func p(n node) fixed.Point26_6 {
x, y := 20+n.x/4, 380-n.y/4
return fixed.Point26_6{
X: fixed.Int26_6(x << 6),
Y: fixed.Int26_6(y << 6),
}
}
// unscaledVMetric returns the unscaled vertical metrics for the glyph with
// the given index. yMax is the top of the glyph's bounding box.
func (f *Font) unscaledVMetric(i Index, yMax fixed.Int26_6) (v VMetric) {
j := int(i)
if j < 0 || f.nGlyph <= j {
return VMetric{}
}
if 4*j+4 <= len(f.vmtx) {
return VMetric{
AdvanceHeight: fixed.Int26_6(u16(f.vmtx, 4*j)),
TopSideBearing: fixed.Int26_6(int16(u16(f.vmtx, 4*j+2))),
}
}
// The OS/2 table has grown over time.
// https://developer.apple.com/fonts/TTRefMan/RM06/Chap6OS2.html
// says that it was originally 68 bytes. Optional fields, including
// the ascender and descender, are described at
// http://www.microsoft.com/typography/otspec/os2.htm
if len(f.os2) >= 72 {
sTypoAscender := fixed.Int26_6(int16(u16(f.os2, 68)))
sTypoDescender := fixed.Int26_6(int16(u16(f.os2, 70)))
return VMetric{
AdvanceHeight: sTypoAscender - sTypoDescender,
TopSideBearing: sTypoAscender - yMax,
}
}
return VMetric{
AdvanceHeight: fixed.Int26_6(f.fUnitsPerEm),
TopSideBearing: 0,
}
}
// rasterize returns the advance width, glyph mask and integer-pixel offset
// to render the given glyph at the given sub-pixel offsets.
// The 26.6 fixed point arguments fx and fy must be in the range [0, 1).
func (c *Context) rasterize(glyph truetype.Index, fx, fy fixed.Int26_6) (
fixed.Int26_6, *image.Alpha, image.Point, error) {
if err := c.glyphBuf.Load(c.f, c.scale, glyph, c.hinting); err != nil {
return 0, nil, image.Point{}, err
}
// Calculate the integer-pixel bounds for the glyph.
xmin := int(fx+c.glyphBuf.Bounds.Min.X) >> 6
ymin := int(fy-c.glyphBuf.Bounds.Max.Y) >> 6
xmax := int(fx+c.glyphBuf.Bounds.Max.X+0x3f) >> 6
ymax := int(fy-c.glyphBuf.Bounds.Min.Y+0x3f) >> 6
if xmin > xmax || ymin > ymax {
return 0, nil, image.Point{}, errors.New("freetype: negative sized glyph")
}
// A TrueType's glyph's nodes can have negative co-ordinates, but the
// rasterizer clips anything left of x=0 or above y=0. xmin and ymin are
// the pixel offsets, based on the font's FUnit metrics, that let a
// negative co-ordinate in TrueType space be non-negative in rasterizer
// space. xmin and ymin are typically <= 0.
fx -= fixed.Int26_6(xmin << 6)
fy -= fixed.Int26_6(ymin << 6)
// Rasterize the glyph's vectors.
c.r.Clear()
e0 := 0
for _, e1 := range c.glyphBuf.Ends {
c.drawContour(c.glyphBuf.Points[e0:e1], fx, fy)
e0 = e1
}
a := image.NewAlpha(image.Rect(0, 0, xmax-xmin, ymax-ymin))
c.r.Rasterize(raster.NewAlphaSrcPainter(a))
return c.glyphBuf.AdvanceWidth, a, image.Point{xmin, ymin}, nil
}
// 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)}
}
// TestParse tests that the luxisr.ttf metrics and glyphs are parsed correctly.
// The numerical values can be manually verified by examining luxisr.ttx.
func TestParse(t *testing.T) {
f, _, err := parseTestdataFont("luxisr")
if err != nil {
t.Fatal(err)
}
if got, want := f.FUnitsPerEm(), int32(2048); got != want {
t.Errorf("FUnitsPerEm: got %v, want %v", got, want)
}
fupe := fixed.Int26_6(f.FUnitsPerEm())
if got, want := f.Bounds(fupe), mkBounds(-441, -432, 2024, 2033); got != want {
t.Errorf("Bounds: got %v, want %v", got, want)
}
i0 := f.Index('A')
i1 := f.Index('V')
if i0 != 36 || i1 != 57 {
t.Fatalf("Index: i0, i1 = %d, %d, want 36, 57", i0, i1)
}
if got, want := f.HMetric(fupe, i0), (HMetric{1366, 19}); got != want {
t.Errorf("HMetric: got %v, want %v", got, want)
}
if got, want := f.VMetric(fupe, i0), (VMetric{2465, 553}); got != want {
t.Errorf("VMetric: got %v, want %v", got, want)
}
if got, want := f.Kern(fupe, i0, i1), fixed.Int26_6(-144); got != want {
t.Errorf("Kern: got %v, want %v", got, want)
}
g := &GlyphBuf{}
err = g.Load(f, fupe, i0, font.HintingNone)
if err != nil {
t.Fatalf("Load: %v", err)
}
g0 := &GlyphBuf{
Bounds: g.Bounds,
Points: g.Points,
Ends: g.Ends,
}
g1 := &GlyphBuf{
Bounds: mkBounds(19, 0, 1342, 1480),
Points: []Point{
{19, 0, 51},
{581, 1480, 1},
{789, 1480, 51},
{1342, 0, 1},
{1116, 0, 35},
{962, 410, 3},
{368, 410, 33},
{214, 0, 3},
{428, 566, 19},
{904, 566, 33},
{667, 1200, 3},
},
Ends: []int{8, 11},
}
if got, want := fmt.Sprint(g0), fmt.Sprint(g1); got != want {
t.Errorf("GlyphBuf:\ngot %v\nwant %v", got, want)
}
}
// scale returns x divided by f.fUnitsPerEm, rounded to the nearest integer.
func (f *Font) scale(x fixed.Int26_6) fixed.Int26_6 {
if x >= 0 {
x += fixed.Int26_6(f.fUnitsPerEm) / 2
} else {
x -= fixed.Int26_6(f.fUnitsPerEm) / 2
}
return x / fixed.Int26_6(f.fUnitsPerEm)
}
// 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)}
}
// dotProduct returns the dot product of [x, y] and q. It is almost the same as
// px := int64(x)
// py := int64(y)
// qx := int64(q[0])
// qy := int64(q[1])
// return fixed.Int26_6((px*qx + py*qy + 1<<13) >> 14)
// except that the computation is done with 32-bit integers to produce exactly
// the same rounding behavior as C Freetype.
func dotProduct(x, y fixed.Int26_6, q [2]f2dot14) fixed.Int26_6 {
// Compute x*q[0] as 64-bit value.
l := uint32((int32(x) & 0xFFFF) * int32(q[0]))
m := (int32(x) >> 16) * int32(q[0])
lo1 := l + (uint32(m) << 16)
hi1 := (m >> 16) + (int32(l) >> 31) + bool2int32(lo1 < l)
// Compute y*q[1] as 64-bit value.
l = uint32((int32(y) & 0xFFFF) * int32(q[1]))
m = (int32(y) >> 16) * int32(q[1])
lo2 := l + (uint32(m) << 16)
hi2 := (m >> 16) + (int32(l) >> 31) + bool2int32(lo2 < l)
// Add them.
lo := lo1 + lo2
hi := hi1 + hi2 + bool2int32(lo < lo1)
// Divide the result by 2^14 with rounding.
s := hi >> 31
l = lo + uint32(s)
hi += s + bool2int32(l < lo)
lo = l
l = lo + 0x2000
hi += bool2int32(l < lo)
return fixed.Int26_6((uint32(hi) << 18) | (l >> 14))
}
// NewFace returns a new font.Face for the given Font.
func NewFace(f *Font, opts *Options) font.Face {
a := &face{
f: f,
hinting: opts.hinting(),
scale: fixed.Int26_6(0.5 + (opts.size() * opts.dpi() * 64 / 72)),
glyphCache: make([]glyphCacheEntry, opts.glyphCacheEntries()),
}
a.subPixelX, a.subPixelBiasX, a.subPixelMaskX = opts.subPixelsX()
a.subPixelY, a.subPixelBiasY, a.subPixelMaskY = opts.subPixelsY()
// Fill the cache with invalid entries. Valid glyph cache entries have fx
// and fy in the range [0, 64). Valid index cache entries have rune >= 0.
for i := range a.glyphCache {
a.glyphCache[i].key.fy = 0xff
}
for i := range a.indexCache {
a.indexCache[i].rune = -1
}
// Set the rasterizer's bounds to be big enough to handle the largest glyph.
b := f.Bounds(a.scale)
xmin := +int(b.Min.X) >> 6
ymin := -int(b.Max.Y) >> 6
xmax := +int(b.Max.X+63) >> 6
ymax := -int(b.Min.Y-63) >> 6
a.maxw = xmax - xmin
a.maxh = ymax - ymin
a.masks = image.NewAlpha(image.Rect(0, 0, a.maxw, a.maxh*len(a.glyphCache)))
a.r.SetBounds(a.maxw, a.maxh)
a.p = facePainter{a}
return a
}
func (f *subface) GlyphAdvance(r rune) (advance fixed.Int26_6, ok bool) {
r -= f.firstRune
if r < 0 || f.n <= int(r) {
return 0, false
}
return fixed.Int26_6(f.fontchars[r].width) << 6, true
}
func main() {
flag.Parse()
fmt.Printf("Loading fontfile %q\n", *fontfile)
b, err := ioutil.ReadFile(*fontfile)
if err != nil {
log.Println(err)
return
}
f, err := truetype.Parse(b)
if err != nil {
log.Println(err)
return
}
fupe := fixed.Int26_6(f.FUnitsPerEm())
printBounds(f.Bounds(fupe))
fmt.Printf("FUnitsPerEm:%d\n\n", fupe)
c0, c1 := 'A', 'V'
i0 := f.Index(c0)
hm := f.HMetric(fupe, i0)
g := &truetype.GlyphBuf{}
err = g.Load(f, fupe, i0, font.HintingNone)
if err != nil {
log.Println(err)
return
}
fmt.Printf("'%c' glyph\n", c0)
fmt.Printf("AdvanceWidth:%d LeftSideBearing:%d\n", hm.AdvanceWidth, hm.LeftSideBearing)
printGlyph(g)
i1 := f.Index(c1)
fmt.Printf("\n'%c', '%c' Kern:%d\n", c0, c1, f.Kern(fupe, i0, i1))
}
// unscaledHMetric returns the unscaled horizontal metrics for the glyph with
// the given index.
func (f *Font) unscaledHMetric(i Index) (h HMetric) {
j := int(i)
if j < 0 || f.nGlyph <= j {
return HMetric{}
}
if j >= f.nHMetric {
p := 4 * (f.nHMetric - 1)
return HMetric{
AdvanceWidth: fixed.Int26_6(u16(f.hmtx, p)),
LeftSideBearing: fixed.Int26_6(int16(u16(f.hmtx, p+2*(j-f.nHMetric)+4))),
}
}
return HMetric{
AdvanceWidth: fixed.Int26_6(u16(f.hmtx, 4*j)),
LeftSideBearing: fixed.Int26_6(int16(u16(f.hmtx, 4*j+2))),
}
}
// 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--
}
}
}
func (f *Font) parseHead() error {
if len(f.head) != 54 {
return FormatError(fmt.Sprintf("bad head length: %d", len(f.head)))
}
f.fUnitsPerEm = int32(u16(f.head, 18))
f.bounds.Min.X = fixed.Int26_6(int16(u16(f.head, 36)))
f.bounds.Min.Y = fixed.Int26_6(int16(u16(f.head, 38)))
f.bounds.Max.X = fixed.Int26_6(int16(u16(f.head, 40)))
f.bounds.Max.Y = fixed.Int26_6(int16(u16(f.head, 42)))
switch i := u16(f.head, 50); i {
case 0:
f.locaOffsetFormat = locaOffsetFormatShort
case 1:
f.locaOffsetFormat = locaOffsetFormatLong
default:
return FormatError(fmt.Sprintf("bad indexToLocFormat: %d", i))
}
return nil
}
func (h *hinter) move(p *Point, distance fixed.Int26_6, touch bool) {
fvx := int64(h.gs.fv[0])
pvx := int64(h.gs.pv[0])
if fvx == 0x4000 && pvx == 0x4000 {
p.X += fixed.Int26_6(distance)
if touch {
p.Flags |= flagTouchedX
}
return
}
fvy := int64(h.gs.fv[1])
pvy := int64(h.gs.pv[1])
if fvy == 0x4000 && pvy == 0x4000 {
p.Y += fixed.Int26_6(distance)
if touch {
p.Flags |= flagTouchedY
}
return
}
fvDotPv := (fvx*pvx + fvy*pvy) >> 14
if fvx != 0 {
p.X += fixed.Int26_6(mulDiv(fvx, int64(distance), fvDotPv))
if touch {
p.Flags |= flagTouchedX
}
}
if fvy != 0 {
p.Y += fixed.Int26_6(mulDiv(fvy, int64(distance), fvDotPv))
if touch {
p.Flags |= flagTouchedY
}
}
}
func (h *hinter) initializeScaledCVT() {
h.scaledCVTInitialized = true
if n := len(h.font.cvt) / 2; n <= cap(h.scaledCVT) {
h.scaledCVT = h.scaledCVT[:n]
} else {
if n < 32 {
n = 32
}
h.scaledCVT = make([]fixed.Int26_6, len(h.font.cvt)/2, n)
}
for i := range h.scaledCVT {
unscaled := uint16(h.font.cvt[2*i])<<8 | uint16(h.font.cvt[2*i+1])
h.scaledCVT[i] = h.font.scale(h.scale * fixed.Int26_6(int16(unscaled)))
}
}
// rasterize returns the advance width, integer-pixel offset to render at, and
// the width and height of the given glyph at the given sub-pixel offsets.
//
// The 26.6 fixed point arguments fx and fy must be in the range [0, 1).
func (a *face) rasterize(index Index, fx, fy fixed.Int26_6) (v glyphCacheVal, ok bool) {
if err := a.glyphBuf.Load(a.f, a.scale, index, a.hinting); err != nil {
return glyphCacheVal{}, false
}
// Calculate the integer-pixel bounds for the glyph.
xmin := int(fx+a.glyphBuf.Bounds.Min.X) >> 6
ymin := int(fy-a.glyphBuf.Bounds.Max.Y) >> 6
xmax := int(fx+a.glyphBuf.Bounds.Max.X+0x3f) >> 6
ymax := int(fy-a.glyphBuf.Bounds.Min.Y+0x3f) >> 6
if xmin > xmax || ymin > ymax {
return glyphCacheVal{}, false
}
// A TrueType's glyph's nodes can have negative co-ordinates, but the
// rasterizer clips anything left of x=0 or above y=0. xmin and ymin are
// the pixel offsets, based on the font's FUnit metrics, that let a
// negative co-ordinate in TrueType space be non-negative in rasterizer
// space. xmin and ymin are typically <= 0.
fx -= fixed.Int26_6(xmin << 6)
fy -= fixed.Int26_6(ymin << 6)
// Rasterize the glyph's vectors.
a.r.Clear()
pixOffset := a.paintOffset * a.maxw
clear(a.masks.Pix[pixOffset : pixOffset+a.maxw*a.maxh])
e0 := 0
for _, e1 := range a.glyphBuf.Ends {
a.drawContour(a.glyphBuf.Points[e0:e1], fx, fy)
e0 = e1
}
a.r.Rasterize(a.p)
return glyphCacheVal{
a.glyphBuf.AdvanceWidth,
image.Point{xmin, ymin},
xmax - xmin,
ymax - ymin,
}, true
}
func (f *subface) GlyphBounds(r rune) (bounds fixed.Rectangle26_6, advance fixed.Int26_6, ok bool) {
r -= f.firstRune
if r < 0 || f.n <= int(r) {
return fixed.Rectangle26_6{}, 0, false
}
i := &f.fontchars[r+0]
j := &f.fontchars[r+1]
bounds = fixed.R(
int(i.left),
int(i.top)-f.ascent,
int(i.left)+int(j.x-i.x),
int(i.bottom)-f.ascent,
)
return bounds, fixed.Int26_6(i.width) << 6, true
}
// recalc recalculates scale and bounds values from the font size, screen
// resolution and font metrics, and invalidates the glyph cache.
func (c *Context) recalc() {
c.scale = fixed.Int26_6(c.fontSize * c.dpi * (64.0 / 72.0))
if c.f == nil {
c.r.SetBounds(0, 0)
} else {
// Set the rasterizer's bounds to be big enough to handle the largest glyph.
b := c.f.Bounds(c.scale)
xmin := +int(b.Min.X) >> 6
ymin := -int(b.Max.Y) >> 6
xmax := +int(b.Max.X+63) >> 6
ymax := -int(b.Min.Y-63) >> 6
c.r.SetBounds(xmax-xmin, ymax-ymin)
}
for i := range c.cache {
c.cache[i] = cacheEntry{}
}
}
// Kern returns the horizontal adjustment for the given glyph pair. A positive
// kern means to move the glyphs further apart.
func (f *Font) Kern(scale fixed.Int26_6, i0, i1 Index) fixed.Int26_6 {
if f.nKern == 0 {
return 0
}
g := uint32(i0)<<16 | uint32(i1)
lo, hi := 0, f.nKern
for lo < hi {
i := (lo + hi) / 2
ig := u32(f.kern, 18+6*i)
if ig < g {
lo = i + 1
} else if ig > g {
hi = i
} else {
return f.scale(scale * fixed.Int26_6(int16(u16(f.kern, 22+6*i))))
}
}
return 0
}
// scalingTestParse parses a line of points like
// 213 -22 -111 236 555;-22 -111 1, 178 555 1, 236 555 1, 36 -111 1
// The line will not have a trailing "\n".
func scalingTestParse(line string) (ret scalingTestData) {
next := func(s string) (string, fixed.Int26_6) {
t, i := "", strings.Index(s, " ")
if i != -1 {
s, t = s[:i], s[i+1:]
}
x, _ := strconv.Atoi(s)
return t, fixed.Int26_6(x)
}
i := strings.Index(line, ";")
prefix, line := line[:i], line[i+1:]
prefix, ret.advanceWidth = next(prefix)
prefix, ret.bounds.Min.X = next(prefix)
prefix, ret.bounds.Min.Y = next(prefix)
prefix, ret.bounds.Max.X = next(prefix)
prefix, ret.bounds.Max.Y = next(prefix)
ret.points = make([]Point, 0, 1+strings.Count(line, ","))
for len(line) > 0 {
s := line
if i := strings.Index(line, ","); i != -1 {
s, line = line[:i], line[i+1:]
for len(line) > 0 && line[0] == ' ' {
line = line[1:]
}
} else {
line = ""
}
s, x := next(s)
s, y := next(s)
s, f := next(s)
ret.points = append(ret.points, Point{X: x, Y: y, Flags: uint32(f)})
}
return ret
}
func (f *subface) Glyph(dot fixed.Point26_6, r rune) (
dr image.Rectangle, mask image.Image, maskp image.Point, advance fixed.Int26_6, ok bool) {
r -= f.firstRune
if r < 0 || f.n <= int(r) {
return image.Rectangle{}, nil, image.Point{}, 0, false
}
i := &f.fontchars[r+0]
j := &f.fontchars[r+1]
minX := int(dot.X+32)>>6 + int(i.left)
minY := int(dot.Y+32)>>6 + int(i.top) - f.ascent
dr = image.Rectangle{
Min: image.Point{
X: minX,
Y: minY,
},
Max: image.Point{
X: minX + int(j.x-i.x),
Y: minY + int(i.bottom) - int(i.top),
},
}
return dr, f.img, image.Point{int(i.x), int(i.top)}, fixed.Int26_6(i.width) << 6, true
}
func p(x, y int) fixed.Point26_6 {
return fixed.Point26_6{
X: fixed.Int26_6(x * 64),
Y: fixed.Int26_6(y * 64),
}
}
func main() {
const (
n = 17
r = 64 * 80
)
s := fixed.Int26_6(r * math.Sqrt(2) / 2)
t := fixed.Int26_6(r * math.Tan(math.Pi/8))
m := image.NewRGBA(image.Rect(0, 0, 800, 600))
draw.Draw(m, m.Bounds(), image.NewUniform(color.RGBA{63, 63, 63, 255}), image.ZP, draw.Src)
mp := raster.NewRGBAPainter(m)
mp.SetColor(image.Black)
z := raster.NewRasterizer(800, 600)
for i := 0; i < n; i++ {
cx := fixed.Int26_6(6400 + 12800*(i%4))
cy := fixed.Int26_6(640 + 8000*(i/4))
c := fixed.Point26_6{X: cx, Y: cy}
theta := math.Pi * (0.5 + 0.5*float64(i)/(n-1))
dx := fixed.Int26_6(r * math.Cos(theta))
dy := fixed.Int26_6(r * math.Sin(theta))
d := fixed.Point26_6{X: dx, Y: dy}
// Draw a quarter-circle approximated by two quadratic segments,
// with each segment spanning 45 degrees.
z.Start(c)
z.Add1(c.Add(fixed.Point26_6{X: r, Y: 0}))
z.Add2(c.Add(fixed.Point26_6{X: r, Y: t}), c.Add(fixed.Point26_6{X: s, Y: s}))
z.Add2(c.Add(fixed.Point26_6{X: t, Y: r}), c.Add(fixed.Point26_6{X: 0, Y: r}))
// Add another quadratic segment whose angle ranges between 0 and 90
// degrees. For an explanation of the magic constants 128, 150, 181 and
// 256, read the comments in the freetype/raster package.
dot := 256 * pDot(d, fixed.Point26_6{X: 0, Y: r}) / (r * r)
multiple := fixed.Int26_6(150-(150-128)*(dot-181)/(256-181)) >> 2
z.Add2(c.Add(fixed.Point26_6{X: dx, Y: r + dy}.Mul(multiple)), c.Add(d))
// Close the curve.
z.Add1(c)
}
z.Rasterize(mp)
for i := 0; i < n; i++ {
cx := fixed.Int26_6(6400 + 12800*(i%4))
cy := fixed.Int26_6(640 + 8000*(i/4))
for j := 0; j < n; j++ {
theta := math.Pi * float64(j) / (n - 1)
dx := fixed.Int26_6(r * math.Cos(theta))
dy := fixed.Int26_6(r * math.Sin(theta))
m.Set(int((cx+dx)/64), int((cy+dy)/64), color.RGBA{255, 255, 0, 255})
}
}
// Save that RGBA image to disk.
outFile, err := os.Create("out.png")
if err != nil {
log.Println(err)
os.Exit(1)
}
defer outFile.Close()
b := bufio.NewWriter(outFile)
err = png.Encode(b, m)
if err != nil {
log.Println(err)
os.Exit(1)
}
err = b.Flush()
if err != nil {
log.Println(err)
os.Exit(1)
}
fmt.Println("Wrote out.png OK.")
}
// Load loads a glyph's contours from a Font, overwriting any previously loaded
// contours for this GlyphBuf. scale is the number of 26.6 fixed point units in
// 1 em, i is the glyph index, and h is the hinting policy.
func (g *GlyphBuf) Load(f *Font, scale fixed.Int26_6, i Index, h font.Hinting) error {
g.Points = g.Points[:0]
g.Unhinted = g.Unhinted[:0]
g.InFontUnits = g.InFontUnits[:0]
g.Ends = g.Ends[:0]
g.font = f
g.hinting = h
g.scale = scale
g.pp1x = 0
g.phantomPoints = [4]Point{}
g.metricsSet = false
if h != font.HintingNone {
if err := g.hinter.init(f, scale); err != nil {
return err
}
}
if err := g.load(0, i, true); err != nil {
return err
}
// TODO: this selection of either g.pp1x or g.phantomPoints[0].X isn't ideal,
// and should be cleaned up once we have all the testScaling tests passing,
// plus additional tests for Freetype-Go's bounding boxes matching C Freetype's.
pp1x := g.pp1x
if h != font.HintingNone {
pp1x = g.phantomPoints[0].X
}
if pp1x != 0 {
for i := range g.Points {
g.Points[i].X -= pp1x
}
}
advanceWidth := g.phantomPoints[1].X - g.phantomPoints[0].X
if h != font.HintingNone {
if len(f.hdmx) >= 8 {
if n := u32(f.hdmx, 4); n > 3+uint32(i) {
for hdmx := f.hdmx[8:]; uint32(len(hdmx)) >= n; hdmx = hdmx[n:] {
if fixed.Int26_6(hdmx[0]) == scale>>6 {
advanceWidth = fixed.Int26_6(hdmx[2+i]) << 6
break
}
}
}
}
advanceWidth = (advanceWidth + 32) &^ 63
}
g.AdvanceWidth = advanceWidth
// Set g.Bounds to the 'control box', which is the bounding box of the
// Bézier curves' control points. This is easier to calculate, no smaller
// than and often equal to the tightest possible bounding box of the curves
// themselves. This approach is what C Freetype does. We can't just scale
// the nominal bounding box in the glyf data as the hinting process and
// phantom point adjustment may move points outside of that box.
if len(g.Points) == 0 {
g.Bounds = fixed.Rectangle26_6{}
} else {
p := g.Points[0]
g.Bounds.Min.X = p.X
g.Bounds.Max.X = p.X
g.Bounds.Min.Y = p.Y
g.Bounds.Max.Y = p.Y
for _, p := range g.Points[1:] {
if g.Bounds.Min.X > p.X {
g.Bounds.Min.X = p.X
} else if g.Bounds.Max.X < p.X {
g.Bounds.Max.X = p.X
}
if g.Bounds.Min.Y > p.Y {
g.Bounds.Min.Y = p.Y
} else if g.Bounds.Max.Y < p.Y {
g.Bounds.Max.Y = p.Y
}
}
// Snap the box to the grid, if hinting is on.
if h != font.HintingNone {
g.Bounds.Min.X &^= 63
g.Bounds.Min.Y &^= 63
g.Bounds.Max.X += 63
g.Bounds.Max.X &^= 63
g.Bounds.Max.Y += 63
g.Bounds.Max.Y &^= 63
}
}
return nil
}
// subPixels returns q and the bias and mask that leads to q quantized
// sub-pixel locations per full pixel.
//
// For example, q == 4 leads to a bias of 8 and a mask of 0xfffffff0, or -16,
// because we want to round fractions of fixed.Int26_6 as:
// - 0 to 7 rounds to 0.
// - 8 to 23 rounds to 16.
// - 24 to 39 rounds to 32.
// - 40 to 55 rounds to 48.
// - 56 to 63 rounds to 64.
// which means to add 8 and then bitwise-and with -16, in two's complement
// representation.
//
// When q == 1, we want bias == 32 and mask == -64.
// When q == 2, we want bias == 16 and mask == -32.
// When q == 4, we want bias == 8 and mask == -16.
// ...
// When q == 64, we want bias == 0 and mask == -1. (The no-op case).
// The pattern is clear.
func subPixels(q int) (value uint32, bias, mask fixed.Int26_6) {
return uint32(q), 32 / fixed.Int26_6(q), -64 / fixed.Int26_6(q)
}
// PointToFixed converts the given number of points (as in "a 12 point font")
// into a 26.6 fixed point number of pixels.
func (c *Context) PointToFixed(x float64) fixed.Int26_6 {
return fixed.Int26_6(x * float64(c.dpi) * (64.0 / 72.0))
}
// Pt converts from a co-ordinate pair measured in pixels to a fixed.Point26_6
// co-ordinate pair measured in fixed.Int26_6 units.
func Pt(x, y int) fixed.Point26_6 {
return fixed.Point26_6{
X: fixed.Int26_6(x << 6),
Y: fixed.Int26_6(y << 6),
}
}
// 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 106/256.
const tpo8 = 106
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))
}
// 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)}
}