Updating go depencancies. Switching to go1.6 vendoring (#2949)

4 files changed, 1616 insertions, 0 deletions

diff --git a/vendor/github.com/golang/freetype/raster/geom.go b/vendor/github.com/golang/freetype/raster/geom.go
new file mode 100644
index 000000000..f3696ea98
--- /dev/null
+++ b/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")
+		}
+	}
+}
diff --git a/vendor/github.com/golang/freetype/raster/paint.go b/vendor/github.com/golang/freetype/raster/paint.go
new file mode 100644
index 000000000..652256cca
--- /dev/null
+++ b/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
+}
diff --git a/vendor/github.com/golang/freetype/raster/raster.go b/vendor/github.com/golang/freetype/raster/raster.go
new file mode 100644
index 000000000..995925e2a
--- /dev/null
+++ b/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 (
+	"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
+}
diff --git a/vendor/github.com/golang/freetype/raster/stroke.go b/vendor/github.com/golang/freetype/raster/stroke.go
new file mode 100644
index 000000000..bcc66b268
--- /dev/null
+++ b/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:])
+}