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freetype/raster: improve the stroking algorithm.

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It still isn't perfect (e.g. it doesn't join), but it's getting closer.

Also fix the bug where RotateCW and RotateCCW was mixed up, since the
Y-axis grows down in a computer graphics co-ordinate system, not up as
in classical mathematics.

R=r, rsc, rog
CC=golang-dev
http://codereview.appspot.com/1736043
This commit is contained in:
Nigel Tao 2010-06-29 10:46:59 +10:00
parent 2316e5355d
commit c95fb230fe
2 changed files with 121 additions and 33 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

146
freetype/raster/geom.go
View File

@ -10,7 +10,7 @@ import (
"math"
)
// A 24.8 fixed point number.
// A Fixed is a 24.8 fixed point number.
type Fixed int32
// String returns a human-readable representation of a 24.8 fixed point number.
@ -37,11 +37,27 @@ func maxAbs(a, b Fixed) Fixed {
return a
}
// A two-dimensional point or vector, in 24.8 fixed point format.
// A Point represents a two-dimensional point or vector, in 24.8 fixed point
// format.
type Point struct {
X, Y Fixed
}
// Add returns the vector p + q.
func (p Point) Add(q Point) Point {
return Point{p.X + q.X, p.Y + q.Y}
}
// Sub returns the vector p - q.
func (p Point) Sub(q Point) Point {
return Point{p.X - q.X, p.Y - q.Y}
}
// Mul returns the vector k * p.
func (p Point) Mul(k Fixed) Point {
return Point{p.X * k / 256, p.Y * k / 256}
}
// Len returns the length of the vector p.
func (p Point) Len() Fixed {
// TODO(nigeltao): use fixed point math.
@ -62,13 +78,15 @@ func (p Point) Norm(length Fixed) Point {
}
// RotateCW returns the vector p rotated clockwise by 90 degrees.
// Note that the Y-axis grows downwards, so {1, 0}.RotateCW is {0, 1}.
func (p Point) RotateCW() Point {
return Point{p.Y, -p.X}
return Point{-p.Y, p.X}
}
// RotateCCW returns the vector p rotated counter-clockwise by 90 degrees.
// Note that the Y-axis grows downwards, so {1, 0}.RotateCCW is {0, -1}.
func (p Point) RotateCCW() Point {
return Point{-p.Y, p.X}
return Point{p.Y, -p.X}
}
// An Adder accumulates points on a curve.
@ -97,16 +115,16 @@ func (p Path) String() string {
switch p[i] {
case 0:
s += "S0" + fmt.Sprint([]Fixed(p[i+1:i+3]))
i += 3
i += 4
case 1:
s += "A1" + fmt.Sprint([]Fixed(p[i+1:i+3]))
i += 3
i += 4
case 2:
s += "A2" + fmt.Sprint([]Fixed(p[i+1:i+5]))
i += 5
i += 6
case 3:
s += "A3" + fmt.Sprint([]Fixed(p[i+1:i+7]))
i += 7
i += 8
default:
panic("freetype/raster: bad path")
}
@ -134,36 +152,39 @@ func (p *Path) Clear() {
// Start starts a new curve at the given point.
func (p *Path) Start(a Point) {
n := len(*p)
p.grow(3)
p.grow(4)
(*p)[n] = 0
(*p)[n+1] = a.X
(*p)[n+2] = a.Y
(*p)[n+3] = 0
}
// Add1 adds a linear segment to the current curve.
func (p *Path) Add1(b Point) {
n := len(*p)
p.grow(3)
p.grow(4)
(*p)[n] = 1
(*p)[n+1] = b.X
(*p)[n+2] = b.Y
(*p)[n+3] = 1
}
// Add2 adds a quadratic segment to the current curve.
func (p *Path) Add2(b, c Point) {
n := len(*p)
p.grow(5)
p.grow(6)
(*p)[n] = 2
(*p)[n+1] = b.X
(*p)[n+2] = b.Y
(*p)[n+3] = c.X
(*p)[n+4] = c.Y
(*p)[n+5] = 2
}
// Add3 adds a cubic segment to the current curve.
func (p *Path) Add3(b, c, d Point) {
n := len(*p)
p.grow(7)
p.grow(8)
(*p)[n] = 3
(*p)[n+1] = b.X
(*p)[n+2] = b.Y
@ -171,6 +192,7 @@ func (p *Path) Add3(b, c, d Point) {
(*p)[n+4] = c.Y
(*p)[n+5] = d.X
(*p)[n+6] = d.Y
(*p)[n+7] = 3
}
// AddPath adds the Path q to p.
@ -180,6 +202,9 @@ func (p *Path) AddPath(q Path) {
copy((*p)[n:n+m], q)
}
// TODO(nigeltao): should a Cap be a func rather than an int, so that callers
// can specify custom cap styles? Similarly for Join.
// A Cap signifies how to begin or end a stroked curve.
type Cap int
@ -203,7 +228,8 @@ func (p *Path) AddStroke(q Path, width Fixed, cap Cap, join Join) {
Stroke(p, q, width, cap, join)
}
// Stroke adds the stroked Path q to p.
// Stroke adds the stroked Path q to p. The resultant stroked path is typically
// self-intersecting and should be rasterized with UseNonZeroWinding.
func Stroke(p Adder, q Path, width Fixed, cap Cap, join Join) {
if len(q) == 0 {
return
@ -212,43 +238,76 @@ func Stroke(p Adder, q Path, width Fixed, cap Cap, join Join) {
panic("freetype/raster: bad path")
}
i := 0
for j := 3; j < len(q); {
for j := 4; j < len(q); {
switch q[j] {
case 0:
stroke(p, q[i:j], width, cap, join)
i, j = j, j+3
i, j = j, j+4
case 1:
j += 3
j += 4
case 2:
j += 5
j += 6
case 3:
j += 7
j += 8
}
}
stroke(p, q[i:len(q)], width, cap, join)
}
func addCap(p Adder, cap Cap, center, end Point) {
switch cap {
case RoundCap:
// The cubic Bézier approximation to a circle involves the magic number
// (sqrt(2) - 1) * 4/3, which is approximately 141 / 256.
const k = 141
d := end.Sub(center)
e := d.RotateCCW()
side := center.Add(e)
start := center.Sub(d)
d, e = d.Mul(k), e.Mul(k)
p.Add3(start.Add(e), side.Sub(d), side)
p.Add3(side.Add(d), end.Add(e), end)
case ButtCap:
p.Add1(end)
case SquareCap:
d := end.Sub(center)
e := d.RotateCCW()
side := center.Add(e)
p.Add1(side.Sub(d))
p.Add1(side.Add(d))
p.Add1(end)
}
}
// stroke adds the stroked Path q to p, where q consists of exactly one curve.
func stroke(p Adder, q Path, width Fixed, cap Cap, join Join) {
// TODO(nigeltao): replace this placeholder stroking algorithm. It only
// handles linear segments, and it doesn't cap or join but instead only
// fattens each segment independently by half the width, and doesn't
// correct for overlaps.
// Stroking is implemented by deriving two paths each width/2 apart from q.
// The left-hand-side path is added immediately to p; the right-hand-side
// path is accumulated in r, and once we've finished adding the LHS to p
// we add the RHS in reverse order.
r := Path(make([]Fixed, 0, len(q)))
var start Point
a := Point{q[1], q[2]}
for i := 3; i < len(q); {
i := 4
for i < len(q) {
switch q[i] {
case 1:
bx, by := q[i+1], q[i+2]
delta := Point{bx - a.X, by - a.Y}
normal := delta.Norm(width / 2).RotateCCW()
start := Point{a.X + normal.X, a.Y + normal.Y}
p.Start(start)
if i == 4 {
start = Point{a.X + normal.X, a.Y + normal.Y}
p.Start(start)
r.Start(Point{a.X - normal.X, a.Y - normal.Y})
} else {
// TODO(nigeltao): handle joins.
p.Add1(Point{a.X + normal.X, a.Y + normal.Y})
r.Add1(Point{a.X - normal.X, a.Y - normal.Y})
}
p.Add1(Point{bx + normal.X, by + normal.Y})
p.Add1(Point{bx - normal.X, by - normal.Y})
p.Add1(Point{a.X - normal.X, a.Y - normal.Y})
p.Add1(start)
r.Add1(Point{bx - normal.X, by - normal.Y})
a = Point{q[i+1], q[i+2]}
i += 3
i += 4
case 2:
panic("freetype/raster: stroke unimplemented for quadratic segments")
case 3:
@ -257,4 +316,33 @@ func stroke(p Adder, q Path, width Fixed, cap Cap, join Join) {
panic("freetype/raster: bad path")
}
}
i = len(r) - 1
addCap(p, cap, Point{q[len(q)-3], q[len(q)-2]}, Point{r[i-2], r[i-1]})
// Add r reversed to p.
// For example, if r consists of a linear segment from A to B followed by a
// quadratic segment from B to C to D, then the values of r looks like:
// index: 01234567890123
// value: 0AA01BB12CCDD2
// So, when adding r backwards to p, we want to Add2(C, B) followed by Add1(A).
loop:
for {
switch r[i] {
case 0:
break loop
case 1:
i -= 4
p.Add1(Point{r[i-2], r[i-1]})
case 2:
i -= 6
p.Add2(Point{r[i+2], r[i+3]}, Point{r[i-2], r[i-1]})
case 3:
i -= 8
p.Add3(Point{r[i+4], r[i+5]}, Point{r[i+2], r[i+3]}, Point{r[i-2], r[i-1]})
default:
panic("freetype/raster: bad path")
}
}
// TODO(nigeltao): if q is a closed path then we should join the first and
// last segments instead of capping them.
addCap(p, cap, Point{q[1], q[2]}, start)
}

8
freetype/raster/raster.go
View File

@ -426,16 +426,16 @@ func (r *Rasterizer) AddPath(p Path) {
switch p[i] {
case 0:
r.Start(Point{p[i+1], p[i+2]})
i += 3
i += 4
case 1:
r.Add1(Point{p[i+1], p[i+2]})
i += 3
i += 4
case 2:
r.Add2(Point{p[i+1], p[i+2]}, Point{p[i+3], p[i+4]})
i += 5
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 += 7
i += 8
default:
panic("freetype/raster: bad path")
}