// 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)}
}
// 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
}
// GetStringBounds returns the approximate pixel bounds of the string s at x, y.
// The the left edge of the em square of the first character of s
// and the baseline intersect at 0, 0 in the returned coordinates.
// Therefore the top and left coordinates may well be negative.
func (gc *GraphicContext) GetStringBounds(s string) (left, top, right, bottom float64) {
f, err := gc.loadCurrentFont()
if err != nil {
log.Println(err)
return 0, 0, 0, 0
}
top, left, bottom, right = 10e6, 10e6, -10e6, -10e6
cursor := 0.0
prev, hasPrev := truetype.Index(0), false
for _, rune := range s {
index := f.Index(rune)
if hasPrev {
cursor += fUnitsToFloat64(f.Kern(fixed.Int26_6(gc.Current.Scale), prev, index))
}
if err := gc.glyphBuf.Load(gc.Current.Font, fixed.Int26_6(gc.Current.Scale), index, font.HintingNone); err != nil {
log.Println(err)
return 0, 0, 0, 0
}
e0 := 0
for _, e1 := range gc.glyphBuf.Ends {
ps := gc.glyphBuf.Points[e0:e1]
for _, p := range ps {
x, y := pointToF64Point(p)
top = math.Min(top, y)
bottom = math.Max(bottom, y)
left = math.Min(left, x+cursor)
right = math.Max(right, x+cursor)
}
}
cursor += fUnitsToFloat64(f.HMetric(fixed.Int26_6(gc.Current.Scale), index).AdvanceWidth)
prev, hasPrev = index, true
}
return left, top, right, bottom
}
// 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)}
}
// 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
}
// 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))
}
// 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--
}
}
}
// Extents returns the FontExtents for a font.
// TODO needs to read this https://developer.apple.com/fonts/TrueType-Reference-Manual/RM02/Chap2.html#intro
func Extents(font *truetype.Font, size float64) FontExtents {
bounds := font.Bounds(fixed.Int26_6(font.FUnitsPerEm()))
scale := size / float64(font.FUnitsPerEm())
return FontExtents{
Ascent: float64(bounds.Max.Y) * scale,
Descent: float64(bounds.Min.Y) * scale,
Height: float64(bounds.Max.Y-bounds.Min.Y) * scale,
}
}
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 (gc *GraphicContext) drawGlyph(glyph truetype.Index, dx, dy float64) error {
if err := gc.glyphBuf.Load(gc.Current.Font, fixed.Int26_6(gc.Current.Scale), glyph, font.HintingNone); err != nil {
return err
}
e0 := 0
for _, e1 := range gc.glyphBuf.Ends {
DrawContour(gc, gc.glyphBuf.Points[e0:e1], dx, dy)
e0 = e1
}
return nil
}
// CreateStringPath creates a path from the string s at x, y, and returns the string width.
// The text is placed so that the left edge of the em square of the first character of s
// and the baseline intersect at x, y. The majority of the affected pixels will be
// above and to the right of the point, but some may be below or to the left.
// For example, drawing a string that starts with a 'J' in an italic font may
// affect pixels below and left of the point.
func (gc *GraphicContext) CreateStringPath(s string, x, y float64) float64 {
f, err := gc.loadCurrentFont()
if err != nil {
log.Println(err)
return 0.0
}
startx := x
prev, hasPrev := truetype.Index(0), false
for _, rune := range s {
index := f.Index(rune)
if hasPrev {
x += fUnitsToFloat64(f.Kern(fixed.Int26_6(gc.Current.Scale), prev, index))
}
err := gc.drawGlyph(index, x, y)
if err != nil {
log.Println(err)
return startx - x
}
x += fUnitsToFloat64(f.HMetric(fixed.Int26_6(gc.Current.Scale), index).AdvanceWidth)
prev, hasPrev = index, true
}
return x - startx
}
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
}
// 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
}
// 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
}
// 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)
}
func (g *GlyphBuf) load(recursion uint32, i Index, useMyMetrics bool) (err error) {
// The recursion limit here is arbitrary, but defends against malformed glyphs.
if recursion >= 32 {
return UnsupportedError("excessive compound glyph recursion")
}
// Find the relevant slice of g.font.glyf.
var g0, g1 uint32
if g.font.locaOffsetFormat == locaOffsetFormatShort {
g0 = 2 * uint32(u16(g.font.loca, 2*int(i)))
g1 = 2 * uint32(u16(g.font.loca, 2*int(i)+2))
} else {
g0 = u32(g.font.loca, 4*int(i))
g1 = u32(g.font.loca, 4*int(i)+4)
}
// Decode the contour count and nominal bounding box, from the first
// 10 bytes of the glyf data. boundsYMin and boundsXMax, at offsets 4
// and 6, are unused.
glyf, ne, boundsXMin, boundsYMax := []byte(nil), 0, fixed.Int26_6(0), fixed.Int26_6(0)
if g0+10 <= g1 {
glyf = g.font.glyf[g0:g1]
ne = int(int16(u16(glyf, 0)))
boundsXMin = fixed.Int26_6(int16(u16(glyf, 2)))
boundsYMax = fixed.Int26_6(int16(u16(glyf, 8)))
}
// Create the phantom points.
uhm, pp1x := g.font.unscaledHMetric(i), fixed.Int26_6(0)
uvm := g.font.unscaledVMetric(i, boundsYMax)
g.phantomPoints = [4]Point{
{X: boundsXMin - uhm.LeftSideBearing},
{X: boundsXMin - uhm.LeftSideBearing + uhm.AdvanceWidth},
{X: uhm.AdvanceWidth / 2, Y: boundsYMax + uvm.TopSideBearing},
{X: uhm.AdvanceWidth / 2, Y: boundsYMax + uvm.TopSideBearing - uvm.AdvanceHeight},
}
if len(glyf) == 0 {
g.addPhantomsAndScale(len(g.Points), len(g.Points), true, true)
copy(g.phantomPoints[:], g.Points[len(g.Points)-4:])
g.Points = g.Points[:len(g.Points)-4]
return nil
}
// Load and hint the contours.
if ne < 0 {
if ne != -1 {
// http://developer.apple.com/fonts/TTRefMan/RM06/Chap6glyf.html says that
// "the values -2, -3, and so forth, are reserved for future use."
return UnsupportedError("negative number of contours")
}
pp1x = g.font.scale(g.scale * (boundsXMin - uhm.LeftSideBearing))
if err := g.loadCompound(recursion, uhm, i, glyf, useMyMetrics); err != nil {
return err
}
} else {
np0, ne0 := len(g.Points), len(g.Ends)
program := g.loadSimple(glyf, ne)
g.addPhantomsAndScale(np0, np0, true, true)
pp1x = g.Points[len(g.Points)-4].X
if g.hinting != font.HintingNone {
if len(program) != 0 {
err := g.hinter.run(
program,
g.Points[np0:],
g.Unhinted[np0:],
g.InFontUnits[np0:],
g.Ends[ne0:],
)
if err != nil {
return err
}
}
// Drop the four phantom points.
g.InFontUnits = g.InFontUnits[:len(g.InFontUnits)-4]
g.Unhinted = g.Unhinted[:len(g.Unhinted)-4]
}
if useMyMetrics {
copy(g.phantomPoints[:], g.Points[len(g.Points)-4:])
}
g.Points = g.Points[:len(g.Points)-4]
if np0 != 0 {
// The hinting program expects the []Ends values to be indexed
// relative to the inner glyph, not the outer glyph, so we delay
// adding np0 until after the hinting program (if any) has run.
for i := ne0; i < len(g.Ends); i++ {
g.Ends[i] += np0
}
}
}
if useMyMetrics && !g.metricsSet {
g.metricsSet = true
g.pp1x = pp1x
}
return nil
}
// 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)
}
// Load loads a glyph's contours from a Font, overwriting any previously loaded
// contours for this GlyphBuf. scale is the number of 26.6 fixed point units in
// 1 em, i is the glyph index, and h is the hinting policy.
func (g *GlyphBuf) Load(f *Font, scale fixed.Int26_6, i Index, h font.Hinting) error {
g.Points = g.Points[:0]
g.Unhinted = g.Unhinted[:0]
g.InFontUnits = g.InFontUnits[:0]
g.Ends = g.Ends[:0]
g.font = f
g.hinting = h
g.scale = scale
g.pp1x = 0
g.phantomPoints = [4]Point{}
g.metricsSet = false
if h != font.HintingNone {
if err := g.hinter.init(f, scale); err != nil {
return err
}
}
if err := g.load(0, i, true); err != nil {
return err
}
// TODO: this selection of either g.pp1x or g.phantomPoints[0].X isn't ideal,
// and should be cleaned up once we have all the testScaling tests passing,
// plus additional tests for Freetype-Go's bounding boxes matching C Freetype's.
pp1x := g.pp1x
if h != font.HintingNone {
pp1x = g.phantomPoints[0].X
}
if pp1x != 0 {
for i := range g.Points {
g.Points[i].X -= pp1x
}
}
advanceWidth := g.phantomPoints[1].X - g.phantomPoints[0].X
if h != font.HintingNone {
if len(f.hdmx) >= 8 {
if n := u32(f.hdmx, 4); n > 3+uint32(i) {
for hdmx := f.hdmx[8:]; uint32(len(hdmx)) >= n; hdmx = hdmx[n:] {
if fixed.Int26_6(hdmx[0]) == scale>>6 {
advanceWidth = fixed.Int26_6(hdmx[2+i]) << 6
break
}
}
}
}
advanceWidth = (advanceWidth + 32) &^ 63
}
g.AdvanceWidth = advanceWidth
// Set g.Bounds to the 'control box', which is the bounding box of the
// Bézier curves' control points. This is easier to calculate, no smaller
// than and often equal to the tightest possible bounding box of the curves
// themselves. This approach is what C Freetype does. We can't just scale
// the nominal bounding box in the glyf data as the hinting process and
// phantom point adjustment may move points outside of that box.
if len(g.Points) == 0 {
g.Bounds = fixed.Rectangle26_6{}
} else {
p := g.Points[0]
g.Bounds.Min.X = p.X
g.Bounds.Max.X = p.X
g.Bounds.Min.Y = p.Y
g.Bounds.Max.Y = p.Y
for _, p := range g.Points[1:] {
if g.Bounds.Min.X > p.X {
g.Bounds.Min.X = p.X
} else if g.Bounds.Max.X < p.X {
g.Bounds.Max.X = p.X
}
if g.Bounds.Min.Y > p.Y {
g.Bounds.Min.Y = p.Y
} else if g.Bounds.Max.Y < p.Y {
g.Bounds.Max.Y = p.Y
}
}
// Snap the box to the grid, if hinting is on.
if h != font.HintingNone {
g.Bounds.Min.X &^= 63
g.Bounds.Min.Y &^= 63
g.Bounds.Max.X += 63
g.Bounds.Max.X &^= 63
g.Bounds.Max.Y += 63
g.Bounds.Max.Y &^= 63
}
}
return nil
}
func (g *GlyphBuf) loadCompound(recursion uint32, uhm HMetric, i Index,
glyf []byte, useMyMetrics bool) error {
// Flags for decoding a compound glyph. These flags are documented at
// http://developer.apple.com/fonts/TTRefMan/RM06/Chap6glyf.html.
const (
flagArg1And2AreWords = 1 << iota
flagArgsAreXYValues
flagRoundXYToGrid
flagWeHaveAScale
flagUnused
flagMoreComponents
flagWeHaveAnXAndYScale
flagWeHaveATwoByTwo
flagWeHaveInstructions
flagUseMyMetrics
flagOverlapCompound
)
np0, ne0 := len(g.Points), len(g.Ends)
offset := loadOffset
for {
flags := u16(glyf, offset)
component := Index(u16(glyf, offset+2))
dx, dy, transform, hasTransform := fixed.Int26_6(0), fixed.Int26_6(0), [4]int16{}, false
if flags&flagArg1And2AreWords != 0 {
dx = fixed.Int26_6(int16(u16(glyf, offset+4)))
dy = fixed.Int26_6(int16(u16(glyf, offset+6)))
offset += 8
} else {
dx = fixed.Int26_6(int16(int8(glyf[offset+4])))
dy = fixed.Int26_6(int16(int8(glyf[offset+5])))
offset += 6
}
if flags&flagArgsAreXYValues == 0 {
return UnsupportedError("compound glyph transform vector")
}
if flags&(flagWeHaveAScale|flagWeHaveAnXAndYScale|flagWeHaveATwoByTwo) != 0 {
hasTransform = true
switch {
case flags&flagWeHaveAScale != 0:
transform[0] = int16(u16(glyf, offset+0))
transform[3] = transform[0]
offset += 2
case flags&flagWeHaveAnXAndYScale != 0:
transform[0] = int16(u16(glyf, offset+0))
transform[3] = int16(u16(glyf, offset+2))
offset += 4
case flags&flagWeHaveATwoByTwo != 0:
transform[0] = int16(u16(glyf, offset+0))
transform[1] = int16(u16(glyf, offset+2))
transform[2] = int16(u16(glyf, offset+4))
transform[3] = int16(u16(glyf, offset+6))
offset += 8
}
}
savedPP := g.phantomPoints
np0 := len(g.Points)
componentUMM := useMyMetrics && (flags&flagUseMyMetrics != 0)
if err := g.load(recursion+1, component, componentUMM); err != nil {
return err
}
if flags&flagUseMyMetrics == 0 {
g.phantomPoints = savedPP
}
if hasTransform {
for j := np0; j < len(g.Points); j++ {
p := &g.Points[j]
newX := 0 +
fixed.Int26_6((int64(p.X)*int64(transform[0])+1<<13)>>14) +
fixed.Int26_6((int64(p.Y)*int64(transform[2])+1<<13)>>14)
newY := 0 +
fixed.Int26_6((int64(p.X)*int64(transform[1])+1<<13)>>14) +
fixed.Int26_6((int64(p.Y)*int64(transform[3])+1<<13)>>14)
p.X, p.Y = newX, newY
}
}
dx = g.font.scale(g.scale * dx)
dy = g.font.scale(g.scale * dy)
if flags&flagRoundXYToGrid != 0 {
dx = (dx + 32) &^ 63
dy = (dy + 32) &^ 63
}
for j := np0; j < len(g.Points); j++ {
p := &g.Points[j]
p.X += dx
p.Y += dy
}
// TODO: also adjust g.InFontUnits and g.Unhinted?
if flags&flagMoreComponents == 0 {
break
}
}
instrLen := 0
if g.hinting != font.HintingNone && offset+2 <= len(glyf) {
instrLen = int(u16(glyf, offset))
offset += 2
}
g.addPhantomsAndScale(np0, len(g.Points), false, instrLen > 0)
points, ends := g.Points[np0:], g.Ends[ne0:]
g.Points = g.Points[:len(g.Points)-4]
for j := range points {
points[j].Flags &^= flagTouchedX | flagTouchedY
}
if instrLen == 0 {
if !g.metricsSet {
copy(g.phantomPoints[:], points[len(points)-4:])
}
return nil
}
// Hint the compound glyph.
program := glyf[offset : offset+instrLen]
// Temporarily adjust the ends to be relative to this compound glyph.
if np0 != 0 {
for i := range ends {
ends[i] -= np0
}
}
// Hinting instructions of a composite glyph completely refer to the
// (already) hinted subglyphs.
g.tmp = append(g.tmp[:0], points...)
if err := g.hinter.run(program, points, g.tmp, g.tmp, ends); err != nil {
return err
}
if np0 != 0 {
for i := range ends {
ends[i] += np0
}
}
if !g.metricsSet {
copy(g.phantomPoints[:], points[len(points)-4:])
}
return nil
}
func (g *GlyphBuf) loadSimple(glyf []byte, ne int) (program []byte) {
offset := loadOffset
for i := 0; i < ne; i++ {
g.Ends = append(g.Ends, 1+int(u16(glyf, offset)))
offset += 2
}
// Note the TrueType hinting instructions.
instrLen := int(u16(glyf, offset))
offset += 2
program = glyf[offset : offset+instrLen]
offset += instrLen
np0 := len(g.Points)
np1 := np0 + int(g.Ends[len(g.Ends)-1])
// Decode the flags.
for i := np0; i < np1; {
c := uint32(glyf[offset])
offset++
g.Points = append(g.Points, Point{Flags: c})
i++
if c&flagRepeat != 0 {
count := glyf[offset]
offset++
for ; count > 0; count-- {
g.Points = append(g.Points, Point{Flags: c})
i++
}
}
}
// Decode the co-ordinates.
var x int16
for i := np0; i < np1; i++ {
f := g.Points[i].Flags
if f&flagXShortVector != 0 {
dx := int16(glyf[offset])
offset++
if f&flagPositiveXShortVector == 0 {
x -= dx
} else {
x += dx
}
} else if f&flagThisXIsSame == 0 {
x += int16(u16(glyf, offset))
offset += 2
}
g.Points[i].X = fixed.Int26_6(x)
}
var y int16
for i := np0; i < np1; i++ {
f := g.Points[i].Flags
if f&flagYShortVector != 0 {
dy := int16(glyf[offset])
offset++
if f&flagPositiveYShortVector == 0 {
y -= dy
} else {
y += dy
}
} else if f&flagThisYIsSame == 0 {
y += int16(u16(glyf, offset))
offset += 2
}
g.Points[i].Y = fixed.Int26_6(y)
}
return program
}
// 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--
}
}
}
// 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))
}