// Copyright 2010 The Freetype-Go Authors. All rights reserved.
// Use of this source code is governed by your choice of either the
// FreeType License or the GNU General Public License version 2 (or
// any later version), both of which can be found in the LICENSE file.
// 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 (
"strconv"
)
// A cell is part of a linked list (for a given yi co-ordinate) of accumulated
// area/coverage for the pixel at (xi, yi).
type cell struct {
xi int
area, cover int
next int
}
type Rasterizer struct {
// If false, the default behavior is to use the even-odd winding fill
// rule during Rasterize.
UseNonZeroWinding bool
// An offset (in pixels) to the painted spans.
Dx, Dy int
// The width of the Rasterizer. The height is implicit in len(cellIndex).
width int
// splitScaleN is the scaling factor used to determine how many times
// to decompose a quadratic or cubic segment into a linear approximation.
splitScale2, splitScale3 int
// The current pen position.
a 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
spanBuf [64]Span
}
// findCell returns the index in r.cell for the cell corresponding to
// (r.xi, r.yi). The cell is created if necessary.
func (r *Rasterizer) findCell() int {
if r.yi < 0 || r.yi >= len(r.cellIndex) {
return -1
}
xi := r.xi
if xi < 0 {
xi = -1
} else if xi > r.width {
xi = r.width
}
i, prev := r.cellIndex[r.yi], -1
for i != -1 && r.cell[i].xi <= xi {
if r.cell[i].xi == xi {
return i
}
i, prev = r.cell[i].next, i
}
c := len(r.cell)
if c == cap(r.cell) {
buf := make([]cell, c, 4*c)
copy(buf, r.cell)
r.cell = buf[0 : c+1]
} else {
r.cell = r.cell[0 : c+1]
}
r.cell[c] = cell{xi, 0, 0, i}
if prev == -1 {
r.cellIndex[r.yi] = c
} else {
r.cell[prev].next = c
}
return c
}
// saveCell saves any accumulated r.area/r.cover for (r.xi, r.yi).
func (r *Rasterizer) saveCell() {
if r.area != 0 || r.cover != 0 {
i := r.findCell()
if i != -1 {
r.cell[i].area += r.area
r.cell[i].cover += r.cover
}
r.area = 0
r.cover = 0
}
}
// setCell sets the (xi, yi) cell that r is accumulating area/coverage for.
func (r *Rasterizer) setCell(xi, yi int) {
if r.xi != xi || r.yi != yi {
r.saveCell()
r.xi, r.yi = xi, yi
}
}
// scan accumulates area/coverage for the yi'th scanline, going from
// x0 to x1 in the horizontal direction (in 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 Fix32) {
// Break the 24.8 fixed point X co-ordinates into integral and fractional parts.
x0i := int(x0) / 256
x0f := x0 - Fix32(256*x0i)
x1i := int(x1) / 256
x1f := x1 - Fix32(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 Fix32
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
}
// Add1 adds a linear segment to the current curve.
func (r *Rasterizer) Add1(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 - Fix32(256*y0i)
y1i := int(y1) / 256
y1f := y1 - Fix32(256*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 Fix32
yiDelta int
)
if dy > 0 {
edge0, edge1, yiDelta = 0, 256, 1
} else {
edge0, edge1, yiDelta = 256, 0, -1
}
x0i, yi := int(x0)/256, y0i
x0fTimes2 := (int(x0) - (256 * 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 256
// units in 24.8 fixed point format.
var (
p, q, edge0, edge1 Fix32
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
}
// Add2 adds a quadratic segment to the current curve.
func (r *Rasterizer) Add2(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.
dev := maxAbs(r.a.X-2*b.X+c.X, r.a.Y-2*b.Y+c.Y) / Fix32(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]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]
p := pStack[2*i:]
if s > 0 {
// Split the quadratic curve p[0:3] into an equivalent set of two shorter curves:
// p[0:3] 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(Point{midx, midy})
r.Add1(p[0])
i--
}
}
}
// Add3 adds a cubic segment to the current curve.
func (r *Rasterizer) Add3(b, c, d Point) {
// 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) / Fix32(r.splitScale2)
dev3 := maxAbs(r.a.X-2*b.X+d.X, r.a.Y-2*b.Y+d.Y) / Fix32(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]Point
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[0:4] into an equivalent set of two shorter curves:
// p[0:4] 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(Point{midx, midy})
r.Add1(p[0])
i--
}
}
}
// AddPath adds the given Path.
func (r *Rasterizer) AddPath(p Path) {
for i := 0; i < len(p); {
switch p[i] {
case 0:
r.Start(Point{p[i+1], p[i+2]})
i += 4
case 1:
r.Add1(Point{p[i+1], p[i+2]})
i += 4
case 2:
r.Add2(Point{p[i+1], p[i+2]}, Point{p[i+3], p[i+4]})
i += 6
case 3:
r.Add3(Point{p[i+1], p[i+2]}, Point{p[i+3], p[i+4]}, Point{p[i+5], p[i+6]})
i += 8
default:
panic("freetype/raster: bad path")
}
}
}
// AddStroke adds a stroked Path.
func (r *Rasterizer) AddStroke(q Path, width Fix32, cr Capper, jr Joiner) {
Stroke(r, q, width, cr, jr)
}
// 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 <= X0 < X1 <= r.width) and non-zero A, except
// for the final Span, which has Y, X0, X1 and A all equal to zero.
func (r *Rasterizer) Rasterize(p Painter) {
r.saveCell()
s := 0
for yi := 0; yi < len(r.cellIndex); yi++ {
xi, cover := 0, 0
for c := r.cellIndex[yi]; c != -1; c = r.cell[c].next {
if cover != 0 && r.cell[c].xi > xi {
alpha := r.areaToAlpha(cover * 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 {
r.spanBuf[s] = Span{yi + r.Dy, xi0 + r.Dx, xi1 + r.Dx, alpha}
s++
}
}
}
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 {
r.spanBuf[s] = Span{yi + r.Dy, xi0 + r.Dx, xi1 + r.Dx, alpha}
s++
}
}
if s > len(r.spanBuf)-2 {
p.Paint(r.spanBuf[0:s], false)
s = 0
}
}
}
p.Paint(r.spanBuf[0:s], true)
}
// Clear cancels any previous calls to r.Start or r.AddXxx.
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
}
}
// SetBounds sets the maximum width and height of the rasterized image and
// calls Clear. The width and height are in pixels, not Fix32 units.
func (r *Rasterizer) SetBounds(width, height int) {
if width < 0 {
width = 0
}
if height < 0 {
height = 0
}
// Use the same ssN heuristic as the C Freetype implementation.
// The C implementation uses the values 32, 16, but those are in
// 26.6 fixed point units, and we use 24.8 fixed point everywhere.
ss2, ss3 := 128, 64
if width > 24 || height > 24 {
ss2, ss3 = 2*ss2, 2*ss3
if width > 120 || height > 120 {
ss2, ss3 = 2*ss2, 2*ss3
}
}
r.width = width
r.splitScale2 = ss2
r.splitScale3 = ss3
r.cell = r.cellBuf[0:0]
if height > len(r.cellIndexBuf) {
r.cellIndex = make([]int, height)
} else {
r.cellIndex = r.cellIndexBuf[0:height]
}
r.Clear()
}
// NewRasterizer creates a new Rasterizer with the given bounds.
func NewRasterizer(width, height int) *Rasterizer {
r := new(Rasterizer)
r.SetBounds(width, height)
return r
}