)
+
+	if y0i == y1i {
+		// There is only one scanline.
+		r.scan(y0i, x0, y0f, x1, y1f)
+
+	} else if dx == 0 {
+		// This is a vertical line segment. We avoid calling r.scan and instead
+		// manipulate r.area and r.cover directly.
+		var (
+			edge0, edge1 fixed.Int26_6
+			yiDelta      int
+		)
+		if dy > 0 {
+			edge0, edge1, yiDelta = 0, 64, 1
+		} else {
+			edge0, edge1, yiDelta = 64, 0, -1
+		}
+		x0i, yi := int(x0)/64, y0i
+		x0fTimes2 := (int(x0) - (64 * x0i)) * 2
+		// Do the first pixel.
+		dcover := int(edge1 - y0f)
+		darea := int(x0fTimes2 * dcover)
+		r.area += darea
+		r.cover += dcover
+		yi += yiDelta
+		r.setCell(x0i, yi)
+		// Do all the intermediate pixels.
+		dcover = int(edge1 - edge0)
+		darea = int(x0fTimes2 * dcover)
+		for yi != y1i {
+			r.area += darea
+			r.cover += dcover
+			yi += yiDelta
+			r.setCell(x0i, yi)
+		}
+		// Do the last pixel.
+		dcover = int(y1f - edge0)
+		darea = int(x0fTimes2 * dcover)
+		r.area += darea
+		r.cover += dcover
+
+	} else {
+		// There are at least two scanlines. Apart from the first and last
+		// scanlines, all intermediate scanlines go through the full height of
+		// the row, or 64 units in 26.6 fixed point format.
+		var (
+			p, q, edge0, edge1 fixed.Int26_6
+			yiDelta            int
+		)
+		if dy > 0 {
+			p, q = (64-y0f)*dx, dy
+			edge0, edge1, yiDelta = 0, 64, 1
+		} else {
+			p, q = y0f*dx, -dy
+			edge0, edge1, yiDelta = 64, 0, -1
+		}
+		xDelta, xRem := p/q, p%q
+		if xRem < 0 {
+			xDelta -= 1
+			xRem += q
+		}
+		// Do the first scanline.
+		x, yi := x0, y0i
+		r.scan(yi, x, y0f, x+xDelta, edge1)
+		x, yi = x+xDelta, yi+yiDelta
+		r.setCell(int(x)/64, yi)
+		if yi != y1i {
+			// Do all the intermediate scanlines.
+			p = 64 * dx
+			fullDelta, fullRem := p/q, p%q
+			if fullRem < 0 {
+				fullDelta -= 1
+				fullRem += q
+			}
+			xRem -= q
+			for yi != y1i {
+				xDelta = fullDelta
+				xRem += fullRem
+				if xRem >= 0 {
+					xDelta += 1
+					xRem -= q
+				}
+				r.scan(yi, x, edge0, x+xDelta, edge1)
+				x, yi = x+xDelta, yi+yiDelta
+				r.setCell(int(x)/64, yi)
+			}
+		}
+		// Do the last scanline.
+		r.scan(yi, x, edge0, x1, y1f)
+	}
+	// The next lineTo starts from b.
+	r.a = b
+}
+
+// Add2 adds a quadratic segment to the current curve.
+func (r *Rasterizer) Add2(b, c fixed.Point26_6) {
+	// Calculate nSplit (the number of recursive decompositions) based on how
+	// 'curvy' it is. Specifically, how much the middle point b deviates from
+	// (a+c)/2.
+	dev := maxAbs(r.a.X-2*b.X+c.X, r.a.Y-2*b.Y+c.Y) / fixed.Int26_6(r.splitScale2)
+	nsplit := 0
+	for dev > 0 {
+		dev /= 4
+		nsplit++
+	}
+	// dev is 32-bit, and nsplit++ every time we shift off 2 bits, so maxNsplit
+	// is 16.
+	const maxNsplit = 16
+	if nsplit > maxNsplit {
+		panic("freetype/raster: Add2 nsplit too large: " + strconv.Itoa(nsplit))
+	}
+	// Recursively decompose the curve nSplit levels deep.
+	var (
+		pStack [2*maxNsplit + 3]fixed.Point26_6
+		sStack [maxNsplit + 1]int
+		i      int
+	)
+	sStack[0] = nsplit
+	pStack[0] = c
+	pStack[1] = b
+	pStack[2] = r.a
+	for i >= 0 {
+		s := sStack[i]
+		p := pStack[2*i:]
+		if s > 0 {
+			// Split the quadratic curve p[:3] into an equivalent set of two
+			// shorter curves: p[:3] and p[2:5]. The new p[4] is the old p[2],
+			// and p[0] is unchanged.
+			mx := p[1].X
+			p[4].X = p[2].X
+			p[3].X = (p[4].X + mx) / 2
+			p[1].X = (p[0].X + mx) / 2
+			p[2].X = (p[1].X + p[3].X) / 2
+			my := p[1].Y
+			p[4].Y = p[2].Y
+			p[3].Y = (p[4].Y + my) / 2
+			p[1].Y = (p[0].Y + my) / 2
+			p[2].Y = (p[1].Y + p[3].Y) / 2
+			// The two shorter curves have one less split to do.
+			sStack[i] = s - 1
+			sStack[i+1] = s - 1
+			i++
+		} else {
+			// Replace the level-0 quadratic with a two-linear-piece
+			// approximation.
+			midx := (p[0].X + 2*p[1].X + p[2].X) / 4
+			midy := (p[0].Y + 2*p[1].Y + p[2].Y) / 4
+			r.Add1(fixed.Point26_6{midx, midy})
+			r.Add1(p[0])
+			i--
+		}
+	}
+}
+
+// Add3 adds a cubic segment to the current curve.
+func (r *Rasterizer) Add3(b, c, d fixed.Point26_6) {
+	// Calculate nSplit (the number of recursive decompositions) based on how
+	// 'curvy' it is.
+	dev2 := maxAbs(r.a.X-3*(b.X+c.X)+d.X, r.a.Y-3*(b.Y+c.Y)+d.Y) / fixed.Int26_6(r.splitScale2)
+	dev3 := maxAbs(r.a.X-2*b.X+d.X, r.a.Y-2*b.Y+d.Y) / fixed.Int26_6(r.splitScale3)
+	nsplit := 0
+	for dev2 > 0 || dev3 > 0 {
+		dev2 /= 8
+		dev3 /= 4
+		nsplit++
+	}
+	// devN is 32-bit, and nsplit++ every time we shift off 2 bits, so
+	// maxNsplit is 16.
+	const maxNsplit = 16
+	if nsplit > maxNsplit {
+		panic("freetype/raster: Add3 nsplit too large: " + strconv.Itoa(nsplit))
+	}
+	// Recursively decompose the curve nSplit levels deep.
+	var (
+		pStack [3*maxNsplit + 4]fixed.Point26_6
+		sStack [maxNsplit + 1]int
+		i      int
+	)
+	sStack[0] = nsplit
+	pStack[0] = d
+	pStack[1] = c
+	pStack[2] = b
+	pStack[3] = r.a
+	for i >= 0 {
+		s := sStack[i]
+		p := pStack[3*i:]
+		if s > 0 {
+			// Split the cubic curve p[:4] into an equivalent set of two
+			// shorter curves: p[:4] and p[3:7]. The new p[6] is the old p[3],
+			// and p[0] is unchanged.
+			m01x := (p[0].X + p[1].X) / 2
+			m12x := (p[1].X + p[2].X) / 2
+			m23x := (p[2].X + p[3].X) / 2
+			p[6].X = p[3].X
+			p[5].X = m23x
+			p[1].X = m01x
+			p[2].X = (m01x + m12x) / 2
+			p[4].X = (m12x + m23x) / 2
+			p[3].X = (p[2].X + p[4].X) / 2
+			m01y := (p[0].Y + p[1].Y) / 2
+			m12y := (p[1].Y + p[2].Y) / 2
+			m23y := (p[2].Y + p[3].Y) / 2
+			p[6].Y = p[3].Y
+			p[5].Y = m23y
+			p[1].Y = m01y
+			p[2].Y = (m01y + m12y) / 2
+			p[4].Y = (m12y + m23y) / 2
+			p[3].Y = (p[2].Y + p[4].Y) / 2
+			// The two shorter curves have one less split to do.
+			sStack[i] = s - 1
+			sStack[i+1] = s - 1
+			i++
+		} else {
+			// Replace the level-0 cubic with a two-linear-piece approximation.
+			midx := (p[0].X + 3*(p[1].X+p[2].X) + p[3].X) / 8
+			midy := (p[0].Y + 3*(p[1].Y+p[2].Y) + p[3].Y) / 8
+			r.Add1(fixed.Point26_6{midx, midy})
+			r.Add1(p[0])
+			i--
+		}
+	}
+}
+
+// AddPath adds the given Path.
+func (r *Rasterizer) AddPath(p Path) {
+	for i := 0; i < len(p); {
+		switch p[i] {
+		case 0:
+			r.Start(
+				fixed.Point26_6{p[i+1], p[i+2]},
+			)
+			i += 4
+		case 1:
+			r.Add1(
+				fixed.Point26_6{p[i+1], p[i+2]},
+			)
+			i += 4
+		case 2:
+			r.Add2(
+				fixed.Point26_6{p[i+1], p[i+2]},
+				fixed.Point26_6{p[i+3], p[i+4]},
+			)
+			i += 6
+		case 3:
+			r.Add3(
+				fixed.Point26_6{p[i+1], p[i+2]},
+				fixed.Point26_6{p[i+3], p[i+4]},
+				fixed.Point26_6{p[i+5], p[i+6]},
+			)
+			i += 8
+		default:
+			panic("freetype/raster: bad path")
+		}
+	}
+}
+
+// AddStroke adds a stroked Path.
+func (r *Rasterizer) AddStroke(q Path, width fixed.Int26_6, cr Capper, jr Joiner) {
+	Stroke(r, q, width, cr, jr)
+}
+
+// areaToAlpha converts an area value to a uint32 alpha value. A completely
+// filled pixel corresponds to an area of 64*64*2, and an alpha of 0xffff. The
+// conversion of area values greater than this depends on the winding rule:
+// even-odd or non-zero.
+func (r *Rasterizer) areaToAlpha(area int) uint32 {
+	// The C Freetype implementation (version 2.3.12) does "alpha := area>>1"
+	// without the +1. Round-to-nearest gives a more symmetric result than
+	// round-down. The C implementation also returns 8-bit alpha, not 16-bit
+	// alpha.
+	a := (area + 1) >> 1
+	if a < 0 {
+		a = -a
+	}
+	alpha := uint32(a)
+	if r.UseNonZeroWinding {
+		if alpha > 0x0fff {
+			alpha = 0x0fff
+		}
+	} else {
+		alpha &= 0x1fff
+		if alpha > 0x1000 {
+			alpha = 0x2000 - alpha
+		} else if alpha == 0x1000 {
+			alpha = 0x0fff
+		}
+	}
+	// alpha is now in the range [0x0000, 0x0fff]. Convert that 12-bit alpha to
+	// 16-bit alpha.
+	return alpha<<4 | alpha>>8
+}
+
+// Rasterize converts r's accumulated curves into Spans for p. The Spans passed
+// to p are non-overlapping, and sorted by Y and then X. They all have non-zero
+// width (and 0 <= X0 < X1 <= r.width) and non-zero A, except for the final
+// Span, which has Y, X0, X1 and A all equal to zero.
+func (r *Rasterizer) Rasterize(p Painter) {
+	r.saveCell()
+	s := 0
+	for yi := 0; yi < len(r.cellIndex); yi++ {
+		xi, cover := 0, 0
+		for c := r.cellIndex[yi]; c != -1; c = r.cell[c].next {
+			if cover != 0 && r.cell[c].xi > xi {
+				alpha := r.areaToAlpha(cover * 64 * 2)
+				if alpha != 0 {
+					xi0, xi1 := xi, r.cell[c].xi
+					if xi0 < 0 {
+						xi0 = 0
+					}
+					if xi1 >= r.width {
+						xi1 = r.width
+					}
+					if xi0 < xi1 {
+						r.spanBuf[s] = Span{yi + r.Dy, xi0 + r.Dx, xi1 + r.Dx, alpha}
+						s++
+					}
+				}
+			}
+			cover += r.cell[c].cover
+			alpha := r.areaToAlpha(cover*64*2 - r.cell[c].area)
+			xi = r.cell[c].xi + 1
+			if alpha != 0 {
+				xi0, xi1 := r.cell[c].xi, xi
+				if xi0 < 0 {
+					xi0 = 0
+				}
+				if xi1 >= r.width {
+					xi1 = r.width
+				}
+				if xi0 < xi1 {
+					r.spanBuf[s] = Span{yi + r.Dy, xi0 + r.Dx, xi1 + r.Dx, alpha}
+					s++
+				}
+			}
+			if s > len(r.spanBuf)-2 {
+				p.Paint(r.spanBuf[:s], false)
+				s = 0
+			}
+		}
+	}
+	p.Paint(r.spanBuf[:s], true)
+}
+
+// Clear cancels any previous calls to r.Start or r.AddXxx.
+func (r *Rasterizer) Clear() {
+	r.a = fixed.Point26_6{}
+	r.xi = 0
+	r.yi = 0
+	r.area = 0
+	r.cover = 0
+	r.cell = r.cell[:0]
+	for i := 0; i < len(r.cellIndex); i++ {
+		r.cellIndex[i] = -1
+	}
+}
+
+// SetBounds sets the maximum width and height of the rasterized image and
+// calls Clear. The width and height are in pixels, not fixed.Int26_6 units.
+func (r *Rasterizer) SetBounds(width, height int) {
+	if width < 0 {
+		width = 0
+	}
+	if height < 0 {
+		height = 0
+	}
+	// Use the same ssN heuristic as the C Freetype (version 2.4.0)
+	// implementation.
+	ss2, ss3 := 32, 16
+	if width > 24 || height > 24 {
+		ss2, ss3 = 2*ss2, 2*ss3
+		if width > 120 || height > 120 {
+			ss2, ss3 = 2*ss2, 2*ss3
+		}
+	}
+	r.width = width
+	r.splitScale2 = ss2
+	r.splitScale3 = ss3
+	r.cell = r.cellBuf[:0]
+	if height > len(r.cellIndexBuf) {
+		r.cellIndex = make([]int, height)
+	} else {
+		r.cellIndex = r.cellIndexBuf[:height]
+	}
+	r.Clear()
+}
+
+// NewRasterizer creates a new Rasterizer with the given bounds.
+func NewRasterizer(width, height int) *Rasterizer {
+	r := new(Rasterizer)
+	r.SetBounds(width, height)
+	return r
+}

vendor/github.com/golang/freetype/raster/stroke.go

@@ -0,0 +1,483 @@
+// Copyright 2010 The Freetype-Go Authors. All rights reserved.
+// Use of this source code is governed by your choice of either the
+// FreeType License or the GNU General Public License version 2 (or
+// any later version), both of which can be found in the LICENSE file.
+
+package raster
+
+import (
+	"golang.org/x/image/math/fixed"
+)
+
+// Two points are considered practically equal if the square of the distance
+// between them is less than one quarter (i.e. 1024 / 4096).
+const epsilon = fixed.Int52_12(1024)
+
+// A Capper signifies how to begin or end a stroked path.
+type Capper interface {
+	// Cap adds a cap to p given a pivot point and the normal vector of a
+	// terminal segment. The normal's length is half of the stroke width.
+	Cap(p Adder, halfWidth fixed.Int26_6, pivot, n1 fixed.Point26_6)
+}
+
+// The CapperFunc type adapts an ordinary function to be a Capper.
+type CapperFunc func(Adder, fixed.Int26_6, fixed.Point26_6, fixed.Point26_6)
+
+func (f CapperFunc) Cap(p Adder, halfWidth fixed.Int26_6, pivot, n1 fixed.Point26_6) {
+	f(p, halfWidth, pivot, n1)
+}
+
+// A Joiner signifies how to join interior nodes of a stroked path.
+type Joiner interface {
+	// Join adds a join to the two sides of a stroked path given a pivot
+	// point and the normal vectors of the trailing and leading segments.
+	// Both normals have length equal to half of the stroke width.
+	Join(lhs, rhs Adder, halfWidth fixed.Int26_6, pivot, n0, n1 fixed.Point26_6)
+}
+
+// The JoinerFunc type adapts an ordinary function to be a Joiner.
+type JoinerFunc func(lhs, rhs Adder, halfWidth fixed.Int26_6, pivot, n0, n1 fixed.Point26_6)
+
+func (f JoinerFunc) Join(lhs, rhs Adder, halfWidth fixed.Int26_6, pivot, n0, n1 fixed.Point26_6) {
+	f(lhs, rhs, halfWidth, pivot, n0, n1)
+}
+
+// RoundCapper adds round caps to a stroked path.
+var RoundCapper Capper = CapperFunc(roundCapper)
+
+func roundCapper(p Adder, halfWidth fixed.Int26_6, pivot, n1 fixed.Point26_6) {
+	// The cubic Bézier approximation to a circle involves the magic number
+	// (√2 - 1) * 4/3, which is approximately 35/64.
+	const k = 35
+	e := pRot90CCW(n1)
+	side := pivot.Add(e)
+	start, end := pivot.Sub(n1), pivot.Add(n1)
+	d, e := n1.Mul(k), e.Mul(k)
+	p.Add3(start.Add(e), side.Sub(d), side)
+	p.Add3(side.Add(d), end.Add(e), end)
+}
+
+// ButtCapper adds butt caps to a stroked path.
+var ButtCapper Capper = CapperFunc(buttCapper)
+
+func buttCapper(p Adder, halfWidth fixed.Int26_6, pivot, n1 fixed.Point26_6) {
+	p.Add1(pivot.Add(n1))
+}
+
+// SquareCapper adds square caps to a stroked path.
+var SquareCapper Capper = CapperFunc(squareCapper)
+
+func squareCapper(p Adder, halfWidth fixed.Int26_6, pivot, n1 fixed.Point26_6) {
+	e := pRot90CCW(n1)
+	side := pivot.Add(e)
+	p.Add1(side.Sub(n1))
+	p.Add1(side.Add(n1))
+	p.Add1(pivot.Add(n1))
+}
+
+// RoundJoiner adds round joins to a stroked path.
+var RoundJoiner Joiner = JoinerFunc(roundJoiner)
+
+func roundJoiner(lhs, rhs Adder, haflWidth fixed.Int26_6, pivot, n0, n1 fixed.Point26_6) {
+	dot := pDot(pRot90CW(n0), n1)
+	if dot >= 0 {
+		addArc(lhs, pivot, n0, n1)
+		rhs.Add1(pivot.Sub(n1))
+	} else {
+		lhs.Add1(pivot.Add(n1))
+		addArc(rhs, pivot, pNeg(n0), pNeg(n1))
+	}
+}
+
+// BevelJoiner adds bevel joins to a stroked path.
+var BevelJoiner Joiner = JoinerFunc(bevelJoiner)
+
+func bevelJoiner(lhs, rhs Adder, haflWidth fixed.Int26_6, pivot, n0, n1 fixed.Point26_6) {
+	lhs.Add1(pivot.Add(n1))
+	rhs.Add1(pivot.Sub(n1))
+}
+
+// addArc adds a circular arc from pivot+n0 to pivot+n1 to p. The shorter of
+// the two possible arcs is taken, i.e. the one spanning <= 180 degrees. The
+// two vectors n0 and n1 must be of equal length.
+func addArc(p Adder, pivot, n0, n1 fixed.Point26_6) {
+	// r2 is the square of the length of n0.
+	r2 := pDot(n0, n0)
+	if r2 < epsilon {
+		// The arc radius is so small that we collapse to a straight line.
+		p.Add1(pivot.Add(n1))
+		return
+	}
+	// We approximate the arc by 0, 1, 2 or 3 45-degree quadratic segments plus
+	// a final quadratic segment from s to n1. Each 45-degree segment has
+	// control points {1, 0}, {1, tan(π/8)} and {1/√2, 1/√2} suitably scaled,
+	// rotated and translated. tan(π/8) is approximately 27/64.
+	const tpo8 = 27
+	var s fixed.Point26_6
+	// We determine which octant the angle between n0 and n1 is in via three
+	// dot products. m0, m1 and m2 are n0 rotated clockwise by 45, 90 and 135
+	// degrees.
+	m0 := pRot45CW(n0)
+	m1 := pRot90CW(n0)
+	m2 := pRot90CW(m0)
+	if pDot(m1, n1) >= 0 {
+		if pDot(n0, n1) >= 0 {
+			if pDot(m2, n1) <= 0 {
+				// n1 is between 0 and 45 degrees clockwise of n0.
+				s = n0
+			} else {
+				// n1 is between 45 and 90 degrees clockwise of n0.
+				p.Add2(pivot.Add(n0).Add(m1.Mul(tpo8)), pivot.Add(m0))
+				s = m0
+			}
+		} else {
+			pm1, n0t := pivot.Add(m1), n0.Mul(tpo8)
+			p.Add2(pivot.Add(n0).Add(m1.Mul(tpo8)), pivot.Add(m0))
+			p.Add2(pm1.Add(n0t), pm1)
+			if pDot(m0, n1) >= 0 {
+				// n1 is between 90 and 135 degrees clockwise of n0.
+				s = m1
+			} else {
+				// n1 is between 135 and 180 degrees clockwise of n0.
+				p.Add2(pm1.Sub(n0t), pivot.Add(m2))
+				s = m2
+			}
+		}
+	} else {
+		if pDot(n0, n1) >= 0 {
+			if pDot(m0, n1) >= 0 {
+				// n1 is between 0 and 45 degrees counter-clockwise of n0.
+				s = n0
+			} else {
+				// n1 is between 45 and 90 degrees counter-clockwise of n0.
+				p.Add2(pivot.Add(n0).Sub(m1.Mul(tpo8)), pivot.Sub(m2))
+				s = pNeg(m2)
+			}
+		} else {
+			pm1, n0t := pivot.Sub(m1), n0.Mul(tpo8)
+			p.Add2(pivot.Add(n0).Sub(m1.Mul(tpo8)), pivot.Sub(m2))
+			p.Add2(pm1.Add(n0t), pm1)
+			if pDot(m2, n1) <= 0 {
+				// n1 is between 90 and 135 degrees counter-clockwise of n0.
+				s = pNeg(m1)
+			} else {
+				// n1 is between 135 and 180 degrees counter-clockwise of n0.
+				p.Add2(pm1.Sub(n0t), pivot.Sub(m0))
+				s = pNeg(m0)
+			}
+		}
+	}
+	// The final quadratic segment has two endpoints s and n1 and the middle
+	// control point is a multiple of s.Add(n1), i.e. it is on the angle
+	// bisector of those two points. The multiple ranges between 128/256 and
+	// 150/256 as the angle between s and n1 ranges between 0 and 45 degrees.
+	//
+	// When the angle is 0 degrees (i.e. s and n1 are coincident) then
+	// s.Add(n1) is twice s and so the middle control point of the degenerate
+	// quadratic segment should be half s.Add(n1), and half = 128/256.
+	//
+	// When the angle is 45 degrees then 150/256 is the ratio of the lengths of
+	// the two vectors {1, tan(π/8)} and {1 + 1/√2, 1/√2}.
+	//
+	// d is the normalized dot product between s and n1. Since the angle ranges
+	// between 0 and 45 degrees then d ranges between 256/256 and 181/256.
+	d := 256 * pDot(s, n1) / r2
+	multiple := fixed.Int26_6(150-(150-128)*(d-181)/(256-181)) >> 2
+	p.Add2(pivot.Add(s.Add(n1).Mul(multiple)), pivot.Add(n1))
+}
+
+// midpoint returns the midpoint of two Points.
+func midpoint(a, b fixed.Point26_6) fixed.Point26_6 {
+	return fixed.Point26_6{(a.X + b.X) / 2, (a.Y + b.Y) / 2}
+}
+
+// angleGreaterThan45 returns whether the angle between two vectors is more
+// than 45 degrees.
+func angleGreaterThan45(v0, v1 fixed.Point26_6) bool {
+	v := pRot45CCW(v0)
+	return pDot(v, v1) < 0 || pDot(pRot90CW(v), v1) < 0
+}
+
+// interpolate returns the point (1-t)*a + t*b.
+func interpolate(a, b fixed.Point26_6, t fixed.Int52_12) fixed.Point26_6 {
+	s := 1<<12 - t
+	x := s*fixed.Int52_12(a.X) + t*fixed.Int52_12(b.X)
+	y := s*fixed.Int52_12(a.Y) + t*fixed.Int52_12(b.Y)
+	return fixed.Point26_6{fixed.Int26_6(x >> 12), fixed.Int26_6(y >> 12)}
+}
+
+// curviest2 returns the value of t for which the quadratic parametric curve
+// (1-t)²*a + 2*t*(1-t).b + t²*c has maximum curvature.
+//
+// The curvature of the parametric curve f(t) = (x(t), y(t)) is
+// |x′y″-y′x″| / (x′²+y′²)^(3/2).
+//
+// Let d = b-a and e = c-2*b+a, so that f′(t) = 2*d+2*e*t and f″(t) = 2*e.
+// The curvature's numerator is (2*dx+2*ex*t)*(2*ey)-(2*dy+2*ey*t)*(2*ex),
+// which simplifies to 4*dx*ey-4*dy*ex, which is constant with respect to t.
+//
+// Thus, curvature is extreme where the denominator is extreme, i.e. where
+// (x′²+y′²) is extreme. The first order condition is that
+// 2*x′*x″+2*y′*y″ = 0, or (dx+ex*t)*ex + (dy+ey*t)*ey = 0.
+// Solving for t gives t = -(dx*ex+dy*ey) / (ex*ex+ey*ey).
+func curviest2(a, b, c fixed.Point26_6) fixed.Int52_12 {
+	dx := int64(b.X - a.X)
+	dy := int64(b.Y - a.Y)
+	ex := int64(c.X - 2*b.X + a.X)
+	ey := int64(c.Y - 2*b.Y + a.Y)
+	if ex == 0 && ey == 0 {
+		return 2048
+	}
+	return fixed.Int52_12(-4096 * (dx*ex + dy*ey) / (ex*ex + ey*ey))
+}
+
+// A stroker holds state for stroking a path.
+type stroker struct {
+	// p is the destination that records the stroked path.
+	p Adder
+	// u is the half-width of the stroke.
+	u fixed.Int26_6
+	// cr and jr specify how to end and connect path segments.
+	cr Capper
+	jr Joiner
+	// r is the reverse path. Stroking a path involves constructing two
+	// parallel paths 2*u apart. The first path is added immediately to p,
+	// the second path is accumulated in r and eventually added in reverse.
+	r Path
+	// a is the most recent segment point. anorm is the segment normal of
+	// length u at that point.
+	a, anorm fixed.Point26_6
+}
+
+// addNonCurvy2 adds a quadratic segment to the stroker, where the segment
+// defined by (k.a, b, c) achieves maximum curvature at either k.a or c.
+func (k *stroker) addNonCurvy2(b, c fixed.Point26_6) {
+	// We repeatedly divide the segment at its middle until it is straight
+	// enough to approximate the stroke by just translating the control points.
+	// ds and ps are stacks of depths and points. t is the top of the stack.
+	const maxDepth = 5
+	var (
+		ds [maxDepth + 1]int
+		ps [2*maxDepth + 3]fixed.Point26_6
+		t  int
+	)
+	// Initially the ps stack has one quadratic segment of depth zero.
+	ds[0] = 0
+	ps[2] = k.a
+	ps[1] = b
+	ps[0] = c
+	anorm := k.anorm
+	var cnorm fixed.Point26_6
+
+	for {
+		depth := ds[t]
+		a := ps[2*t+2]
+		b := ps[2*t+1]
+		c := ps[2*t+0]
+		ab := b.Sub(a)
+		bc := c.Sub(b)
+		abIsSmall := pDot(ab, ab) < fixed.Int52_12(1<<12)
+		bcIsSmall := pDot(bc, bc) < fixed.Int52_12(1<<12)
+		if abIsSmall && bcIsSmall {
+			// Approximate the segment by a circular arc.
+			cnorm = pRot90CCW(pNorm(bc, k.u))
+			mac := midpoint(a, c)
+			addArc(k.p, mac, anorm, cnorm)
+			addArc(&k.r, mac, pNeg(anorm), pNeg(cnorm))
+		} else if depth < maxDepth && angleGreaterThan45(ab, bc) {
+			// Divide the segment in two and push both halves on the stack.
+			mab := midpoint(a, b)
+			mbc := midpoint(b, c)
+			t++
+			ds[t+0] = depth + 1
+			ds[t-1] = depth + 1
+			ps[2*t+2] = a
+			ps[2*t+1] = mab
+			ps[2*t+0] = midpoint(mab, mbc)
+			ps[2*t-1] = mbc
+			continue
+		} else {
+			// Translate the control points.
+			bnorm := pRot90CCW(pNorm(c.Sub(a), k.u))
+			cnorm = pRot90CCW(pNorm(bc, k.u))
+			k.p.Add2(b.Add(bnorm), c.Add(cnorm))
+			k.r.Add2(b.Sub(bnorm), c.Sub(cnorm))
+		}
+		if t == 0 {
+			k.a, k.anorm = c, cnorm
+			return
+		}
+		t--
+		anorm = cnorm
+	}
+	panic("unreachable")
+}
+
+// Add1 adds a linear segment to the stroker.
+func (k *stroker) Add1(b fixed.Point26_6) {
+	bnorm := pRot90CCW(pNorm(b.Sub(k.a), k.u))
+	if len(k.r) == 0 {
+		k.p.Start(k.a.Add(bnorm))
+		k.r.Start(k.a.Sub(bnorm))
+	} else {
+		k.jr.Join(k.p, &k.r, k.u, k.a, k.anorm, bnorm)
+	}
+	k.p.Add1(b.Add(bnorm))
+	k.r.Add1(b.Sub(bnorm))
+	k.a, k.anorm = b, bnorm
+}
+
+// Add2 adds a quadratic segment to the stroker.
+func (k *stroker) Add2(b, c fixed.Point26_6) {
+	ab := b.Sub(k.a)
+	bc := c.Sub(b)
+	abnorm := pRot90CCW(pNorm(ab, k.u))
+	if len(k.r) == 0 {
+		k.p.Start(k.a.Add(abnorm))
+		k.r.Start(k.a.Sub(abnorm))
+	} else {
+		k.jr.Join(k.p, &k.r, k.u, k.a, k.anorm, abnorm)
+	}
+
+	// Approximate nearly-degenerate quadratics by linear segments.
+	abIsSmall := pDot(ab, ab) < epsilon
+	bcIsSmall := pDot(bc, bc) < epsilon
+	if abIsSmall || bcIsSmall {
+		acnorm := pRot90CCW(pNorm(c.Sub(k.a), k.u))
+		k.p.Add1(c.Add(acnorm))
+		k.r.Add1(c.Sub(acnorm))
+		k.a, k.anorm = c, acnorm
+		return
+	}
+
+	// The quadratic segment (k.a, b, c) has a point of maximum curvature.
+	// If this occurs at an end point, we process the segment as a whole.
+	t := curviest2(k.a, b, c)
+	if t <= 0 || 4096 <= t {
+		k.addNonCurvy2(b, c)
+		return
+	}
+
+	// Otherwise, we perform a de Casteljau decomposition at the point of
+	// maximum curvature and process the two straighter parts.
+	mab := interpolate(k.a, b, t)
+	mbc := interpolate(b, c, t)
+	mabc := interpolate(mab, mbc, t)
+
+	// If the vectors ab and bc are close to being in opposite directions,
+	// then the decomposition can become unstable, so we approximate the
+	// quadratic segment by two linear segments joined by an arc.
+	bcnorm := pRot90CCW(pNorm(bc, k.u))
+	if pDot(abnorm, bcnorm) < -fixed.Int52_12(k.u)*fixed.Int52_12(k.u)*2047/2048 {
+		pArc := pDot(abnorm, bc) < 0
+
+		k.p.Add1(mabc.Add(abnorm))
+		if pArc {
+			z := pRot90CW(abnorm)
+			addArc(k.p, mabc, abnorm, z)
+			addArc(k.p, mabc, z, bcnorm)
+		}
+		k.p.Add1(mabc.Add(bcnorm))
+		k.p.Add1(c.Add(bcnorm))
+
+		k.r.Add1(mabc.Sub(abnorm))
+		if !pArc {
+			z := pRot90CW(abnorm)
+			addArc(&k.r, mabc, pNeg(abnorm), z)
+			addArc(&k.r, mabc, z, pNeg(bcnorm))
+		}
+		k.r.Add1(mabc.Sub(bcnorm))
+		k.r.Add1(c.Sub(bcnorm))
+
+		k.a, k.anorm = c, bcnorm
+		return
+	}
+
+	// Process the decomposed parts.
+	k.addNonCurvy2(mab, mabc)
+	k.addNonCurvy2(mbc, c)
+}
+
+// Add3 adds a cubic segment to the stroker.
+func (k *stroker) Add3(b, c, d fixed.Point26_6) {
+	panic("freetype/raster: stroke unimplemented for cubic segments")
+}
+
+// stroke adds the stroked Path q to p, where q consists of exactly one curve.
+func (k *stroker) stroke(q Path) {
+	// Stroking is implemented by deriving two paths each k.u apart from q.
+	// The left-hand-side path is added immediately to k.p; the right-hand-side
+	// path is accumulated in k.r. Once we've finished adding the LHS to k.p,
+	// we add the RHS in reverse order.
+	k.r = make(Path, 0, len(q))
+	k.a = fixed.Point26_6{q[1], q[2]}
+	for i := 4; i < len(q); {
+		switch q[i] {
+		case 1:
+			k.Add1(
+				fixed.Point26_6{q[i+1], q[i+2]},
+			)
+			i += 4
+		case 2:
+			k.Add2(
+				fixed.Point26_6{q[i+1], q[i+2]},
+				fixed.Point26_6{q[i+3], q[i+4]},
+			)
+			i += 6
+		case 3:
+			k.Add3(
+				fixed.Point26_6{q[i+1], q[i+2]},
+				fixed.Point26_6{q[i+3], q[i+4]},
+				fixed.Point26_6{q[i+5], q[i+6]},
+			)
+			i += 8
+		default:
+			panic("freetype/raster: bad path")
+		}
+	}
+	if len(k.r) == 0 {
+		return
+	}
+	// TODO(nigeltao): if q is a closed curve then we should join the first and
+	// last segments instead of capping them.
+	k.cr.Cap(k.p, k.u, q.lastPoint(), pNeg(k.anorm))
+	addPathReversed(k.p, k.r)
+	pivot := q.firstPoint()
+	k.cr.Cap(k.p, k.u, pivot, pivot.Sub(fixed.Point26_6{k.r[1], k.r[2]}))
+}
+
+// Stroke adds q stroked with the given width to p. The result is typically
+// self-intersecting and should be rasterized with UseNonZeroWinding.
+// cr and jr may be nil, which defaults to a RoundCapper or RoundJoiner.
+func Stroke(p Adder, q Path, width fixed.Int26_6, cr Capper, jr Joiner) {
+	if len(q) == 0 {
+		return
+	}
+	if cr == nil {
+		cr = RoundCapper
+	}
+	if jr == nil {
+		jr = RoundJoiner
+	}
+	if q[0] != 0 {
+		panic("freetype/raster: bad path")
+	}
+	s := stroker{p: p, u: width / 2, cr: cr, jr: jr}
+	i := 0
+	for j := 4; j < len(q); {
+		switch q[j] {
+		case 0:
+			s.stroke(q[i:j])
+			i, j = j, j+4
+		case 1:
+			j += 4
+		case 2:
+			j += 6
+		case 3:
+			j += 8
+		default:
+			panic("freetype/raster: bad path")
+		}
+	}
+	s.stroke(q[i:])
+}

vendor/github.com/golang/freetype/truetype/face.go

@@ -0,0 +1,507 @@
+// Copyright 2015 The Freetype-Go Authors. All rights reserved.
+// Use of this source code is governed by your choice of either the
+// FreeType License or the GNU General Public License version 2 (or
+// any later version), both of which can be found in the LICENSE file.
+
+package truetype
+
+import (
+	"image"
+	"math"
+
+	"github.com/golang/freetype/raster"
+	"golang.org/x/image/font"
+	"golang.org/x/image/math/fixed"
+)
+
+func powerOf2(i int) bool {
+	return i != 0 && (i&(i-1)) == 0
+}
+
+// Options are optional arguments to NewFace.
+type Options struct {
+	// Size is the font size in points, as in "a 10 point font size".
+	//
+	// A zero value means to use a 12 point font size.
+	Size float64
+
+	// DPI is the dots-per-inch resolution.
+	//
+	// A zero value means to use 72 DPI.
+	DPI float64
+
+	// Hinting is how to quantize the glyph nodes.
+	//
+	// A zero value means to use no hinting.
+	Hinting font.Hinting
+
+	// GlyphCacheEntries is the number of entries in the glyph mask image
+	// cache.
+	//
+	// If non-zero, it must be a power of 2.
+	//
+	// A zero value means to use 512 entries.
+	GlyphCacheEntries int
+
+	// SubPixelsX is the number of sub-pixel locations a glyph's dot is
+	// quantized to, in the horizontal direction. For example, a value of 8
+	// means that the dot is quantized to 1/8th of a pixel. This quantization
+	// only affects the glyph mask image, not its bounding box or advance
+	// width. A higher value gives a more faithful glyph image, but reduces the
+	// effectiveness of the glyph cache.
+	//
+	// If non-zero, it must be a power of 2, and be between 1 and 64 inclusive.
+	//
+	// A zero value means to use 4 sub-pixel locations.
+	SubPixelsX int
+
+	// SubPixelsY is the number of sub-pixel locations a glyph's dot is
+	// quantized to, in the vertical direction. For example, a value of 8
+	// means that the dot is quantized to 1/8th of a pixel. This quantization
+	// only affects the glyph mask image, not its bounding box or advance
+	// width. A higher value gives a more faithful glyph image, but reduces the
+	// effectiveness of the glyph cache.
+	//
+	// If non-zero, it must be a power of 2, and be between 1 and 64 inclusive.
+	//
+	// A zero value means to use 1 sub-pixel location.
+	SubPixelsY int
+}
+
+func (o *Options) size() float64 {
+	if o != nil && o.Size > 0 {
+		return o.Size
+	}
+	return 12
+}
+
+func (o *Options) dpi() float64 {
+	if o != nil && o.DPI > 0 {
+		return o.DPI
+	}
+	return 72
+}
+
+func (o *Options) hinting() font.Hinting {
+	if o != nil {
+		switch o.Hinting {
+		case font.HintingVertical, font.HintingFull:
+			// TODO: support vertical hinting.
+			return font.HintingFull
+		}
+	}
+	return font.HintingNone
+}
+
+func (o *Options) glyphCacheEntries() int {
+	if o != nil && powerOf2(o.GlyphCacheEntries) {
+		return o.GlyphCacheEntries
+	}
+	// 512 is 128 * 4 * 1, which lets us cache 128 glyphs at 4 * 1 subpixel
+	// locations in the X and Y direction.
+	return 512
+}
+
+func (o *Options) subPixelsX() (value uint32, halfQuantum, mask fixed.Int26_6) {
+	if o != nil {
+		switch o.SubPixelsX {
+		case 1, 2, 4, 8, 16, 32, 64:
+			return subPixels(o.SubPixelsX)
+		}
+	}
+	// This default value of 4 isn't based on anything scientific, merely as
+	// small a number as possible that looks almost as good as no quantization,
+	// or returning subPixels(64).
+	return subPixels(4)
+}
+
+func (o *Options) subPixelsY() (value uint32, halfQuantum, mask fixed.Int26_6) {
+	if o != nil {
+		switch o.SubPixelsX {
+		case 1, 2, 4, 8, 16, 32, 64:
+			return subPixels(o.SubPixelsX)
+		}
+	}
+	// This default value of 1 isn't based on anything scientific, merely that
+	// vertical sub-pixel glyph rendering is pretty rare. Baseline locations
+	// can usually afford to snap to the pixel grid, so the vertical direction
+	// doesn't have the deal with the horizontal's fractional advance widths.
+	return subPixels(1)
+}
+
+// subPixels returns q and the bias and mask that leads to q quantized
+// sub-pixel locations per full pixel.
+//
+// For example, q == 4 leads to a bias of 8 and a mask of 0xfffffff0, or -16,
+// because we want to round fractions of fixed.Int26_6 as:
+//	-  0 to  7 rounds to 0.
+//	-  8 to 23 rounds to 16.
+//	- 24 to 39 rounds to 32.
+//	- 40 to 55 rounds to 48.
+//	- 56 to 63 rounds to 64.
+// which means to add 8 and then bitwise-and with -16, in two's complement
+// representation.
+//
+// When q ==  1, we want bias == 32 and mask == -64.
+// When q ==  2, we want bias == 16 and mask == -32.
+// When q ==  4, we want bias ==  8 and mask == -16.
+// ...
+// When q == 64, we want bias ==  0 and mask ==  -1. (The no-op case).
+// The pattern is clear.
+func subPixels(q int) (value uint32, bias, mask fixed.Int26_6) {
+	return uint32(q), 32 / fixed.Int26_6(q), -64 / fixed.Int26_6(q)
+}
+
+// glyphCacheEntry caches the arguments and return values of rasterize.
+type glyphCacheEntry struct {
+	key glyphCacheKey
+	val glyphCacheVal
+}
+
+type glyphCacheKey struct {
+	index  Index
+	fx, fy uint8
+}
+
+type glyphCacheVal struct {
+	advanceWidth fixed.Int26_6
+	offset       image.Point
+	gw           int
+	gh           int
+}
+
+type indexCacheEntry struct {
+	rune  rune
+	index Index
+}
+
+// NewFace returns a new font.Face for the given Font.
+func NewFace(f *Font, opts *Options) font.Face {
+	a := &face{
+		f:          f,
+		hinting:    opts.hinting(),
+		scale:      fixed.Int26_6(0.5 + (opts.size() * opts.dpi() * 64 / 72)),
+		glyphCache: make([]glyphCacheEntry, opts.glyphCacheEntries()),
+	}
+	a.subPixelX, a.subPixelBiasX, a.subPixelMaskX = opts.subPixelsX()
+	a.subPixelY, a.subPixelBiasY, a.subPixelMaskY = opts.subPixelsY()
+
+	// Fill the cache with invalid entries. Valid glyph cache entries have fx
+	// and fy in the range [0, 64). Valid index cache entries have rune >= 0.
+	for i := range a.glyphCache {
+		a.glyphCache[i].key.fy = 0xff
+	}
+	for i := range a.indexCache {
+		a.indexCache[i].rune = -1
+	}
+
+	// Set the rasterizer's bounds to be big enough to handle the largest glyph.
+	b := f.Bounds(a.scale)
+	xmin := +int(b.Min.X) >> 6
+	ymin := -int(b.Max.Y) >> 6
+	xmax := +int(b.Max.X+63) >> 6
+	ymax := -int(b.Min.Y-63) >> 6
+	a.maxw = xmax - xmin
+	a.maxh = ymax - ymin
+	a.masks = image.NewAlpha(image.Rect(0, 0, a.maxw, a.maxh*len(a.glyphCache)))
+	a.r.SetBounds(a.maxw, a.maxh)
+	a.p = facePainter{a}
+
+	return a
+}
+
+type face struct {
+	f             *Font
+	hinting       font.Hinting
+	scale         fixed.Int26_6
+	subPixelX     uint32
+	subPixelBiasX fixed.Int26_6
+	subPixelMaskX fixed.Int26_6
+	subPixelY     uint32
+	subPixelBiasY fixed.Int26_6
+	subPixelMaskY fixed.Int26_6
+	masks         *image.Alpha
+	glyphCache    []glyphCacheEntry
+	r             raster.Rasterizer
+	p             raster.Painter
+	paintOffset   int
+	maxw          int
+	maxh          int
+	glyphBuf      GlyphBuf
+	indexCache    [indexCacheLen]indexCacheEntry
+
+	// TODO: clip rectangle?
+}
+
+const indexCacheLen = 256
+
+func (a *face) index(r rune) Index {
+	const mask = indexCacheLen - 1
+	c := &a.indexCache[r&mask]
+	if c.rune == r {
+		return c.index
+	}
+	i := a.f.Index(r)
+	c.rune = r
+	c.index = i
+	return i
+}
+
+// Close satisfies the font.Face interface.
+func (a *face) Close() error { return nil }
+
+// Metrics satisfies the font.Face interface.
+func (a *face) Metrics() font.Metrics {
+	scale := float64(a.scale)
+	fupe := float64(a.f.FUnitsPerEm())
+	return font.Metrics{
+		Height:  a.scale,
+		Ascent:  fixed.Int26_6(math.Ceil(scale * float64(+a.f.ascent) / fupe)),
+		Descent: fixed.Int26_6(math.Ceil(scale * float64(-a.f.descent) / fupe)),
+	}
+}
+
+// Kern satisfies the font.Face interface.
+func (a *face) Kern(r0, r1 rune) fixed.Int26_6 {
+	i0 := a.index(r0)
+	i1 := a.index(r1)
+	kern := a.f.Kern(a.scale, i0, i1)
+	if a.hinting != font.HintingNone {
+		kern = (kern + 32) &^ 63
+	}
+	return kern
+}
+
+// Glyph satisfies the font.Face interface.
+func (a *face) Glyph(dot fixed.Point26_6, r rune) (
+	dr image.Rectangle, mask image.Image, maskp image.Point, advance fixed.Int26_6, ok bool) {
+
+	// Quantize to the sub-pixel granularity.
+	dotX := (dot.X + a.subPixelBiasX) & a.subPixelMaskX
+	dotY := (dot.Y + a.subPixelBiasY) & a.subPixelMaskY
+
+	// Split the coordinates into their integer and fractional parts.
+	ix, fx := int(dotX>>6), dotX&0x3f
+	iy, fy := int(dotY>>6), dotY&0x3f
+
+	index := a.index(r)
+	cIndex := uint32(index)
+	cIndex = cIndex*a.subPixelX - uint32(fx/a.subPixelMaskX)
+	cIndex = cIndex*a.subPixelY - uint32(fy/a.subPixelMaskY)
+	cIndex &= uint32(len(a.glyphCache) - 1)
+	a.paintOffset = a.maxh * int(cIndex)
+	k := glyphCacheKey{
+		index: index,
+		fx:    uint8(fx),
+		fy:    uint8(fy),
+	}
+	var v glyphCacheVal
+	if a.glyphCache[cIndex].key != k {
+		var ok bool
+		v, ok = a.rasterize(index, fx, fy)
+		if !ok {
+			return image.Rectangle{}, nil, image.Point{}, 0, false
+		}
+		a.glyphCache[cIndex] = glyphCacheEntry{k, v}
+	} else {
+		v = a.glyphCache[cIndex].val
+	}
+
+	dr.Min = image.Point{
+		X: ix + v.offset.X,
+		Y: iy + v.offset.Y,
+	}
+	dr.Max = image.Point{
+		X: dr.Min.X + v.gw,
+		Y: dr.Min.Y + v.gh,
+	}
+	return dr, a.masks, image.Point{Y: a.paintOffset}, v.advanceWidth, true
+}
+
+func (a *face) GlyphBounds(r rune) (bounds fixed.Rectangle26_6, advance fixed.Int26_6, ok bool) {
+	if err := a.glyphBuf.Load(a.f, a.scale, a.index(r), a.hinting); err != nil {
+		return fixed.Rectangle26_6{}, 0, false
+	}
+	xmin := +a.glyphBuf.Bounds.Min.X
+	ymin := -a.glyphBuf.Bounds.Max.Y
+	xmax := +a.glyphBuf.Bounds.Max.X
+	ymax := -a.glyphBuf.Bounds.Min.Y
+	if xmin > xmax || ymin > ymax {
+		return fixed.Rectangle26_6{}, 0, false
+	}
+	return fixed.Rectangle26_6{
+		Min: fixed.Point26_6{
+			X: xmin,
+			Y: ymin,
+		},
+		Max: fixed.Point26_6{
+			X: xmax,
+			Y: ymax,
+		},
+	}, a.glyphBuf.AdvanceWidth, true
+}
+
+func (a *face) GlyphAdvance(r rune) (advance fixed.Int26_6, ok bool) {
+	if err := a.glyphBuf.Load(a.f, a.scale, a.index(r), a.hinting); err != nil {
+		return 0, false
+	}
+	return a.glyphBuf.AdvanceWidth, true
+}
+
+// rasterize returns the advance width, integer-pixel offset to render at, and
+// the width and height of the given glyph at the given sub-pixel offsets.
+//
+// The 26.6 fixed point arguments fx and fy must be in the range [0, 1).
+func (a *face) rasterize(index Index, fx, fy fixed.Int26_6) (v glyphCacheVal, ok bool) {
+	if err := a.glyphBuf.Load(a.f, a.scale, index, a.hinting); err != nil {
+		return glyphCacheVal{}, false
+	}
+	// Calculate the integer-pixel bounds for the glyph.
+	xmin := int(fx+a.glyphBuf.Bounds.Min.X) >> 6
+	ymin := int(fy-a.glyphBuf.Bounds.Max.Y) >> 6
+	xmax := int(fx+a.glyphBuf.Bounds.Max.X+0x3f) >> 6
+	ymax := int(fy-a.glyphBuf.Bounds.Min.Y+0x3f) >> 6
+	if xmin > xmax || ymin > ymax {
+		return glyphCacheVal{}, false
+	}
+	// A TrueType's glyph's nodes can have negative co-ordinates, but the
+	// rasterizer clips anything left of x=0 or above y=0. xmin and ymin are
+	// the pixel offsets, based on the font's FUnit metrics, that let a
+	// negative co-ordinate in TrueType space be non-negative in rasterizer
+	// space. xmin and ymin are typically <= 0.
+	fx -= fixed.Int26_6(xmin << 6)
+	fy -= fixed.Int26_6(ymin << 6)
+	// Rasterize the glyph's vectors.
+	a.r.Clear()
+	pixOffset := a.paintOffset * a.maxw
+	clear(a.masks.Pix[pixOffset : pixOffset+a.maxw*a.maxh])
+	e0 := 0
+	for _, e1 := range a.glyphBuf.Ends {
+		a.drawContour(a.glyphBuf.Points[e0:e1], fx, fy)
+		e0 = e1
+	}
+	a.r.Rasterize(a.p)
+	return glyphCacheVal{
+		a.glyphBuf.AdvanceWidth,
+		image.Point{xmin, ymin},
+		xmax - xmin,
+		ymax - ymin,
+	}, true
+}
+
+func clear(pix []byte) {
+	for i := range pix {
+		pix[i] = 0
+	}
+}
+
+// drawContour draws the given closed contour with the given offset.
+func (a *face) drawContour(ps []Point, dx, dy fixed.Int26_6) {
+	if len(ps) == 0 {
+		return
+	}
+
+	// The low bit of each point's Flags value is whether the point is on the
+	// curve. Truetype fonts only have quadratic Bézier curves, not cubics.
+	// Thus, two consecutive off-curve points imply an on-curve point in the
+	// middle of those two.
+	//
+	// See http://chanae.walon.org/pub/ttf/ttf_glyphs.htm for more details.
+
+	// ps[0] is a truetype.Point measured in FUnits and positive Y going
+	// upwards. start is the same thing measured in fixed point units and
+	// positive Y going downwards, and offset by (dx, dy).
+	start := fixed.Point26_6{
+		X: dx + ps[0].X,
+		Y: dy - ps[0].Y,
+	}
+	var others []Point
+	if ps[0].Flags&0x01 != 0 {
+		others = ps[1:]
+	} else {
+		last := fixed.Point26_6{
+			X: dx + ps[len(ps)-1].X,
+			Y: dy - ps[len(ps)-1].Y,
+		}
+		if ps[len(ps)-1].Flags&0x01 != 0 {
+			start = last
+			others = ps[:len(ps)-1]
+		} else {
+			start = fixed.Point26_6{
+				X: (start.X + last.X) / 2,
+				Y: (start.Y + last.Y) / 2,
+			}
+			others = ps
+		}
+	}
+	a.r.Start(start)
+	q0, on0 := start, true
+	for _, p := range others {
+		q := fixed.Point26_6{
+			X: dx + p.X,
+			Y: dy - p.Y,
+		}
+		on := p.Flags&0x01 != 0
+		if on {
+			if on0 {
+				a.r.Add1(q)
+			} else {
+				a.r.Add2(q0, q)
+			}
+		} else {
+			if on0 {
+				// No-op.
+			} else {
+				mid := fixed.Point26_6{
+					X: (q0.X + q.X) / 2,
+					Y: (q0.Y + q.Y) / 2,
+				}
+				a.r.Add2(q0, mid)
+			}
+		}
+		q0, on0 = q, on
+	}
+	// Close the curve.
+	if on0 {
+		a.r.Add1(start)
+	} else {
+		a.r.Add2(q0, start)
+	}
+}
+
+// facePainter is like a raster.AlphaSrcPainter, with an additional Y offset
+// (face.paintOffset) to the painted spans.
+type facePainter struct {
+	a *face
+}
+
+func (p facePainter) Paint(ss []raster.Span, done bool) {
+	m := p.a.masks
+	b := m.Bounds()
+	b.Min.Y = p.a.paintOffset
+	b.Max.Y = p.a.paintOffset + p.a.maxh
+	for _, s := range ss {
+		s.Y += p.a.paintOffset
+		if s.Y < b.Min.Y {
+			continue
+		}
+		if s.Y >= b.Max.Y {
+			return
+		}
+		if s.X0 < b.Min.X {
+			s.X0 = b.Min.X
+		}
+		if s.X1 > b.Max.X {
+			s.X1 = b.Max.X
+		}
+		if s.X0 >= s.X1 {
+			continue
+		}
+		base := (s.Y-m.Rect.Min.Y)*m.Stride - m.Rect.Min.X
+		p := m.Pix[base+s.X0 : base+s.X1]
+		color := uint8(s.Alpha >> 8)
+		for i := range p {
+			p[i] = color
+		}
+	}
+}

vendor/github.com/golang/freetype/truetype/glyph.go

@@ -0,0 +1,522 @@
+// Copyright 2010 The Freetype-Go Authors. All rights reserved.
+// Use of this source code is governed by your choice of either the
+// FreeType License or the GNU General Public License version 2 (or
+// any later version), both of which can be found in the LICENSE file.
+
+package truetype
+
+import (
+	"golang.org/x/image/font"
+	"golang.org/x/image/math/fixed"
+)
+
+// TODO: implement VerticalHinting.
+
+// A Point is a co-ordinate pair plus whether it is 'on' a contour or an 'off'
+// control point.
+type Point struct {
+	X, Y fixed.Int26_6
+	// The Flags' LSB means whether or not this Point is 'on' the contour.
+	// Other bits are reserved for internal use.
+	Flags uint32
+}
+
+// A GlyphBuf holds a glyph's contours. A GlyphBuf can be re-used to load a
+// series of glyphs from a Font.
+type GlyphBuf struct {
+	// AdvanceWidth is the glyph's advance width.
+	AdvanceWidth fixed.Int26_6
+	// Bounds is the glyph's bounding box.
+	Bounds fixed.Rectangle26_6
+	// Points contains all Points from all contours of the glyph. If hinting
+	// was used to load a glyph then Unhinted contains those Points before they
+	// were hinted, and InFontUnits contains those Points before they were
+	// hinted and scaled.
+	Points, Unhinted, InFontUnits []Point
+	// Ends is the point indexes of the end point of each contour. The length
+	// of Ends is the number of contours in the glyph. The i'th contour
+	// consists of points Points[Ends[i-1]:Ends[i]], where Ends[-1] is
+	// interpreted to mean zero.
+	Ends []int
+
+	font    *Font
+	scale   fixed.Int26_6
+	hinting font.Hinting
+	hinter  hinter
+	// phantomPoints are the co-ordinates of the synthetic phantom points
+	// used for hinting and bounding box calculations.
+	phantomPoints [4]Point
+	// pp1x is the X co-ordinate of the first phantom point. The '1' is
+	// using 1-based indexing; pp1x is almost always phantomPoints[0].X.
+	// TODO: eliminate this and consistently use phantomPoints[0].X.
+	pp1x fixed.Int26_6
+	// metricsSet is whether the glyph's metrics have been set yet. For a
+	// compound glyph, a sub-glyph may override the outer glyph's metrics.
+	metricsSet bool
+	// tmp is a scratch buffer.
+	tmp []Point
+}
+
+// Flags for decoding a glyph's contours. These flags are documented at
+// http://developer.apple.com/fonts/TTRefMan/RM06/Chap6glyf.html.
+const (
+	flagOnCurve = 1 << iota
+	flagXShortVector
+	flagYShortVector
+	flagRepeat
+	flagPositiveXShortVector
+	flagPositiveYShortVector
+
+	// The remaining flags are for internal use.
+	flagTouchedX
+	flagTouchedY
+)
+
+// The same flag bits (0x10 and 0x20) are overloaded to have two meanings,
+// dependent on the value of the flag{X,Y}ShortVector bits.
+const (
+	flagThisXIsSame = flagPositiveXShortVector
+	flagThisYIsSame = flagPositiveYShortVector
+)
+
+// Load loads a glyph's contours from a Font, overwriting any previously loaded
+// contours for this GlyphBuf. scale is the number of 26.6 fixed point units in
+// 1 em, i is the glyph index, and h is the hinting policy.
+func (g *GlyphBuf) Load(f *Font, scale fixed.Int26_6, i Index, h font.Hinting) error {
+	g.Points = g.Points[:0]
+	g.Unhinted = g.Unhinted[:0]
+	g.InFontUnits = g.InFontUnits[:0]
+	g.Ends = g.Ends[:0]
+	g.font = f
+	g.hinting = h
+	g.scale = scale
+	g.pp1x = 0
+	g.phantomPoints = [4]Point{}
+	g.metricsSet = false
+
+	if h != font.HintingNone {
+		if err := g.hinter.init(f, scale); err != nil {
+			return err
+		}
+	}
+	if err := g.load(0, i, true); err != nil {
+		return err
+	}
+	// TODO: this selection of either g.pp1x or g.phantomPoints[0].X isn't ideal,
+	// and should be cleaned up once we have all the testScaling tests passing,
+	// plus additional tests for Freetype-Go's bounding boxes matching C Freetype's.
+	pp1x := g.pp1x
+	if h != font.HintingNone {
+		pp1x = g.phantomPoints[0].X
+	}
+	if pp1x != 0 {
+		for i := range g.Points {
+			g.Points[i].X -= pp1x
+		}
+	}
+
+	advanceWidth := g.phantomPoints[1].X - g.phantomPoints[0].X
+	if h != font.HintingNone {
+		if len(f.hdmx) >= 8 {
+			if n := u32(f.hdmx, 4); n > 3+uint32(i) {
+				for hdmx := f.hdmx[8:]; uint32(len(hdmx)) >= n; hdmx = hdmx[n:] {
+					if fixed.Int26_6(hdmx[0]) == scale>>6 {
+						advanceWidth = fixed.Int26_6(hdmx[2+i]) << 6
+						break
+					}
+				}
+			}
+		}
+		advanceWidth = (advanceWidth + 32) &^ 63
+	}
+	g.AdvanceWidth = advanceWidth
+
+	// Set g.Bounds to the 'control box', which is the bounding box of the
+	// Bézier curves' control points. This is easier to calculate, no smaller
+	// than and often equal to the tightest possible bounding box of the curves
+	// themselves. This approach is what C Freetype does. We can't just scale
+	// the nominal bounding box in the glyf data as the hinting process and
+	// phantom point adjustment may move points outside of that box.
+	if len(g.Points) == 0 {
+		g.Bounds = fixed.Rectangle26_6{}
+	} else {
+		p := g.Points[0]
+		g.Bounds.Min.X = p.X
+		g.Bounds.Max.X = p.X
+		g.Bounds.Min.Y = p.Y
+		g.Bounds.Max.Y = p.Y
+		for _, p := range g.Points[1:] {
+			if g.Bounds.Min.X > p.X {
+				g.Bounds.Min.X = p.X
+			} else if g.Bounds.Max.X < p.X {
+				g.Bounds.Max.X = p.X
+			}
+			if g.Bounds.Min.Y > p.Y {
+				g.Bounds.Min.Y = p.Y
+			} else if g.Bounds.Max.Y < p.Y {
+				g.Bounds.Max.Y = p.Y
+			}
+		}
+		// Snap the box to the grid, if hinting is on.
+		if h != font.HintingNone {
+			g.Bounds.Min.X &^= 63
+			g.Bounds.Min.Y &^= 63
+			g.Bounds.Max.X += 63
+			g.Bounds.Max.X &^= 63
+			g.Bounds.Max.Y += 63
+			g.Bounds.Max.Y &^= 63
+		}
+	}
+	return nil
+}
+
+func (g *GlyphBuf) load(recursion uint32, i Index, useMyMetrics bool) (err error) {
+	// The recursion limit here is arbitrary, but defends against malformed glyphs.
+	if recursion >= 32 {
+		return UnsupportedError("excessive compound glyph recursion")
+	}
+	// Find the relevant slice of g.font.glyf.
+	var g0, g1 uint32
+	if g.font.locaOffsetFormat == locaOffsetFormatShort {
+		g0 = 2 * uint32(u16(g.font.loca, 2*int(i)))
+		g1 = 2 * uint32(u16(g.font.loca, 2*int(i)+2))
+	} else {
+		g0 = u32(g.font.loca, 4*int(i))
+		g1 = u32(g.font.loca, 4*int(i)+4)
+	}
+
+	// Decode the contour count and nominal bounding box, from the first
+	// 10 bytes of the glyf data. boundsYMin and boundsXMax, at offsets 4
+	// and 6, are unused.
+	glyf, ne, boundsXMin, boundsYMax := []byte(nil), 0, fixed.Int26_6(0), fixed.Int26_6(0)
+	if g0+10 <= g1 {
+		glyf = g.font.glyf[g0:g1]
+		ne = int(int16(u16(glyf, 0)))
+		boundsXMin = fixed.Int26_6(int16(u16(glyf, 2)))
+		boundsYMax = fixed.Int26_6(int16(u16(glyf, 8)))
+	}
+
+	// Create the phantom points.
+	uhm, pp1x := g.font.unscaledHMetric(i), fixed.Int26_6(0)
+	uvm := g.font.unscaledVMetric(i, boundsYMax)
+	g.phantomPoints = [4]Point{
+		{X: boundsXMin - uhm.LeftSideBearing},
+		{X: boundsXMin - uhm.LeftSideBearing + uhm.AdvanceWidth},
+		{X: uhm.AdvanceWidth / 2, Y: boundsYMax + uvm.TopSideBearing},
+		{X: uhm.AdvanceWidth / 2, Y: boundsYMax + uvm.TopSideBearing - uvm.AdvanceHeight},
+	}
+	if len(glyf) == 0 {
+		g.addPhantomsAndScale(len(g.Points), len(g.Points), true, true)
+		copy(g.phantomPoints[:], g.Points[len(g.Points)-4:])
+		g.Points = g.Points[:len(g.Points)-4]
+		// TODO: also trim g.InFontUnits and g.Unhinted?
+		return nil
+	}
+
+	// Load and hint the contours.
+	if ne < 0 {
+		if ne != -1 {
+			// http://developer.apple.com/fonts/TTRefMan/RM06/Chap6glyf.html says that
+			// "the values -2, -3, and so forth, are reserved for future use."
+			return UnsupportedError("negative number of contours")
+		}
+		pp1x = g.font.scale(g.scale * (boundsXMin - uhm.LeftSideBearing))
+		if err := g.loadCompound(recursion, uhm, i, glyf, useMyMetrics); err != nil {
+			return err
+		}
+	} else {
+		np0, ne0 := len(g.Points), len(g.Ends)
+		program := g.loadSimple(glyf, ne)
+		g.addPhantomsAndScale(np0, np0, true, true)
+		pp1x = g.Points[len(g.Points)-4].X
+		if g.hinting != font.HintingNone {
+			if len(program) != 0 {
+				err := g.hinter.run(
+					program,
+					g.Points[np0:],
+					g.Unhinted[np0:],
+					g.InFontUnits[np0:],
+					g.Ends[ne0:],
+				)
+				if err != nil {
+					return err
+				}
+			}
+			// Drop the four phantom points.
+			g.InFontUnits = g.InFontUnits[:len(g.InFontUnits)-4]
+			g.Unhinted = g.Unhinted[:len(g.Unhinted)-4]
+		}
+		if useMyMetrics {
+			copy(g.phantomPoints[:], g.Points[len(g.Points)-4:])
+		}
+		g.Points = g.Points[:len(g.Points)-4]
+		if np0 != 0 {
+			// The hinting program expects the []Ends values to be indexed
+			// relative to the inner glyph, not the outer glyph, so we delay
+			// adding np0 until after the hinting program (if any) has run.
+			for i := ne0; i < len(g.Ends); i++ {
+				g.Ends[i] += np0
+			}
+		}
+	}
+	if useMyMetrics && !g.metricsSet {
+		g.metricsSet = true
+		g.pp1x = pp1x
+	}
+	return nil
+}
+
+// loadOffset is the initial offset for loadSimple and loadCompound. The first
+// 10 bytes are the number of contours and the bounding box.
+const loadOffset = 10
+
+func (g *GlyphBuf) loadSimple(glyf []byte, ne int) (program []byte) {
+	offset := loadOffset
+	for i := 0; i < ne; i++ {
+		g.Ends = append(g.Ends, 1+int(u16(glyf, offset)))
+		offset += 2
+	}
+
+	// Note the TrueType hinting instructions.
+	instrLen := int(u16(glyf, offset))
+	offset += 2
+	program = glyf[offset : offset+instrLen]
+	offset += instrLen
+
+	if ne == 0 {
+		return program
+	}
+
+	np0 := len(g.Points)
+	np1 := np0 + int(g.Ends[len(g.Ends)-1])
+
+	// Decode the flags.
+	for i := np0; i < np1; {
+		c := uint32(glyf[offset])
+		offset++
+		g.Points = append(g.Points, Point{Flags: c})
+		i++
+		if c&flagRepeat != 0 {
+			count := glyf[offset]
+			offset++
+			for ; count > 0; count-- {
+				g.Points = append(g.Points, Point{Flags: c})
+				i++
+			}
+		}
+	}
+
+	// Decode the co-ordinates.
+	var x int16
+	for i := np0; i < np1; i++ {
+		f := g.Points[i].Flags
+		if f&flagXShortVector != 0 {
+			dx := int16(glyf[offset])
+			offset++
+			if f&flagPositiveXShortVector == 0 {
+				x -= dx
+			} else {
+				x += dx
+			}
+		} else if f&flagThisXIsSame == 0 {
+			x += int16(u16(glyf, offset))
+			offset += 2
+		}
+		g.Points[i].X = fixed.Int26_6(x)
+	}
+	var y int16
+	for i := np0; i < np1; i++ {
+		f := g.Points[i].Flags
+		if f&flagYShortVector != 0 {
+			dy := int16(glyf[offset])
+			offset++
+			if f&flagPositiveYShortVector == 0 {
+				y -= dy
+			} else {
+				y += dy
+			}
+		} else if f&flagThisYIsSame == 0 {
+			y += int16(u16(glyf, offset))
+			offset += 2
+		}
+		g.Points[i].Y = fixed.Int26_6(y)
+	}
+
+	return program
+}
+
+func (g *GlyphBuf) loadCompound(recursion uint32, uhm HMetric, i Index,
+	glyf []byte, useMyMetrics bool) error {
+
+	// Flags for decoding a compound glyph. These flags are documented at
+	// http://developer.apple.com/fonts/TTRefMan/RM06/Chap6glyf.html.
+	const (
+		flagArg1And2AreWords = 1 << iota
+		flagArgsAreXYValues
+		flagRoundXYToGrid
+		flagWeHaveAScale
+		flagUnused
+		flagMoreComponents
+		flagWeHaveAnXAndYScale
+		flagWeHaveATwoByTwo
+		flagWeHaveInstructions
+		flagUseMyMetrics
+		flagOverlapCompound
+	)
+	np0, ne0 := len(g.Points), len(g.Ends)
+	offset := loadOffset
+	for {
+		flags := u16(glyf, offset)
+		component := Index(u16(glyf, offset+2))
+		dx, dy, transform, hasTransform := fixed.Int26_6(0), fixed.Int26_6(0), [4]int16{}, false
+		if flags&flagArg1And2AreWords != 0 {
+			dx = fixed.Int26_6(int16(u16(glyf, offset+4)))
+			dy = fixed.Int26_6(int16(u16(glyf, offset+6)))
+			offset += 8
+		} else {
+			dx = fixed.Int26_6(int16(int8(glyf[offset+4])))
+			dy = fixed.Int26_6(int16(int8(glyf[offset+5])))
+			offset += 6
+		}
+		if flags&flagArgsAreXYValues == 0 {
+			return UnsupportedError("compound glyph transform vector")
+		}
+		if flags&(flagWeHaveAScale|flagWeHaveAnXAndYScale|flagWeHaveATwoByTwo) != 0 {
+			hasTransform = true
+			switch {
+			case flags&flagWeHaveAScale != 0:
+				transform[0] = int16(u16(glyf, offset+0))
+				transform[3] = transform[0]
+				offset += 2
+			case flags&flagWeHaveAnXAndYScale != 0:
+				transform[0] = int16(u16(glyf, offset+0))
+				transform[3] = int16(u16(glyf, offset+2))
+				offset += 4
+			case flags&flagWeHaveATwoByTwo != 0:
+				transform[0] = int16(u16(glyf, offset+0))
+				transform[1] = int16(u16(glyf, offset+2))
+				transform[2] = int16(u16(glyf, offset+4))
+				transform[3] = int16(u16(glyf, offset+6))
+				offset += 8
+			}
+		}
+		savedPP := g.phantomPoints
+		np0 := len(g.Points)
+		componentUMM := useMyMetrics && (flags&flagUseMyMetrics != 0)
+		if err := g.load(recursion+1, component, componentUMM); err != nil {
+			return err
+		}
+		if flags&flagUseMyMetrics == 0 {
+			g.phantomPoints = savedPP
+		}
+		if hasTransform {
+			for j := np0; j < len(g.Points); j++ {
+				p := &g.Points[j]
+				newX := 0 +
+					fixed.Int26_6((int64(p.X)*int64(transform[0])+1<<13)>>14) +
+					fixed.Int26_6((int64(p.Y)*int64(transform[2])+1<<13)>>14)
+				newY := 0 +
+					fixed.Int26_6((int64(p.X)*int64(transform[1])+1<<13)>>14) +
+					fixed.Int26_6((int64(p.Y)*int64(transform[3])+1<<13)>>14)
+				p.X, p.Y = newX, newY
+			}
+		}
+		dx = g.font.scale(g.scale * dx)
+		dy = g.font.scale(g.scale * dy)
+		if flags&flagRoundXYToGrid != 0 {
+			dx = (dx + 32) &^ 63
+			dy = (dy + 32) &^ 63
+		}
+		for j := np0; j < len(g.Points); j++ {
+			p := &g.Points[j]
+			p.X += dx
+			p.Y += dy
+		}
+		// TODO: also adjust g.InFontUnits and g.Unhinted?
+		if flags&flagMoreComponents == 0 {
+			break
+		}
+	}
+
+	instrLen := 0
+	if g.hinting != font.HintingNone && offset+2 <= len(glyf) {
+		instrLen = int(u16(glyf, offset))
+		offset += 2
+	}
+
+	g.addPhantomsAndScale(np0, len(g.Points), false, instrLen > 0)
+	points, ends := g.Points[np0:], g.Ends[ne0:]
+	g.Points = g.Points[:len(g.Points)-4]
+	for j := range points {
+		points[j].Flags &^= flagTouchedX | flagTouchedY
+	}
+
+	if instrLen == 0 {
+		if !g.metricsSet {
+			copy(g.phantomPoints[:], points[len(points)-4:])
+		}
+		return nil
+	}
+
+	// Hint the compound glyph.
+	program := glyf[offset : offset+instrLen]
+	// Temporarily adjust the ends to be relative to this compound glyph.
+	if np0 != 0 {
+		for i := range ends {
+			ends[i] -= np0
+		}
+	}
+	// Hinting instructions of a composite glyph completely refer to the
+	// (already) hinted subglyphs.
+	g.tmp = append(g.tmp[:0], points...)
+	if err := g.hinter.run(program, points, g.tmp, g.tmp, ends); err != nil {
+		return err
+	}
+	if np0 != 0 {
+		for i := range ends {
+			ends[i] += np0
+		}
+	}
+	if !g.metricsSet {
+		copy(g.phantomPoints[:], points[len(points)-4:])
+	}
+	return nil
+}
+
+func (g *GlyphBuf) addPhantomsAndScale(np0, np1 int, simple, adjust bool) {
+	// Add the four phantom points.
+	g.Points = append(g.Points, g.phantomPoints[:]...)
+	// Scale the points.
+	if simple && g.hinting != font.HintingNone {
+		g.InFontUnits = append(g.InFontUnits, g.Points[np1:]...)
+	}
+	for i := np1; i < len(g.Points); i++ {
+		p := &g.Points[i]
+		p.X = g.font.scale(g.scale * p.X)
+		p.Y = g.font.scale(g.scale * p.Y)
+	}
+	if g.hinting == font.HintingNone {
+		return
+	}
+	// Round the 1st phantom point to the grid, shifting all other points equally.
+	// Note that "all other points" starts from np0, not np1.
+	// TODO: delete this adjustment and the np0/np1 distinction, when
+	// we update the compatibility tests to C Freetype 2.5.3.
+	// See http://git.savannah.gnu.org/cgit/freetype/freetype2.git/commit/?id=05c786d990390a7ca18e62962641dac740bacb06
+	if adjust {
+		pp1x := g.Points[len(g.Points)-4].X
+		if dx := ((pp1x + 32) &^ 63) - pp1x; dx != 0 {
+			for i := np0; i < len(g.Points); i++ {
+				g.Points[i].X += dx
+			}
+		}
+	}
+	if simple {
+		g.Unhinted = append(g.Unhinted, g.Points[np1:]...)
+	}
+	// Round the 2nd and 4th phantom point to the grid.
+	p := &g.Points[len(g.Points)-3]
+	p.X = (p.X + 32) &^ 63
+	p = &g.Points[len(g.Points)-1]
+	p.Y = (p.Y + 32) &^ 63
+}

vendor/github.com/golang/freetype/truetype/opcodes.go

@@ -0,0 +1,289 @@
+// Copyright 2012 The Freetype-Go Authors. All rights reserved.
+// Use of this source code is governed by your choice of either the
+// FreeType License or the GNU General Public License version 2 (or
+// any later version), both of which can be found in the LICENSE file.
+
+package truetype
+
+// The Truetype opcodes are summarized at
+// https://developer.apple.com/fonts/TTRefMan/RM07/appendixA.html
+
+const (
+	opSVTCA0    = 0x00 // Set freedom and projection Vectors To Coordinate Axis
+	opSVTCA1    = 0x01 // .
+	opSPVTCA0   = 0x02 // Set Projection Vector To Coordinate Axis
+	opSPVTCA1   = 0x03 // .
+	opSFVTCA0   = 0x04 // Set Freedom Vector to Coordinate Axis
+	opSFVTCA1   = 0x05 // .
+	opSPVTL0    = 0x06 // Set Projection Vector To Line
+	opSPVTL1    = 0x07 // .
+	opSFVTL0    = 0x08 // Set Freedom Vector To Line
+	opSFVTL1    = 0x09 // .
+	opSPVFS     = 0x0a // Set Projection Vector From Stack
+	opSFVFS     = 0x0b // Set Freedom Vector From Stack
+	opGPV       = 0x0c // Get Projection Vector
+	opGFV       = 0x0d // Get Freedom Vector
+	opSFVTPV    = 0x0e // Set Freedom Vector To Projection Vector
+	opISECT     = 0x0f // moves point p to the InterSECTion of two lines
+	opSRP0      = 0x10 // Set Reference Point 0
+	opSRP1      = 0x11 // Set Reference Point 1
+	opSRP2      = 0x12 // Set Reference Point 2
+	opSZP0      = 0x13 // Set Zone Pointer 0
+	opSZP1      = 0x14 // Set Zone Pointer 1
+	opSZP2      = 0x15 // Set Zone Pointer 2
+	opSZPS      = 0x16 // Set Zone PointerS
+	opSLOOP     = 0x17 // Set LOOP variable
+	opRTG       = 0x18 // Round To Grid
+	opRTHG      = 0x19 // Round To Half Grid
+	opSMD       = 0x1a // Set Minimum Distance
+	opELSE      = 0x1b // ELSE clause
+	opJMPR      = 0x1c // JuMP Relative
+	opSCVTCI    = 0x1d // Set Control Value Table Cut-In
+	opSSWCI     = 0x1e // Set Single Width Cut-In
+	opSSW       = 0x1f // Set Single Width
+	opDUP       = 0x20 // DUPlicate top stack element
+	opPOP       = 0x21 // POP top stack element
+	opCLEAR     = 0x22 // CLEAR the stack
+	opSWAP      = 0x23 // SWAP the top two elements on the stack
+	opDEPTH     = 0x24 // DEPTH of the stack
+	opCINDEX    = 0x25 // Copy the INDEXed element to the top of the stack
+	opMINDEX    = 0x26 // Move the INDEXed element to the top of the stack
+	opALIGNPTS  = 0x27 // ALIGN PoinTS
+	op_0x28     = 0x28 // deprecated
+	opUTP       = 0x29 // UnTouch Point
+	opLOOPCALL  = 0x2a // LOOP and CALL function
+	opCALL      = 0x2b // CALL function
+	opFDEF      = 0x2c // Function DEFinition
+	opENDF      = 0x2d // END Function definition
+	opMDAP0     = 0x2e // Move Direct Absolute Point
+	opMDAP1     = 0x2f // .
+	opIUP0      = 0x30 // Interpolate Untouched Points through the outline
+	opIUP1      = 0x31 // .
+	opSHP0      = 0x32 // SHift Point using reference point
+	opSHP1      = 0x33 // .
+	opSHC0      = 0x34 // SHift Contour using reference point
+	opSHC1      = 0x35 // .
+	opSHZ0      = 0x36 // SHift Zone using reference point
+	opSHZ1      = 0x37 // .
+	opSHPIX     = 0x38 // SHift point by a PIXel amount
+	opIP        = 0x39 // Interpolate Point
+	opMSIRP0    = 0x3a // Move Stack Indirect Relative Point
+	opMSIRP1    = 0x3b // .
+	opALIGNRP   = 0x3c // ALIGN to Reference Point
+	opRTDG      = 0x3d // Round To Double Grid
+	opMIAP0     = 0x3e // Move Indirect Absolute Point
+	opMIAP1     = 0x3f // .
+	opNPUSHB    = 0x40 // PUSH N Bytes
+	opNPUSHW    = 0x41 // PUSH N Words
+	opWS        = 0x42 // Write Store
+	opRS        = 0x43 // Read Store
+	opWCVTP     = 0x44 // Write Control Value Table in Pixel units
+	opRCVT      = 0x45 // Read Control Value Table entry
+	opGC0       = 0x46 // Get Coordinate projected onto the projection vector
+	opGC1       = 0x47 // .
+	opSCFS      = 0x48 // Sets Coordinate From the Stack using projection vector and freedom vector
+	opMD0       = 0x49 // Measure Distance
+	opMD1       = 0x4a // .
+	opMPPEM     = 0x4b // Measure Pixels Per EM
+	opMPS       = 0x4c // Measure Point Size
+	opFLIPON    = 0x4d // set the auto FLIP Boolean to ON
+	opFLIPOFF   = 0x4e // set the auto FLIP Boolean to OFF
+	opDEBUG     = 0x4f // DEBUG call
+	opLT        = 0x50 // Less Than
+	opLTEQ      = 0x51 // Less Than or EQual
+	opGT        = 0x52 // Greater Than
+	opGTEQ      = 0x53 // Greater Than or EQual
+	opEQ        = 0x54 // EQual
+	opNEQ       = 0x55 // Not EQual
+	opODD       = 0x56 // ODD
+	opEVEN      = 0x57 // EVEN
+	opIF        = 0x58 // IF test
+	opEIF       = 0x59 // End IF
+	opAND       = 0x5a // logical AND
+	opOR        = 0x5b // logical OR
+	opNOT       = 0x5c // logical NOT
+	opDELTAP1   = 0x5d // DELTA exception P1
+	opSDB       = 0x5e // Set Delta Base in the graphics state
+	opSDS       = 0x5f // Set Delta Shift in the graphics state
+	opADD       = 0x60 // ADD
+	opSUB       = 0x61 // SUBtract
+	opDIV       = 0x62 // DIVide
+	opMUL       = 0x63 // MULtiply
+	opABS       = 0x64 // ABSolute value
+	opNEG       = 0x65 // NEGate
+	opFLOOR     = 0x66 // FLOOR
+	opCEILING   = 0x67 // CEILING
+	opROUND00   = 0x68 // ROUND value
+	opROUND01   = 0x69 // .
+	opROUND10   = 0x6a // .
+	opROUND11   = 0x6b // .
+	opNROUND00  = 0x6c // No ROUNDing of value
+	opNROUND01  = 0x6d // .
+	opNROUND10  = 0x6e // .
+	opNROUND11  = 0x6f // .
+	opWCVTF     = 0x70 // Write Control Value Table in Funits
+	opDELTAP2   = 0x71 // DELTA exception P2
+	opDELTAP3   = 0x72 // DELTA exception P3
+	opDELTAC1   = 0x73 // DELTA exception C1
+	opDELTAC2   = 0x74 // DELTA exception C2
+	opDELTAC3   = 0x75 // DELTA exception C3
+	opSROUND    = 0x76 // Super ROUND
+	opS45ROUND  = 0x77 // Super ROUND 45 degrees
+	opJROT      = 0x78 // Jump Relative On True
+	opJROF      = 0x79 // Jump Relative On False
+	opROFF      = 0x7a // Round OFF
+	op_0x7b     = 0x7b // deprecated
+	opRUTG      = 0x7c // Round Up To Grid
+	opRDTG      = 0x7d // Round Down To Grid
+	opSANGW     = 0x7e // Set ANGle Weight
+	opAA        = 0x7f // Adjust Angle
+	opFLIPPT    = 0x80 // FLIP PoinT
+	opFLIPRGON  = 0x81 // FLIP RanGe ON
+	opFLIPRGOFF = 0x82 // FLIP RanGe OFF
+	op_0x83     = 0x83 // deprecated
+	op_0x84     = 0x84 // deprecated
+	opSCANCTRL  = 0x85 // SCAN conversion ConTRoL
+	opSDPVTL0   = 0x86 // Set Dual Projection Vector To Line
+	opSDPVTL1   = 0x87 // .
+	opGETINFO   = 0x88 // GET INFOrmation
+	opIDEF      = 0x89 // Instruction DEFinition
+	opROLL      = 0x8a // ROLL the top three stack elements
+	opMAX       = 0x8b // MAXimum of top two stack elements
+	opMIN       = 0x8c // MINimum of top two stack elements
+	opSCANTYPE  = 0x8d // SCANTYPE
+	opINSTCTRL  = 0x8e // INSTRuction execution ConTRoL
+	op_0x8f     = 0x8f
+	op_0x90     = 0x90
+	op_0x91     = 0x91
+	op_0x92     = 0x92
+	op_0x93     = 0x93
+	op_0x94     = 0x94
+	op_0x95     = 0x95
+	op_0x96     = 0x96
+	op_0x97     = 0x97
+	op_0x98     = 0x98
+	op_0x99     = 0x99
+	op_0x9a     = 0x9a
+	op_0x9b     = 0x9b
+	op_0x9c     = 0x9c
+	op_0x9d     = 0x9d
+	op_0x9e     = 0x9e
+	op_0x9f     = 0x9f
+	op_0xa0     = 0xa0
+	op_0xa1     = 0xa1
+	op_0xa2     = 0xa2
+	op_0xa3     = 0xa3
+	op_0xa4     = 0xa4
+	op_0xa5     = 0xa5
+	op_0xa6     = 0xa6
+	op_0xa7     = 0xa7
+	op_0xa8     = 0xa8
+	op_0xa9     = 0xa9
+	op_0xaa     = 0xaa
+	op_0xab     = 0xab
+	op_0xac     = 0xac
+	op_0xad     = 0xad
+	op_0xae     = 0xae
+	op_0xaf     = 0xaf
+	opPUSHB000  = 0xb0 // PUSH Bytes
+	opPUSHB001  = 0xb1 // .
+	opPUSHB010  = 0xb2 // .
+	opPUSHB011  = 0xb3 // .
+	opPUSHB100  = 0xb4 // .
+	opPUSHB101  = 0xb5 // .
+	opPUSHB110  = 0xb6 // .
+	opPUSHB111  = 0xb7 // .
+	opPUSHW000  = 0xb8 // PUSH Words
+	opPUSHW001  = 0xb9 // .
+	opPUSHW010  = 0xba // .
+	opPUSHW011  = 0xbb // .
+	opPUSHW100  = 0xbc // .
+	opPUSHW101  = 0xbd // .
+	opPUSHW110  = 0xbe // .
+	opPUSHW111  = 0xbf // .
+	opMDRP00000 = 0xc0 // Move Direct Relative Point
+	opMDRP00001 = 0xc1 // .
+	opMDRP00010 = 0xc2 // .
+	opMDRP00011 = 0xc3 // .
+	opMDRP00100 = 0xc4 // .
+	opMDRP00101 = 0xc5 // .
+	opMDRP00110 = 0xc6 // .
+	opMDRP00111 = 0xc7 // .
+	opMDRP01000 = 0xc8 // .
+	opMDRP01001 = 0xc9 // .
+	opMDRP01010 = 0xca // .
+	opMDRP01011 = 0xcb // .
+	opMDRP01100 = 0xcc // .
+	opMDRP01101 = 0xcd // .
+	opMDRP01110 = 0xce // .
+	opMDRP01111 = 0xcf // .
+	opMDRP10000 = 0xd0 // .
+	opMDRP10001 = 0xd1 // .
+	opMDRP10010 = 0xd2 // .
+	opMDRP10011 = 0xd3 // .
+	opMDRP10100 = 0xd4 // .
+	opMDRP10101 = 0xd5 // .
+	opMDRP10110 = 0xd6 // .
+	opMDRP10111 = 0xd7 // .
+	opMDRP11000 = 0xd8 // .
+	opMDRP11001 = 0xd9 // .
+	opMDRP11010 = 0xda // .
+	opMDRP11011 = 0xdb // .
+	opMDRP11100 = 0xdc // .
+	opMDRP11101 = 0xdd // .
+	opMDRP11110 = 0xde // .
+	opMDRP11111 = 0xdf // .
+	opMIRP00000 = 0xe0 // Move Indirect Relative Point
+	opMIRP00001 = 0xe1 // .
+	opMIRP00010 = 0xe2 // .
+	opMIRP00011 = 0xe3 // .
+	opMIRP00100 = 0xe4 // .
+	opMIRP00101 = 0xe5 // .
+	opMIRP00110 = 0xe6 // .
+	opMIRP00111 = 0xe7 // .
+	opMIRP01000 = 0xe8 // .
+	opMIRP01001 = 0xe9 // .
+	opMIRP01010 = 0xea // .
+	opMIRP01011 = 0xeb // .
+	opMIRP01100 = 0xec // .
+	opMIRP01101 = 0xed // .
+	opMIRP01110 = 0xee // .
+	opMIRP01111 = 0xef // .
+	opMIRP10000 = 0xf0 // .
+	opMIRP10001 = 0xf1 // .
+	opMIRP10010 = 0xf2 // .
+	opMIRP10011 = 0xf3 // .
+	opMIRP10100 = 0xf4 // .
+	opMIRP10101 = 0xf5 // .
+	opMIRP10110 = 0xf6 // .
+	opMIRP10111 = 0xf7 // .
+	opMIRP11000 = 0xf8 // .
+	opMIRP11001 = 0xf9 // .
+	opMIRP11010 = 0xfa // .
+	opMIRP11011 = 0xfb // .
+	opMIRP11100 = 0xfc // .
+	opMIRP11101 = 0xfd // .
+	opMIRP11110 = 0xfe // .
+	opMIRP11111 = 0xff // .
+)
+
+// popCount is the number of stack elements that each opcode pops.
+var popCount = [256]uint8{
+	// 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f
+	0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 5, // 0x00 - 0x0f
+	1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, // 0x10 - 0x1f
+	1, 1, 0, 2, 0, 1, 1, 2, 0, 1, 2, 1, 1, 0, 1, 1, // 0x20 - 0x2f
+	0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 2, 2, 0, 0, 2, 2, // 0x30 - 0x3f
+	0, 0, 2, 1, 2, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, // 0x40 - 0x4f
+	2, 2, 2, 2, 2, 2, 1, 1, 1, 0, 2, 2, 1, 1, 1, 1, // 0x50 - 0x5f
+	2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, // 0x60 - 0x6f
+	2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 1, 1, // 0x70 - 0x7f
+	0, 2, 2, 0, 0, 1, 2, 2, 1, 1, 3, 2, 2, 1, 2, 0, // 0x80 - 0x8f
+	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 0x90 - 0x9f
+	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 0xa0 - 0xaf
+	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 0xb0 - 0xbf
+	1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, // 0xc0 - 0xcf
+	1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, // 0xd0 - 0xdf
+	2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, // 0xe0 - 0xef
+	2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, // 0xf0 - 0xff
+}

vendor/github.com/golang/freetype/truetype/truetype.go

@@ -0,0 +1,653 @@
+// Copyright 2010 The Freetype-Go Authors. All rights reserved.
+// Use of this source code is governed by your choice of either the
+// FreeType License or the GNU General Public License version 2 (or
+// any later version), both of which can be found in the LICENSE file.
+
+// Package truetype provides a parser for the TTF and TTC file formats.
+// Those formats are documented at http://developer.apple.com/fonts/TTRefMan/
+// and http://www.microsoft.com/typography/otspec/
+//
+// Some of a font's methods provide lengths or co-ordinates, e.g. bounds, font
+// metrics and control points. All these methods take a scale parameter, which
+// is the number of pixels in 1 em, expressed as a 26.6 fixed point value. For
+// example, if 1 em is 10 pixels then scale is fixed.I(10), which is equal to
+// fixed.Int26_6(10 << 6).
+//
+// To measure a TrueType font in ideal FUnit space, use scale equal to
+// font.FUnitsPerEm().
+package truetype // import "github.com/golang/freetype/truetype"
+
+import (
+	"fmt"
+
+	"golang.org/x/image/math/fixed"
+)
+
+// An Index is a Font's index of a rune.
+type Index uint16
+
+// A NameID identifies a name table entry.
+//
+// See https://developer.apple.com/fonts/TrueType-Reference-Manual/RM06/Chap6name.html
+type NameID uint16
+
+const (
+	NameIDCopyright          NameID = 0
+	NameIDFontFamily                = 1
+	NameIDFontSubfamily             = 2
+	NameIDUniqueSubfamilyID         = 3
+	NameIDFontFullName              = 4
+	NameIDNameTableVersion          = 5
+	NameIDPostscriptName            = 6
+	NameIDTrademarkNotice           = 7
+	NameIDManufacturerName          = 8
+	NameIDDesignerName              = 9
+	NameIDFontDescription           = 10
+	NameIDFontVendorURL             = 11
+	NameIDFontDesignerURL           = 12
+	NameIDFontLicense               = 13
+	NameIDFontLicenseURL            = 14
+	NameIDPreferredFamily           = 16
+	NameIDPreferredSubfamily        = 17
+	NameIDCompatibleName            = 18
+	NameIDSampleText                = 19
+)
+
+const (
+	// A 32-bit encoding consists of a most-significant 16-bit Platform ID and a
+	// least-significant 16-bit Platform Specific ID. The magic numbers are
+	// specified at https://www.microsoft.com/typography/otspec/name.htm
+	unicodeEncodingBMPOnly  = 0x00000003 // PID = 0 (Unicode), PSID = 3 (Unicode 2.0 BMP Only)
+	unicodeEncodingFull     = 0x00000004 // PID = 0 (Unicode), PSID = 4 (Unicode 2.0 Full Repertoire)
+	microsoftSymbolEncoding = 0x00030000 // PID = 3 (Microsoft), PSID = 0 (Symbol)
+	microsoftUCS2Encoding   = 0x00030001 // PID = 3 (Microsoft), PSID = 1 (UCS-2)
+	microsoftUCS4Encoding   = 0x0003000a // PID = 3 (Microsoft), PSID = 10 (UCS-4)
+)
+
+// An HMetric holds the horizontal metrics of a single glyph.
+type HMetric struct {
+	AdvanceWidth, LeftSideBearing fixed.Int26_6
+}
+
+// A VMetric holds the vertical metrics of a single glyph.
+type VMetric struct {
+	AdvanceHeight, TopSideBearing fixed.Int26_6
+}
+
+// A FormatError reports that the input is not a valid TrueType font.
+type FormatError string
+
+func (e FormatError) Error() string {
+	return "freetype: invalid TrueType format: " + string(e)
+}
+
+// An UnsupportedError reports that the input uses a valid but unimplemented
+// TrueType feature.
+type UnsupportedError string
+
+func (e UnsupportedError) Error() string {
+	return "freetype: unsupported TrueType feature: " + string(e)
+}
+
+// u32 returns the big-endian uint32 at b[i:].
+func u32(b []byte, i int) uint32 {
+	return uint32(b[i])<<24 | uint32(b[i+1])<<16 | uint32(b[i+2])<<8 | uint32(b[i+3])
+}
+
+// u16 returns the big-endian uint16 at b[i:].
+func u16(b []byte, i int) uint16 {
+	return uint16(b[i])<<8 | uint16(b[i+1])
+}
+
+// readTable returns a slice of the TTF data given by a table's directory entry.
+func readTable(ttf []byte, offsetLength []byte) ([]byte, error) {
+	offset := int(u32(offsetLength, 0))
+	if offset < 0 {
+		return nil, FormatError(fmt.Sprintf("offset too large: %d", uint32(offset)))
+	}
+	length := int(u32(offsetLength, 4))
+	if length < 0 {
+		return nil, FormatError(fmt.Sprintf("length too large: %d", uint32(length)))
+	}
+	end := offset + length
+	if end < 0 || end > len(ttf) {
+		return nil, FormatError(fmt.Sprintf("offset + length too large: %d", uint32(offset)+uint32(length)))
+	}
+	return ttf[offset:end], nil
+}
+
+// parseSubtables returns the offset and platformID of the best subtable in
+// table, where best favors a Unicode cmap encoding, and failing that, a
+// Microsoft cmap encoding. offset is the offset of the first subtable in
+// table, and size is the size of each subtable.
+//
+// If pred is non-nil, then only subtables that satisfy that predicate will be
+// considered.
+func parseSubtables(table []byte, name string, offset, size int, pred func([]byte) bool) (
+	bestOffset int, bestPID uint32, retErr error) {
+
+	if len(table) < 4 {
+		return 0, 0, FormatError(name + " too short")
+	}
+	nSubtables := int(u16(table, 2))
+	if len(table) < size*nSubtables+offset {
+		return 0, 0, FormatError(name + " too short")
+	}
+	ok := false
+	for i := 0; i < nSubtables; i, offset = i+1, offset+size {
+		if pred != nil && !pred(table[offset:]) {
+			continue
+		}
+		// We read the 16-bit Platform ID and 16-bit Platform Specific ID as a single uint32.
+		// All values are big-endian.
+		pidPsid := u32(table, offset)
+		// We prefer the Unicode cmap encoding. Failing to find that, we fall
+		// back onto the Microsoft cmap encoding.
+		if pidPsid == unicodeEncodingBMPOnly || pidPsid == unicodeEncodingFull {
+			bestOffset, bestPID, ok = offset, pidPsid>>16, true
+			break
+
+		} else if pidPsid == microsoftSymbolEncoding ||
+			pidPsid == microsoftUCS2Encoding ||
+			pidPsid == microsoftUCS4Encoding {
+
+			bestOffset, bestPID, ok = offset, pidPsid>>16, true
+			// We don't break out of the for loop, so that Unicode can override Microsoft.
+		}
+	}
+	if !ok {
+		return 0, 0, UnsupportedError(name + " encoding")
+	}
+	return bestOffset, bestPID, nil
+}
+
+const (
+	locaOffsetFormatUnknown int = iota
+	locaOffsetFormatShort
+	locaOffsetFormatLong
+)
+
+// A cm holds a parsed cmap entry.
+type cm struct {
+	start, end, delta, offset uint32
+}
+
+// A Font represents a Truetype font.
+type Font struct {
+	// Tables sliced from the TTF data. The different tables are documented
+	// at http://developer.apple.com/fonts/TTRefMan/RM06/Chap6.html
+	cmap, cvt, fpgm, glyf, hdmx, head, hhea, hmtx, kern, loca, maxp, name, os2, prep, vmtx []byte
+
+	cmapIndexes []byte
+
+	// Cached values derived from the raw ttf data.
+	cm                      []cm
+	locaOffsetFormat        int
+	nGlyph, nHMetric, nKern int
+	fUnitsPerEm             int32
+	ascent                  int32               // In FUnits.
+	descent                 int32               // In FUnits; typically negative.
+	bounds                  fixed.Rectangle26_6 // In FUnits.
+	// Values from the maxp section.
+	maxTwilightPoints, maxStorage, maxFunctionDefs, maxStackElements uint16
+}
+
+func (f *Font) parseCmap() error {
+	const (
+		cmapFormat4         = 4
+		cmapFormat12        = 12
+		languageIndependent = 0
+	)
+
+	offset, _, err := parseSubtables(f.cmap, "cmap", 4, 8, nil)
+	if err != nil {
+		return err
+	}
+	offset = int(u32(f.cmap, offset+4))
+	if offset <= 0 || offset > len(f.cmap) {
+		return FormatError("bad cmap offset")
+	}
+
+	cmapFormat := u16(f.cmap, offset)
+	switch cmapFormat {
+	case cmapFormat4:
+		language := u16(f.cmap, offset+4)
+		if language != languageIndependent {
+			return UnsupportedError(fmt.Sprintf("language: %d", language))
+		}
+		segCountX2 := int(u16(f.cmap, offset+6))
+		if segCountX2%2 == 1 {
+			return FormatError(fmt.Sprintf("bad segCountX2: %d", segCountX2))
+		}
+		segCount := segCountX2 / 2
+		offset += 14
+		f.cm = make([]cm, segCount)
+		for i := 0; i < segCount; i++ {
+			f.cm[i].end = uint32(u16(f.cmap, offset))
+			offset += 2
+		}
+		offset += 2
+		for i := 0; i < segCount; i++ {
+			f.cm[i].start = uint32(u16(f.cmap, offset))
+			offset += 2
+		}
+		for i := 0; i < segCount; i++ {
+			f.cm[i].delta = uint32(u16(f.cmap, offset))
+			offset += 2
+		}
+		for i := 0; i < segCount; i++ {
+			f.cm[i].offset = uint32(u16(f.cmap, offset))
+			offset += 2
+		}
+		f.cmapIndexes = f.cmap[offset:]
+		return nil
+
+	case cmapFormat12:
+		if u16(f.cmap, offset+2) != 0 {
+			return FormatError(fmt.Sprintf("cmap format: % x", f.cmap[offset:offset+4]))
+		}
+		length := u32(f.cmap, offset+4)
+		language := u32(f.cmap, offset+8)
+		if language != languageIndependent {
+			return UnsupportedError(fmt.Sprintf("language: %d", language))
+		}
+		nGroups := u32(f.cmap, offset+12)
+		if length != 12*nGroups+16 {
+			return FormatError("inconsistent cmap length")
+		}
+		offset += 16
+		f.cm = make([]cm, nGroups)
+		for i := uint32(0); i < nGroups; i++ {
+			f.cm[i].start = u32(f.cmap, offset+0)
+			f.cm[i].end = u32(f.cmap, offset+4)
+			f.cm[i].delta = u32(f.cmap, offset+8) - f.cm[i].start
+			offset += 12
+		}
+		return nil
+	}
+	return UnsupportedError(fmt.Sprintf("cmap format: %d", cmapFormat))
+}
+
+func (f *Font) parseHead() error {
+	if len(f.head) != 54 {
+		return FormatError(fmt.Sprintf("bad head length: %d", len(f.head)))
+	}
+	f.fUnitsPerEm = int32(u16(f.head, 18))
+	f.bounds.Min.X = fixed.Int26_6(int16(u16(f.head, 36)))
+	f.bounds.Min.Y = fixed.Int26_6(int16(u16(f.head, 38)))
+	f.bounds.Max.X = fixed.Int26_6(int16(u16(f.head, 40)))
+	f.bounds.Max.Y = fixed.Int26_6(int16(u16(f.head, 42)))
+	switch i := u16(f.head, 50); i {
+	case 0:
+		f.locaOffsetFormat = locaOffsetFormatShort
+	case 1:
+		f.locaOffsetFormat = locaOffsetFormatLong
+	default:
+		return FormatError(fmt.Sprintf("bad indexToLocFormat: %d", i))
+	}
+	return nil
+}
+
+func (f *Font) parseHhea() error {
+	if len(f.hhea) != 36 {
+		return FormatError(fmt.Sprintf("bad hhea length: %d", len(f.hhea)))
+	}
+	f.ascent = int32(int16(u16(f.hhea, 4)))
+	f.descent = int32(int16(u16(f.hhea, 6)))
+	f.nHMetric = int(u16(f.hhea, 34))
+	if 4*f.nHMetric+2*(f.nGlyph-f.nHMetric) != len(f.hmtx) {
+		return FormatError(fmt.Sprintf("bad hmtx length: %d", len(f.hmtx)))
+	}
+	return nil
+}
+
+func (f *Font) parseKern() error {
+	// Apple's TrueType documentation (http://developer.apple.com/fonts/TTRefMan/RM06/Chap6kern.html) says:
+	// "Previous versions of the 'kern' table defined both the version and nTables fields in the header
+	// as UInt16 values and not UInt32 values. Use of the older format on the Mac OS is discouraged
+	// (although AAT can sense an old kerning table and still make correct use of it). Microsoft
+	// Windows still uses the older format for the 'kern' table and will not recognize the newer one.
+	// Fonts targeted for the Mac OS only should use the new format; fonts targeted for both the Mac OS
+	// and Windows should use the old format."
+	// Since we expect that almost all fonts aim to be Windows-compatible, we only parse the "older" format,
+	// just like the C Freetype implementation.
+	if len(f.kern) == 0 {
+		if f.nKern != 0 {
+			return FormatError("bad kern table length")
+		}
+		return nil
+	}
+	if len(f.kern) < 18 {
+		return FormatError("kern data too short")
+	}
+	version, offset := u16(f.kern, 0), 2
+	if version != 0 {
+		return UnsupportedError(fmt.Sprintf("kern version: %d", version))
+	}
+
+	n, offset := u16(f.kern, offset), offset+2
+	if n == 0 {
+		return UnsupportedError("kern nTables: 0")
+	}
+	// TODO: support multiple subtables. In practice, almost all .ttf files
+	// have only one subtable, if they have a kern table at all. But it's not
+	// impossible. Xolonium Regular (https://fontlibrary.org/en/font/xolonium)
+	// has 3 subtables. Those subtables appear to be disjoint, rather than
+	// being the same kerning pairs encoded in three different ways.
+	//
+	// For now, we'll use only the first subtable.
+
+	offset += 2 // Skip the version.
+	length, offset := int(u16(f.kern, offset)), offset+2
+	coverage, offset := u16(f.kern, offset), offset+2
+	if coverage != 0x0001 {
+		// We only support horizontal kerning.
+		return UnsupportedError(fmt.Sprintf("kern coverage: 0x%04x", coverage))
+	}
+	f.nKern, offset = int(u16(f.kern, offset)), offset+2
+	if 6*f.nKern != length-14 {
+		return FormatError("bad kern table length")
+	}
+	return nil
+}
+
+func (f *Font) parseMaxp() error {
+	if len(f.maxp) != 32 {
+		return FormatError(fmt.Sprintf("bad maxp length: %d", len(f.maxp)))
+	}
+	f.nGlyph = int(u16(f.maxp, 4))
+	f.maxTwilightPoints = u16(f.maxp, 16)
+	f.maxStorage = u16(f.maxp, 18)
+	f.maxFunctionDefs = u16(f.maxp, 20)
+	f.maxStackElements = u16(f.maxp, 24)
+	return nil
+}
+
+// scale returns x divided by f.fUnitsPerEm, rounded to the nearest integer.
+func (f *Font) scale(x fixed.Int26_6) fixed.Int26_6 {
+	if x >= 0 {
+		x += fixed.Int26_6(f.fUnitsPerEm) / 2
+	} else {
+		x -= fixed.Int26_6(f.fUnitsPerEm) / 2
+	}
+	return x / fixed.Int26_6(f.fUnitsPerEm)
+}
+
+// Bounds returns the union of a Font's glyphs' bounds.
+func (f *Font) Bounds(scale fixed.Int26_6) fixed.Rectangle26_6 {
+	b := f.bounds
+	b.Min.X = f.scale(scale * b.Min.X)
+	b.Min.Y = f.scale(scale * b.Min.Y)
+	b.Max.X = f.scale(scale * b.Max.X)
+	b.Max.Y = f.scale(scale * b.Max.Y)
+	return b
+}
+
+// FUnitsPerEm returns the number of FUnits in a Font's em-square's side.
+func (f *Font) FUnitsPerEm() int32 {
+	return f.fUnitsPerEm
+}
+
+// Index returns a Font's index for the given rune.
+func (f *Font) Index(x rune) Index {
+	c := uint32(x)
+	for i, j := 0, len(f.cm); i < j; {
+		h := i + (j-i)/2
+		cm := &f.cm[h]
+		if c < cm.start {
+			j = h
+		} else if cm.end < c {
+			i = h + 1
+		} else if cm.offset == 0 {
+			return Index(c + cm.delta)
+		} else {
+			offset := int(cm.offset) + 2*(h-len(f.cm)+int(c-cm.start))
+			return Index(u16(f.cmapIndexes, offset))
+		}
+	}
+	return 0
+}
+
+// Name returns the Font's name value for the given NameID. It returns "" if
+// there was an error, or if that name was not found.
+func (f *Font) Name(id NameID) string {
+	x, platformID, err := parseSubtables(f.name, "name", 6, 12, func(b []byte) bool {
+		return NameID(u16(b, 6)) == id
+	})
+	if err != nil {
+		return ""
+	}
+	offset, length := u16(f.name, 4)+u16(f.name, x+10), u16(f.name, x+8)
+	// Return the ASCII value of the encoded string.
+	// The string is encoded as UTF-16 on non-Apple platformIDs; Apple is platformID 1.
+	src := f.name[offset : offset+length]
+	var dst []byte
+	if platformID != 1 { // UTF-16.
+		if len(src)&1 != 0 {
+			return ""
+		}
+		dst = make([]byte, len(src)/2)
+		for i := range dst {
+			dst[i] = printable(u16(src, 2*i))
+		}
+	} else { // ASCII.
+		dst = make([]byte, len(src))
+		for i, c := range src {
+			dst[i] = printable(uint16(c))
+		}
+	}
+	return string(dst)
+}
+
+func printable(r uint16) byte {
+	if 0x20 <= r && r < 0x7f {
+		return byte(r)
+	}
+	return '?'
+}
+
+// unscaledHMetric returns the unscaled horizontal metrics for the glyph with
+// the given index.
+func (f *Font) unscaledHMetric(i Index) (h HMetric) {
+	j := int(i)
+	if j < 0 || f.nGlyph <= j {
+		return HMetric{}
+	}
+	if j >= f.nHMetric {
+		p := 4 * (f.nHMetric - 1)
+		return HMetric{
+			AdvanceWidth:    fixed.Int26_6(u16(f.hmtx, p)),
+			LeftSideBearing: fixed.Int26_6(int16(u16(f.hmtx, p+2*(j-f.nHMetric)+4))),
+		}
+	}
+	return HMetric{
+		AdvanceWidth:    fixed.Int26_6(u16(f.hmtx, 4*j)),
+		LeftSideBearing: fixed.Int26_6(int16(u16(f.hmtx, 4*j+2))),
+	}
+}
+
+// HMetric returns the horizontal metrics for the glyph with the given index.
+func (f *Font) HMetric(scale fixed.Int26_6, i Index) HMetric {
+	h := f.unscaledHMetric(i)
+	h.AdvanceWidth = f.scale(scale * h.AdvanceWidth)
+	h.LeftSideBearing = f.scale(scale * h.LeftSideBearing)
+	return h
+}
+
+// unscaledVMetric returns the unscaled vertical metrics for the glyph with
+// the given index. yMax is the top of the glyph's bounding box.
+func (f *Font) unscaledVMetric(i Index, yMax fixed.Int26_6) (v VMetric) {
+	j := int(i)
+	if j < 0 || f.nGlyph <= j {
+		return VMetric{}
+	}
+	if 4*j+4 <= len(f.vmtx) {
+		return VMetric{
+			AdvanceHeight:  fixed.Int26_6(u16(f.vmtx, 4*j)),
+			TopSideBearing: fixed.Int26_6(int16(u16(f.vmtx, 4*j+2))),
+		}
+	}
+	// The OS/2 table has grown over time.
+	// https://developer.apple.com/fonts/TTRefMan/RM06/Chap6OS2.html
+	// says that it was originally 68 bytes. Optional fields, including
+	// the ascender and descender, are described at
+	// http://www.microsoft.com/typography/otspec/os2.htm
+	if len(f.os2) >= 72 {
+		sTypoAscender := fixed.Int26_6(int16(u16(f.os2, 68)))
+		sTypoDescender := fixed.Int26_6(int16(u16(f.os2, 70)))
+		return VMetric{
+			AdvanceHeight:  sTypoAscender - sTypoDescender,
+			TopSideBearing: sTypoAscender - yMax,
+		}
+	}
+	return VMetric{
+		AdvanceHeight:  fixed.Int26_6(f.fUnitsPerEm),
+		TopSideBearing: 0,
+	}
+}
+
+// VMetric returns the vertical metrics for the glyph with the given index.
+func (f *Font) VMetric(scale fixed.Int26_6, i Index) VMetric {
+	// TODO: should 0 be bounds.YMax?
+	v := f.unscaledVMetric(i, 0)
+	v.AdvanceHeight = f.scale(scale * v.AdvanceHeight)
+	v.TopSideBearing = f.scale(scale * v.TopSideBearing)
+	return v
+}
+
+// Kern returns the horizontal adjustment for the given glyph pair. A positive
+// kern means to move the glyphs further apart.
+func (f *Font) Kern(scale fixed.Int26_6, i0, i1 Index) fixed.Int26_6 {
+	if f.nKern == 0 {
+		return 0
+	}
+	g := uint32(i0)<<16 | uint32(i1)
+	lo, hi := 0, f.nKern
+	for lo < hi {
+		i := (lo + hi) / 2
+		ig := u32(f.kern, 18+6*i)
+		if ig < g {
+			lo = i + 1
+		} else if ig > g {
+			hi = i
+		} else {
+			return f.scale(scale * fixed.Int26_6(int16(u16(f.kern, 22+6*i))))
+		}
+	}
+	return 0
+}
+
+// Parse returns a new Font for the given TTF or TTC data.
+//
+// For TrueType Collections, the first font in the collection is parsed.
+func Parse(ttf []byte) (font *Font, err error) {
+	return parse(ttf, 0)
+}
+
+func parse(ttf []byte, offset int) (font *Font, err error) {
+	if len(ttf)-offset < 12 {
+		err = FormatError("TTF data is too short")
+		return
+	}
+	originalOffset := offset
+	magic, offset := u32(ttf, offset), offset+4
+	switch magic {
+	case 0x00010000:
+		// No-op.
+	case 0x74746366: // "ttcf" as a big-endian uint32.
+		if originalOffset != 0 {
+			err = FormatError("recursive TTC")
+			return
+		}
+		ttcVersion, offset := u32(ttf, offset), offset+4
+		if ttcVersion != 0x00010000 && ttcVersion != 0x00020000 {
+			err = FormatError("bad TTC version")
+			return
+		}
+		numFonts, offset := int(u32(ttf, offset)), offset+4
+		if numFonts <= 0 {
+			err = FormatError("bad number of TTC fonts")
+			return
+		}
+		if len(ttf[offset:])/4 < numFonts {
+			err = FormatError("TTC offset table is too short")
+			return
+		}
+		// TODO: provide an API to select which font in a TrueType collection to return,
+		// not just the first one. This may require an API to parse a TTC's name tables,
+		// so users of this package can select the font in a TTC by name.
+		offset = int(u32(ttf, offset))
+		if offset <= 0 || offset > len(ttf) {
+			err = FormatError("bad TTC offset")
+			return
+		}
+		return parse(ttf, offset)
+	default:
+		err = FormatError("bad TTF version")
+		return
+	}
+	n, offset := int(u16(ttf, offset)), offset+2
+	offset += 6 // Skip the searchRange, entrySelector and rangeShift.
+	if len(ttf) < 16*n+offset {
+		err = FormatError("TTF data is too short")
+		return
+	}
+	f := new(Font)
+	// Assign the table slices.
+	for i := 0; i < n; i++ {
+		x := 16*i + offset
+		switch string(ttf[x : x+4]) {
+		case "cmap":
+			f.cmap, err = readTable(ttf, ttf[x+8:x+16])
+		case "cvt ":
+			f.cvt, err = readTable(ttf, ttf[x+8:x+16])
+		case "fpgm":
+			f.fpgm, err = readTable(ttf, ttf[x+8:x+16])
+		case "glyf":
+			f.glyf, err = readTable(ttf, ttf[x+8:x+16])
+		case "hdmx":
+			f.hdmx, err = readTable(ttf, ttf[x+8:x+16])
+		case "head":
+			f.head, err = readTable(ttf, ttf[x+8:x+16])
+		case "hhea":
+			f.hhea, err = readTable(ttf, ttf[x+8:x+16])
+		case "hmtx":
+			f.hmtx, err = readTable(ttf, ttf[x+8:x+16])
+		case "kern":
+			f.kern, err = readTable(ttf, ttf[x+8:x+16])
+		case "loca":
+			f.loca, err = readTable(ttf, ttf[x+8:x+16])
+		case "maxp":
+			f.maxp, err = readTable(ttf, ttf[x+8:x+16])
+		case "name":
+			f.name, err = readTable(ttf, ttf[x+8:x+16])
+		case "OS/2":
+			f.os2, err = readTable(ttf, ttf[x+8:x+16])
+		case "prep":
+			f.prep, err = readTable(ttf, ttf[x+8:x+16])
+		case "vmtx":
+			f.vmtx, err = readTable(ttf, ttf[x+8:x+16])
+		}
+		if err != nil {
+			return
+		}
+	}
+	// Parse and sanity-check the TTF data.
+	if err = f.parseHead(); err != nil {
+		return
+	}
+	if err = f.parseMaxp(); err != nil {
+		return
+	}
+	if err = f.parseCmap(); err != nil {
+		return
+	}
+	if err = f.parseKern(); err != nil {
+		return
+	}
+	if err = f.parseHhea(); err != nil {
+		return
+	}
+	font = f
+	return
+}