Freetype-Go: Initial code check-in.

R=r, rsc
CC=golang-dev
http://codereview.appspot.com/841042

AUTHORS

+# 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.

CONTRIBUTORS

+# 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.
+
+Nigel Tao <nigeltao@golang.org>
+Rob Pike <r@golang.org>
+Russ Cox <rsc@golang.org>

LICENSE

+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
+

README

+This is a port of the Freetype font rasterizer (www.freetype.org) to the Go
+programming language (golang.org).
+
+It is an incomplete port:
+  * It only supports TrueType fonts, and not Type 1 fonts nor bitmap fonts.
+  * It only supports the Unicode encoding.
+
+There are also some implementation differences:
+  * It uses a 24.8 fixed point co-ordinate system everywhere internally,
+    as opposed to the original Freetype's mix of 26.6 (or 10.6 for 16-bit
+	systems) in some places, and 24.8 in the "smooth" rasterizer.
+
+Freetype-Go is derived from Freetype, which is written in C. Freetype is
+copyright 1996-2010 David Turner, Robert Wilhelm, and Werner Lemberg.
+Freetype-Go is copyright The Freetype-Go Authors, who are listed in the
+AUTHORS file.
+
+The Freetype-Go homepage is http://code.google.com/p/freetype-go/
+

example/raster/main.go

+// 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,
+// both of which can be found in the LICENSE file.
+
+package main
+
+import (
+	"bufio"
+	"exp/draw"
+	"fmt"
+	"image"
+	"image/png"
+	"log"
+	"os"
+
+	"freetype-go.googlecode.com/hg/freetype/raster"
+)
+
+type node struct {
+	x, y, degree int
+}
+
+// These contours "outside" and "inside" are from the `A' glyph from the Droid
+// Serif Regular font.
+
+var outside = []node{
+	node{414, 489, 1},
+	node{336, 274, 2},
+	node{327, 250, 0},
+	node{322, 226, 2},
+	node{317, 203, 0},
+	node{317, 186, 2},
+	node{317, 134, 0},
+	node{350, 110, 2},
+	node{384, 86, 0},
+	node{453, 86, 1},
+	node{500, 86, 1},
+	node{500, 0, 1},
+	node{0, 0, 1},
+	node{0, 86, 1},
+	node{39, 86, 2},
+	node{69, 86, 0},
+	node{90, 92, 2},
+	node{111, 99, 0},
+	node{128, 117, 2},
+	node{145, 135, 0},
+	node{160, 166, 2},
+	node{176, 197, 0},
+	node{195, 246, 1},
+	node{649, 1462, 1},
+	node{809, 1462, 1},
+	node{1272, 195, 2},
+	node{1284, 163, 0},
+	node{1296, 142, 2},
+	node{1309, 121, 0},
+	node{1326, 108, 2},
+	node{1343, 96, 0},
+	node{1365, 91, 2},
+	node{1387, 86, 0},
+	node{1417, 86, 1},
+	node{1444, 86, 1},
+	node{1444, 0, 1},
+	node{881, 0, 1},
+	node{881, 86, 1},
+	node{928, 86, 2},
+	node{1051, 86, 0},
+	node{1051, 184, 2},
+	node{1051, 201, 0},
+	node{1046, 219, 2},
+	node{1042, 237, 0},
+	node{1034, 260, 1},
+	node{952, 489, 1},
+	node{414, 489, -1},
+}
+
+var inside = []node{
+	node{686, 1274, 1},
+	node{453, 592, 1},
+	node{915, 592, 1},
+	node{686, 1274, -1},
+}
+
+func p(n node) raster.Point {
+	x, y := 20+n.x/4, 380-n.y/4
+	return raster.Point{raster.Fixed(x * 256), raster.Fixed(y * 256)}
+}
+
+func contour(r *raster.Rasterizer, ns []node) {
+	if len(ns) == 0 {
+		return
+	}
+	i := 0
+	r.Start(p(ns[i]))
+	for {
+		switch ns[i].degree {
+		case -1:
+			// -1 signifies end-of-contour.
+			return
+		case 1:
+			i += 1
+			r.Move1(p(ns[i]))
+		case 2:
+			i += 2
+			r.Move2(p(ns[i-1]), p(ns[i]))
+		default:
+			panic("bad degree")
+		}
+	}
+}
+
+func showNodes(m *image.RGBA, ns []node) {
+	for _, n := range ns {
+		p := p(n)
+		x, y := int(p.X)/256, int(p.Y)/256
+		if x < 0 || x >= m.Width() || y < 0 || y >= m.Height() {
+			continue
+		}
+		var c image.Color
+		switch n.degree {
+		case 0:
+			c = image.Aqua
+		case 1:
+			c = image.Red
+		case 2:
+			c = image.Red
+		}
+		if c != nil {
+			m.Set(x, y, c)
+		}
+	}
+}
+
+func main() {
+	// Rasterize the contours to a mask image.
+	const (
+		w = 400
+		h = 400
+	)
+	r := raster.New(w, h)
+	contour(r, outside)
+	contour(r, inside)
+	mask := image.NewAlpha(w, h)
+	r.Rasterize(raster.AlphaSrcPainter(mask))
+
+	// Draw the mask image (in gray) onto an RGBA image.
+	rgba := image.NewRGBA(w, h)
+	gray := image.ColorImage{image.AlphaColor{0x1f}}
+	draw.Draw(rgba, draw.Rect(0, 0, w, h), image.Black, draw.ZP)
+	draw.DrawMask(rgba, draw.Rect(0, 0, w, h), gray, draw.ZP, mask, draw.ZP, draw.Over)
+	showNodes(rgba, outside)
+	showNodes(rgba, inside)
+
+	// Save that RGBA image to disk.
+	f, err := os.Open("out.png", os.O_CREAT|os.O_WRONLY, 0600)
+	if err != nil {
+		log.Stderr(err)
+		return
+	}
+	defer f.Close()
+	b := bufio.NewWriter(f)
+	err = png.Encode(b, rgba)
+	if err != nil {
+		log.Stderr(err)
+		return
+	}
+	err = b.Flush()
+	if err != nil {
+		log.Stderr(err)
+		return
+	}
+	fmt.Println("Wrote out.png OK.")
+}

freetype/raster/Makefile

+# 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,
+# both of which can be found in the LICENSE file.
+
+include $(GOROOT)/src/Make.$(GOARCH)
+
+TARG=freetype-go.googlecode.com/hg/freetype/raster
+GOFILES=\
+	raster.go\
+
+include $(GOROOT)/src/Make.pkg
+

freetype/raster/raster.go

+// 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,
+// both of which can be found in the LICENSE file.
+
+// The raster package provides an anti-aliasing 2-D rasterizer.
+//
+// It is part of the larger Freetype-Go suite of font-related packages,
+// but the raster package is not specific to font rasterization, and can
+// be used standalone without any other Freetype-Go 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 (
+	"fmt"
+	"image"
+	"strconv"
+)
+
+// A Painter knows how to paint a span, and a span is a horizontal segment
+// of a certain alpha. A fully opaque span has alpha == 1<<32-1. A span's
+// alpha is non-zero until the final Paint call of the rasterization, which
+// has all arguments zero.
+// TODO(nigeltao): Is it worth batching spans, so that Paint takes a []Span
+// instead of a single Span?
+type Painter interface {
+	Paint(yi, xi0, xi1 int, alpha uint32)
+}
+
+// The PainterFunc type adapts an ordinary function to the Painter interface.
+type PainterFunc func(yi, xi0, xi1 int, alpha uint32)
+
+// Paint just delegates the call to f.
+func (f PainterFunc) Paint(yi, xi0, xi1 int, alpha uint32) {
+	f(yi, xi0, xi1, alpha)
+}
+
+// A 24.8 fixed point number.
+type Fixed int32
+
+// Human-readable format for a 24.8 fixed point number. For example, the
+// number one-and-a-quarter becomes "1:064".
+func (x Fixed) String() string {
+	i, f := x/256, x%256
+	if f < 0 {
+		f = -f
+	}
+	return fmt.Sprintf("%d:%03d", i, f)
+}
+
+// Two-dimensional point, in 24.8 fixed point format.
+type Point struct {
+	X, Y Fixed
+}
+
+// A cell is part of a linked list (for a given yi coordinate) 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
+
+	// The width of the Rasterizer. The height is implicit in len(cellIndex).
+	width int
+	// quadSplitScale is the scaling factor used to determine how many times
+	// to decompose a quadratic segment into a linear approximation.
+	quadSplitScale int
+
+	// The current pen position.
+	a Point
+	// 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
+}
+
+// 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 24.8 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) {
+	// Break the 24.8 fixed point X co-ordinates into integral and fractional parts.
+	x0i := int(x0) / 256
+	x0f := x0 - Fixed(256*x0i)
+	x1i := int(x1) / 256
+	x1f := x1 - Fixed(256*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 256 units in 24.8 fixed point format.
+	var (
+		p, q, edge0, edge1 Fixed
+		xiDelta            int
+	)
+	if dx > 0 {
+		p, q = (256-x0f)*dy, dx
+		edge0, edge1, xiDelta = 0, 256, 1
+	} else {
+		p, q = x0f*dy, -dx
+		edge0, edge1, xiDelta = 256, 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 = 256 * (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(256 * 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 Point) {
+	r.setCell(int(a.X/256), int(a.Y/256))
+	r.a = a
+}
+
+// Move1 adds a linear segment to the current curve.
+func (r *Rasterizer) Move1(b Point) {
+	x0, y0 := r.a.X, r.a.Y
+	x1, y1 := b.X, b.Y
+	dx, dy := x1-x0, y1-y0
+	// Break the 24.8 fixed point Y co-ordinates into integral and fractional parts.
+	y0i := int(y0) / 256
+	y0f := y0 - Fixed(256*y0i)
+	y1i := int(y1) / 256
+	y1f := y1 - Fixed(256*y1i)
+
+	if y0i == y1i {
+		// There is only one scanline.
+		r.scan(y0i, x0, y0f, x1, y1f)
+	} 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 256
+		// units in 24.8 fixed point format.
+		var (
+			p, q, edge0, edge1 Fixed
+			yiDelta            int
+		)
+		if dy > 0 {
+			p, q = (256-y0f)*dx, dy
+			edge0, edge1, yiDelta = 0, 256, 1
+		} else {
+			p, q = y0f*dx, -dy
+			edge0, edge1, yiDelta = 256, 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)/256, yi)
+		if yi != y1i {
+			// Do all the intermediate scanlines.
+			p = 256 * 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)/256, yi)
+			}
+		}
+		// Do the last scanline.
+		r.scan(yi, x, edge0, x1, y1f)
+	}
+	// The next lineTo starts from b.
+	r.a = b
+}
+
+// Move2 adds a quadratic segment to the current curve.
+func (r *Rasterizer) Move2(b, c Point) {
+	// 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.
+	dx := r.a.X - 2*b.X + c.X
+	dy := r.a.Y - 2*b.Y + c.Y
+	if dx < 0 {
+		dx = -dx
+	}
+	if dy < 0 {
+		dy = -dy
+	}
+	deviation := dx
+	if deviation < dy {
+		deviation = dy
+	}
+	nsplit := 0
+	deviation /= Fixed(r.quadSplitScale)
+	for deviation > 0 {
+		deviation /= 4
+		nsplit++
+	}
+	// maxd 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: Move2 nsplit too large: " + strconv.Itoa(nsplit))
+	}
+	// Recursively decompose the curve nSplit levels deep.
+	var (
+		pStack [2*maxNsplit + 3]Point
+		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]
+		if s > 0 {
+			pp := pStack[2*i:]
+			// Split the quadratic curve pp[0:3] into an equivalent set of two shorter curves:
+			// pp[0:3] and pp[2:5]. The new pp[4] is the old pp[2], and pp[0] is unchanged.
+			mx := pp[1].X
+			pp[4].X = pp[2].X
+			pp[3].X = (pp[4].X + mx) / 2
+			pp[1].X = (pp[0].X + mx) / 2
+			pp[2].X = (pp[1].X + pp[3].X) / 2
+			my := pp[1].Y
+			pp[4].Y = pp[2].Y
+			pp[3].Y = (pp[4].Y + my) / 2
+			pp[1].Y = (pp[0].Y + my) / 2
+			pp[2].Y = (pp[1].Y + pp[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 := (r.a.X + 2*pStack[2*i+1].X + pStack[2*i].X) / 4
+			midy := (r.a.Y + 2*pStack[2*i+1].Y + pStack[2*i].Y) / 4
+			r.Move1(Point{midx, midy})
+			r.Move1(pStack[2*i])
+			i--
+		}
+	}
+}
+
+// Move3 adds a cubic segment to the current curve.
+func (r *Rasterizer) Move3(b, c, d Point) {
+	// TODO(nigeltao): implement cubic splines, similar to Move2's quadratic splines.
+	panic("not implemented")
+}
+
+// Converts an area value to a uint32 alpha value. A completely filled pixel
+// corresponds to an area of 256*256*2, and an alpha of 1<<32-1. 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 32-bit alpha.
+	a := (area + 1) >> 1
+	if a < 0 {
+		a = -a
+	}
+	alpha := uint32(a)
+	if r.UseNonZeroWinding {
+		if alpha > 0xffff {
+			alpha = 0xffff
+		}
+	} else {
+		alpha &= 0x1ffff
+		if alpha > 0x10000 {
+			alpha = 0x20000 - alpha
+		} else if alpha == 0x10000 {
+			alpha = 0x0ffff
+		}
+	}
+	alpha |= alpha << 16
+	return alpha
+}
+
+// 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 <= xi0 < xi1 <= r.width) and non-zero alpha,
+// except for the final span, which has yi, xi0, xi1 and alpha all equal
+// to zero.
+func (r *Rasterizer) Rasterize(p Painter) {
+	r.saveCell()
+	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 * 256 * 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 {
+						p.Paint(yi, xi0, xi1, alpha)
+					}
+				}
+			}
+			cover += r.cell[c].cover
+			alpha := r.areaToAlpha(cover*256*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 {
+					p.Paint(yi, xi0, xi1, alpha)
+				}
+			}
+		}
+	}
+	p.Paint(0, 0, 0, 0)
+}
+
+// Clear cancels any previous calls to r.Start or r.MoveN.
+func (r *Rasterizer) Clear() {
+	r.a = Point{0, 0}
+	r.xi = 0
+	r.yi = 0
+	r.area = 0
+	r.cover = 0
+	r.cell = r.cell[0:0]
+	for i := 0; i < len(r.cellIndex); i++ {
+		r.cellIndex[i] = -1
+	}
+}
+
+// Creates a new Rasterizer with the given bounds.
+func New(width, height int) *Rasterizer {
+	if width < 0 {
+		width = 0
+	}
+	if height < 0 {
+		height = 0
+	}
+
+	// Use the same qss heuristic as the C Freetype implementation.
+	qss := 128
+	if width > 24 || height > 24 {
+		qss *= 2
+		if width > 120 || height > 120 {
+			qss *= 2
+		}
+	}
+
+	r := new(Rasterizer)
+	r.width = width
+	r.quadSplitScale = qss
+	r.cell = r.cellBuf[0:0]
+	if height > len(r.cellIndexBuf) {
+		r.cellIndex = make([]int, height)
+	} else {
+		r.cellIndex = r.cellIndexBuf[0:height]
+	}
+	for i := 0; i < len(r.cellIndex); i++ {
+		r.cellIndex[i] = -1
+	}
+	return r
+}
+
+// AlphaOverPainter returns a Painter that paints onto the given Alpha image
+// using the "src over dst" Porter-Duff composition operator.
+func AlphaOverPainter(m *image.Alpha) Painter {
+	return PainterFunc(func(yi, xi0, xi1 int, alpha uint32) {
+		a := int(alpha >> 24)
+		p := m.Pixel[yi]
+		for i := xi0; i < xi1; i++ {
+			ai := int(p[i].A)
+			ai = (ai*255 + (255-ai)*a) / 255
+			p[i] = image.AlphaColor{uint8(ai)}
+		}
+	})
+}
+
+// AlphaSrcPainter returns a Painter that paints onto the given Alpha image
+// using the "src" Porter-Duff composition operator.
+func AlphaSrcPainter(m *image.Alpha) Painter {
+	return PainterFunc(func(yi, xi0, xi1 int, alpha uint32) {
+		color := image.AlphaColor{uint8(alpha >> 24)}
+		p := m.Pixel[yi]
+		for i := xi0; i < xi1; i++ {
+			p[i] = color
+		}
+	})
+}

licenses/ftl.txt

+                    The FreeType Project LICENSE
+                    ----------------------------
+
+                            2006-Jan-27
+
+                    Copyright 1996-2002, 2006 by
+          David Turner, Robert Wilhelm, and Werner Lemberg
+
+
+
+Introduction
+============
+
+  The FreeType  Project is distributed in  several archive packages;
+  some of them may contain, in addition to the FreeType font engine,
+  various tools and  contributions which rely on, or  relate to, the
+  FreeType Project.
+
+  This  license applies  to all  files found  in such  packages, and
+  which do not  fall under their own explicit  license.  The license
+  affects  thus  the  FreeType   font  engine,  the  test  programs,
+  documentation and makefiles, at the very least.
+
+  This  license   was  inspired  by  the  BSD,   Artistic,  and  IJG
+  (Independent JPEG  Group) licenses, which  all encourage inclusion
+  and  use of  free  software in  commercial  and freeware  products
+  alike.  As a consequence, its main points are that:
+
+    o We don't promise that this software works. However, we will be
+      interested in any kind of bug reports. (`as is' distribution)
+
+    o You can  use this software for whatever you  want, in parts or
+      full form, without having to pay us. (`royalty-free' usage)
+
+    o You may not pretend that  you wrote this software.  If you use
+      it, or  only parts of it,  in a program,  you must acknowledge
+      somewhere  in  your  documentation  that  you  have  used  the
+      FreeType code. (`credits')
+
+  We  specifically  permit  and  encourage  the  inclusion  of  this
+  software, with  or without modifications,  in commercial products.
+  We  disclaim  all warranties  covering  The  FreeType Project  and
+  assume no liability related to The FreeType Project.
+
+
+  Finally,  many  people  asked  us  for  a  preferred  form  for  a
+  credit/disclaimer to use in compliance with this license.  We thus
+  encourage you to use the following text:
+
+   """
+    Portions of this software are copyright © <year> The FreeType
+    Project (www.freetype.org).  All rights reserved.
+   """
+
+  Please replace <year> with the value from the FreeType version you
+  actually use.
+
+
+Legal Terms
+===========
+
+0. Definitions
+--------------
+
+  Throughout this license,  the terms `package', `FreeType Project',
+  and  `FreeType  archive' refer  to  the  set  of files  originally
+  distributed  by the  authors  (David Turner,  Robert Wilhelm,  and
+  Werner Lemberg) as the `FreeType Project', be they named as alpha,
+  beta or final release.
+
+  `You' refers to  the licensee, or person using  the project, where
+  `using' is a generic term including compiling the project's source
+  code as  well as linking it  to form a  `program' or `executable'.
+  This  program is  referred to  as  `a program  using the  FreeType
+  engine'.
+
+  This  license applies  to all  files distributed  in  the original
+  FreeType  Project,   including  all  source   code,  binaries  and
+  documentation,  unless  otherwise  stated   in  the  file  in  its
+  original, unmodified form as  distributed in the original archive.
+  If you are  unsure whether or not a particular  file is covered by
+  this license, you must contact us to verify this.
+
+  The FreeType  Project is copyright (C) 1996-2000  by David Turner,
+  Robert Wilhelm, and Werner Lemberg.  All rights reserved except as
+  specified below.
+
+1. No Warranty
+--------------
+
+  THE FREETYPE PROJECT  IS PROVIDED `AS IS' WITHOUT  WARRANTY OF ANY
+  KIND, EITHER  EXPRESS OR IMPLIED,  INCLUDING, BUT NOT  LIMITED TO,
+  WARRANTIES  OF  MERCHANTABILITY   AND  FITNESS  FOR  A  PARTICULAR
+  PURPOSE.  IN NO EVENT WILL ANY OF THE AUTHORS OR COPYRIGHT HOLDERS
+  BE LIABLE  FOR ANY DAMAGES CAUSED  BY THE USE OR  THE INABILITY TO
+  USE, OF THE FREETYPE PROJECT.
+
+2. Redistribution
+-----------------
+
+  This  license  grants  a  worldwide, royalty-free,  perpetual  and
+  irrevocable right  and license to use,  execute, perform, compile,
+  display,  copy,   create  derivative  works   of,  distribute  and
+  sublicense the  FreeType Project (in  both source and  object code
+  forms)  and  derivative works  thereof  for  any  purpose; and  to
+  authorize others  to exercise  some or all  of the  rights granted
+  herein, subject to the following conditions:
+
+    o Redistribution of  source code  must retain this  license file
+      (`FTL.TXT') unaltered; any  additions, deletions or changes to
+      the original  files must be clearly  indicated in accompanying
+      documentation.   The  copyright   notices  of  the  unaltered,
+      original  files must  be  preserved in  all  copies of  source
+      files.
+
+    o Redistribution in binary form must provide a  disclaimer  that
+      states  that  the software is based in part of the work of the
+      FreeType Team,  in  the  distribution  documentation.  We also
+      encourage you to put an URL to the FreeType web page  in  your
+      documentation, though this isn't mandatory.
+
+  These conditions  apply to any  software derived from or  based on
+  the FreeType Project,  not just the unmodified files.   If you use
+  our work, you  must acknowledge us.  However, no  fee need be paid
+  to us.
+
+3. Advertising
+--------------
+
+  Neither the  FreeType authors and  contributors nor you  shall use
+  the name of the  other for commercial, advertising, or promotional
+  purposes without specific prior written permission.
+
+  We suggest,  but do not require, that  you use one or  more of the
+  following phrases to refer  to this software in your documentation
+  or advertising  materials: `FreeType Project',  `FreeType Engine',
+  `FreeType library', or `FreeType Distribution'.
+
+  As  you have  not signed  this license,  you are  not  required to
+  accept  it.   However,  as  the FreeType  Project  is  copyrighted
+  material, only  this license, or  another one contracted  with the
+  authors, grants you  the right to use, distribute,  and modify it.
+  Therefore,  by  using,  distributing,  or modifying  the  FreeType
+  Project, you indicate that you understand and accept all the terms
+  of this license.
+
+4. Contacts
+-----------
+
+  There are two mailing lists related to FreeType:
+
+    o freetype@nongnu.org
+
+      Discusses general use and applications of FreeType, as well as
+      future and  wanted additions to the  library and distribution.
+      If  you are looking  for support,  start in  this list  if you
+      haven't found anything to help you in the documentation.
+
+    o freetype-devel@nongnu.org
+
+      Discusses bugs,  as well  as engine internals,  design issues,
+      specific licenses, porting, etc.
+
+  Our home page can be found at
+
+    http://www.freetype.org
+
+
+--- end of FTL.TXT ---

licenses/gpl.txt

+		    GNU GENERAL PUBLIC LICENSE
+		       Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.
+     51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+			    Preamble
+
+  The licenses for most software are designed to take away your
+freedom to share and change it.  By contrast, the GNU General Public
+License is intended to guarantee your freedom to share and change free
+software--to make sure the software is free for all its users.  This
+General Public License applies to most of the Free Software
+Foundation's software and to any other program whose authors commit to
+using it.  (Some other Free Software Foundation software is covered by
+the GNU Library General Public License instead.)  You can apply it to
+your programs, too.
+
+  When we speak of free software, we are referring to freedom, not
+price.  Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
+this service if you wish), that you receive source code or can get it
+if you want it, that you can change the software or use pieces of it
+in new free programs; and that you know you can do these things.
+
+  To protect your rights, we need to make restrictions that forbid
+anyone to deny you these rights or to ask you to surrender the rights.
+These restrictions translate to certain responsibilities for you if you
+distribute copies of the software, or if you modify it.
+
+  For example, if you distribute copies of such a program, whether
+gratis or for a fee, you must give the recipients all the rights that
+you have.  You must make sure that they, too, receive or can get the
+source code.  And you must show them these terms so they know their
+rights.
+
+  We protect your rights with two steps: (1) copyright the software, and
+(2) offer you this license which gives you legal permission to copy,
+distribute and/or modify the software.
+
+  Also, for each author's protection and ours, we want to make certain
+that everyone understands that there is no warranty for this free
+software.  If the software is modified by someone else and passed on, we
+want its recipients to know that what they have is not the original, so
+that any problems introduced by others will not reflect on the original
+authors' reputations.
+
+  Finally, any free program is threatened constantly by software
+patents.  We wish to avoid the danger that redistributors of a free
+program will individually obtain patent licenses, in effect making the
+program proprietary.  To prevent this, we have made it clear that any
+patent must be licensed for everyone's free use or not licensed at all.
+
+  The precise terms and conditions for copying, distribution and
+modification follow.
+
+		    GNU GENERAL PUBLIC LICENSE
+   TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
+
+  0. This License applies to any program or other work which contains
+a notice placed by the copyright holder saying it may be distributed
+under the terms of this General Public License.  The "Program", below,
+refers to any such program or work, and a "work based on the Program"
+means either the Program or any derivative work under copyright law:
+that is to say, a work containing the Program or a portion of it,
+either verbatim or with modifications and/or translated into another
+language.  (Hereinafter, translation is included without limitation in
+the term "modification".)  Each licensee is addressed as "you".
+
+Activities other than copying, distribution and modification are not
+covered by this License; they are outside its scope.  The act of
+running the Program is not restricted, and the output from the Program
+is covered only if its contents constitute a work based on the
+Program (independent of having been made by running the Program).
+Whether that is true depends on what the Program does.
+
+  1. You may copy and distribute verbatim copies of the Program's
+source code as you receive it, in any medium, provided that you
+conspicuously and appropriately publish on each copy an appropriate
+copyright notice and disclaimer of warranty; keep intact all the
+notices that refer to this License and to the absence of any warranty;
+and give any other recipients of the Program a copy of this License
+along with the Program.
+
+You may charge a fee for the physical act of transferring a copy, and
+you may at your option offer warranty protection in exchange for a fee.
+
+  2. You may modify your copy or copies of the Program or any portion
+of it, thus forming a work based on the Program, and copy and
+distribute such modifications or work under the terms of Section 1
+above, provided that you also meet all of these conditions:
+
+    a) You must cause the modified files to carry prominent notices
+    stating that you changed the files and the date of any change.
+
+    b) You must cause any work that you distribute or publish, that in
+    whole or in part contains or is derived from the Program or any
+    part thereof, to be licensed as a whole at no charge to all third
+    parties under the terms of this License.
+
+    c) If the modified program normally reads commands interactively
+    when run, you must cause it, when started running for such
+    interactive use in the most ordinary way, to print or display an
+    announcement including an appropriate copyright notice and a
+    notice that there is no warranty (or else, saying that you provide
+    a warranty) and that users may redistribute the program under
+    these conditions, and telling the user how to view a copy of this
+    License.  (Exception: if the Program itself is interactive but
+    does not normally print such an announcement, your work based on
+    the Program is not required to print an announcement.)
+
+These requirements apply to the modified work as a whole.  If
+identifiable sections of that work are not derived from the Program,
+and can be reasonably considered independent and separate works in
+themselves, then this License, and its terms, do not apply to those
+sections when you distribute them as separate works.  But when you
+distribute the same sections as part of a whole which is a work based
+on the Program, the distribution of the whole must be on the terms of
+this License, whose permissions for other licensees extend to the
+entire whole, and thus to each and every part regardless of who wrote it.
+
+Thus, it is not the intent of this section to claim rights or contest
+your rights to work written entirely by you; rather, the intent is to
+exercise the right to control the distribution of derivative or
+collective works based on the Program.
+
+In addition, mere aggregation of another work not based on the Program
+with the Program (or with a work based on the Program) on a volume of
+a storage or distribution medium does not bring the other work under
+the scope of this License.
+
+  3. You may copy and distribute the Program (or a work based on it,
+under Section 2) in object code or executable form under the terms of
+Sections 1 and 2 above provided that you also do one of the following:
+
+    a) Accompany it with the complete corresponding machine-readable
+    source code, which must be distributed under the terms of Sections
+    1 and 2 above on a medium customarily used for software interchange; or,
+
+    b) Accompany it with a written offer, valid for at least three
+    years, to give any third party, for a charge no more than your
+    cost of physically performing source distribution, a complete
+    machine-readable copy of the corresponding source code, to be
+    distributed under the terms of Sections 1 and 2 above on a medium
+    customarily used for software interchange; or,
+
+    c) Accompany it with the information you received as to the offer
+    to distribute corresponding source code.  (This alternative is
+    allowed only for noncommercial distribution and only if you
+    received the program in object code or executable form with such
+    an offer, in accord with Subsection b above.)
+
+The source code for a work means the preferred form of the work for
+making modifications to it.  For an executable work, complete source
+code means all the source code for all modules it contains, plus any
+associated interface definition files, plus the scripts used to
+control compilation and installation of the executable.  However, as a
+special exception, the source code distributed need not include
+anything that is normally distributed (in either source or binary
+form) with the major components (compiler, kernel, and so on) of the
+operating system on which the executable runs, unless that component
+itself accompanies the executable.
+
+If distribution of executable or object code is made by offering
+access to copy from a designated place, then offering equivalent
+access to copy the source code from the same place counts as
+distribution of the source code, even though third parties are not
+compelled to copy the source along with the object code.
+
+  4. You may not copy, modify, sublicense, or distribute the Program
+except as expressly provided under this License.  Any attempt
+otherwise to copy, modify, sublicense or distribute the Program is
+void, and will automatically terminate your rights under this License.
+However, parties who have received copies, or rights, from you under
+this License will not have their licenses terminated so long as such
+parties remain in full compliance.
+
+  5. You are not required to accept this License, since you have not
+signed it.  However, nothing else grants you permission to modify or
+distribute the Program or its derivative works.  These actions are
+prohibited by law if you do not accept this License.  Therefore, by
+modifying or distributing the Program (or any work based on the
+Program), you indicate your acceptance of this License to do so, and
+all its terms and conditions for copying, distributing or modifying
+the Program or works based on it.
+
+  6. Each time you redistribute the Program (or any work based on the
+Program), the recipient automatically receives a license from the
+original licensor to copy, distribute or modify the Program subject to
+these terms and conditions.  You may not impose any further
+restrictions on the recipients' exercise of the rights granted herein.
+You are not responsible for enforcing compliance by third parties to
+this License.
+
+  7. If, as a consequence of a court judgment or allegation of patent
+infringement or for any other reason (not limited to patent issues),
+conditions are imposed on you (whether by court order, agreement or
+otherwise) that contradict the conditions of this License, they do not
+excuse you from the conditions of this License.  If you cannot
+distribute so as to satisfy simultaneously your obligations under this
+License and any other pertinent obligations, then as a consequence you
+may not distribute the Program at all.  For example, if a patent
+license would not permit royalty-free redistribution of the Program by
+all those who receive copies directly or indirectly through you, then
+the only way you could satisfy both it and this License would be to
+refrain entirely from distribution of the Program.
+
+If any portion of this section is held invalid or unenforceable under
+any particular circumstance, the balance of the section is intended to
+apply and the section as a whole is intended to apply in other
+circumstances.
+
+It is not the purpose of this section to induce you to infringe any
+patents or other property right claims or to contest validity of any
+such claims; this section has the sole purpose of protecting the
+integrity of the free software distribution system, which is
+implemented by public license practices.  Many people have made
+generous contributions to the wide range of software distributed
+through that system in reliance on consistent application of that
+system; it is up to the author/donor to decide if he or she is willing
+to distribute software through any other system and a licensee cannot
+impose that choice.
+
+This section is intended to make thoroughly clear what is believed to
+be a consequence of the rest of this License.
+
+  8. If the distribution and/or use of the Program is restricted in
+certain countries either by patents or by copyrighted interfaces, the
+original copyright holder who places the Program under this License
+may add an explicit geographical distribution limitation excluding
+those countries, so that distribution is permitted only in or among
+countries not thus excluded.  In such case, this License incorporates
+the limitation as if written in the body of this License.
+
+  9. The Free Software Foundation may publish revised and/or new versions
+of the General Public License from time to time.  Such new versions will
+be similar in spirit to the present version, but may differ in detail to
+address new problems or concerns.
+
+Each version is given a distinguishing version number.  If the Program
+specifies a version number of this License which applies to it and "any
+later version", you have the option of following the terms and conditions
+either of that version or of any later version published by the Free
+Software Foundation.  If the Program does not specify a version number of
+this License, you may choose any version ever published by the Free Software
+Foundation.
+
+  10. If you wish to incorporate parts of the Program into other free
+programs whose distribution conditions are different, write to the author
+to ask for permission.  For software which is copyrighted by the Free
+Software Foundation, write to the Free Software Foundation; we sometimes
+make exceptions for this.  Our decision will be guided by the two goals
+of preserving the free status of all derivatives of our free software and
+of promoting the sharing and reuse of software generally.
+
+			    NO WARRANTY
+
+  11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
+FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW.  EXCEPT WHEN
+OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
+PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
+OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.  THE ENTIRE RISK AS
+TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU.  SHOULD THE
+PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
+REPAIR OR CORRECTION.
+
+  12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
+REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
+INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
+OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
+TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
+YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
+PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
+POSSIBILITY OF SUCH DAMAGES.
+
+		     END OF TERMS AND CONDITIONS
+
+	    How to Apply These Terms to Your New Programs
+
+  If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+  To do so, attach the following notices to the program.  It is safest
+to attach them to the start of each source file to most effectively
+convey the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+    <one line to give the program's name and a brief idea of what it does.>
+    Copyright (C) <year>  <name of author>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with this program; if not, write to the Free Software
+    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
+
+
+Also add information on how to contact you by electronic and paper mail.
+
+If the program is interactive, make it output a short notice like this
+when it starts in an interactive mode:
+
+    Gnomovision version 69, Copyright (C) year  name of author
+    Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License.  Of course, the commands you use may
+be called something other than `show w' and `show c'; they could even be
+mouse-clicks or menu items--whatever suits your program.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the program, if
+necessary.  Here is a sample; alter the names:
+
+  Yoyodyne, Inc., hereby disclaims all copyright interest in the program
+  `Gnomovision' (which makes passes at compilers) written by James Hacker.
+
+  <signature of Ty Coon>, 1 April 1989
+  Ty Coon, President of Vice
+
+This General Public License does not permit incorporating your program into
+proprietary programs.  If your program is a subroutine library, you may
+consider it more useful to permit linking proprietary applications with the
+library.  If this is what you want to do, use the GNU Library General
+Public License instead of this License.