freetype: implement stroke for quadratic segments.
Fix bug where the String representation of a Fix32 representing minus one quarter was "0:064" instead of "-0:064". R=r, rsc, rog, nigeltao_gnome CC=golang-dev http://codereview.appspot.com/2275043
This commit is contained in:
Nigel Tao
parent
ad78f67dc2
commit
5792b75123
|
|
@ -10,6 +10,6 @@ GOFILES=\
|
|||
geom.go\
|
||||
paint.go\
|
||||
raster.go\
|
||||
stroke.go\
|
||||
|
||||
include $(GOROOT)/src/Make.pkg
|
||||
|
||||
|
|
|
|||
|
|
@ -19,21 +19,21 @@ type Fix64 int64
|
|||
// String returns a human-readable representation of a 24.8 fixed point number.
|
||||
// For example, the number one-and-a-quarter becomes "1:064".
|
||||
func (x Fix32) String() string {
|
||||
i, f := x/256, x%256
|
||||
if f < 0 {
|
||||
f = -f
|
||||
if x < 0 {
|
||||
x = -x
|
||||
return fmt.Sprintf("-%d:%03d", int32(x/256), int32(x%256))
|
||||
}
|
||||
return fmt.Sprintf("%d:%03d", int32(i), int32(f))
|
||||
return fmt.Sprintf("%d:%03d", int32(x/256), int32(x%256))
|
||||
}
|
||||
|
||||
// String returns a human-readable representation of a 48.16 fixed point number.
|
||||
// For example, the number one-and-a-quarter becomes "1:16384".
|
||||
func (x Fix64) String() string {
|
||||
i, f := x/65536, x%65536
|
||||
if f < 0 {
|
||||
f = -f
|
||||
if x < 0 {
|
||||
x = -x
|
||||
return fmt.Sprintf("-%d:%05d", int64(x/65536), int64(x%65536))
|
||||
}
|
||||
return fmt.Sprintf("%d:%05d", int64(i), int64(f))
|
||||
return fmt.Sprintf("%d:%05d", int64(x/65536), int64(x%65536))
|
||||
}
|
||||
|
||||
// maxAbs returns the maximum of abs(a) and abs(b).
|
||||
|
|
@ -56,6 +56,11 @@ type Point struct {
|
|||
X, Y Fix32
|
||||
}
|
||||
|
||||
// String returns a human-readable representation of a Point.
|
||||
func (p Point) String() string {
|
||||
return "(" + p.X.String() + ", " + p.Y.String() + ")"
|
||||
}
|
||||
|
||||
// Add returns the vector p + q.
|
||||
func (p Point) Add(q Point) Point {
|
||||
return Point{p.X + q.X, p.Y + q.Y}
|
||||
|
|
@ -269,266 +274,47 @@ func (p *Path) AddPath(q Path) {
|
|||
copy((*p)[n:n+m], q)
|
||||
}
|
||||
|
||||
// A Capper signifies how to begin or end a stroked path.
|
||||
type Capper interface {
|
||||
// Cap adds a cap to p given a pivot point and the normal vector of a
|
||||
// terminal segment. The normal's length is half of the stroke width.
|
||||
Cap(p Adder, halfWidth Fix32, pivot, n1 Point)
|
||||
}
|
||||
|
||||
// The CapperFunc type adapts an ordinary function to be a Capper.
|
||||
type CapperFunc func(Adder, Fix32, Point, Point)
|
||||
|
||||
func (f CapperFunc) Cap(p Adder, halfWidth Fix32, pivot, n1 Point) {
|
||||
f(p, halfWidth, pivot, n1)
|
||||
}
|
||||
|
||||
// A Joiner signifies how to join interior nodes of a stroked path.
|
||||
type Joiner interface {
|
||||
// Join adds a join to the two sides of a stroked path given a pivot
|
||||
// point and the normal vectors of the trailing and leading segments.
|
||||
// Both normals have length equal to half of the stroke width.
|
||||
Join(lhs, rhs Adder, halfWidth Fix32, pivot, n0, n1 Point)
|
||||
}
|
||||
|
||||
// The JoinerFunc type adapts an ordinary function to be a Joiner.
|
||||
type JoinerFunc func(lhs, rhs Adder, halfWidth Fix32, pivot, n0, n1 Point)
|
||||
|
||||
func (f JoinerFunc) Join(lhs, rhs Adder, halfWidth Fix32, pivot, n0, n1 Point) {
|
||||
f(lhs, rhs, halfWidth, pivot, n0, n1)
|
||||
}
|
||||
|
||||
// AddStroke adds a stroked Path.
|
||||
func (p *Path) AddStroke(q Path, width Fix32, cr Capper, jr Joiner) {
|
||||
Stroke(p, q, width, cr, jr)
|
||||
}
|
||||
|
||||
// Stroke adds the stroked Path q to p. The resultant stroked path is typically
|
||||
// self-intersecting and should be rasterized with UseNonZeroWinding.
|
||||
// cr and jr may be nil, which defaults to a RoundCapper or RoundJoiner.
|
||||
func Stroke(p Adder, q Path, width Fix32, cr Capper, jr Joiner) {
|
||||
// firstPoint returns the first point in a non-empty Path.
|
||||
func (p Path) firstPoint() Point {
|
||||
return Point{p[1], p[2]}
|
||||
}
|
||||
|
||||
// lastPoint returns the last point in a non-empty Path.
|
||||
func (p Path) lastPoint() Point {
|
||||
return Point{p[len(p)-3], p[len(p)-2]}
|
||||
}
|
||||
|
||||
// addPathReversed adds q reversed to p.
|
||||
// For example, if q consists of a linear segment from A to B followed by a
|
||||
// quadratic segment from B to C to D, then the values of q looks like:
|
||||
// index: 01234567890123
|
||||
// value: 0AA01BB12CCDD2
|
||||
// So, when adding q backwards to p, we want to Add2(C, B) followed by Add1(A).
|
||||
func addPathReversed(p Adder, q Path) {
|
||||
if len(q) == 0 {
|
||||
return
|
||||
}
|
||||
if cr == nil {
|
||||
cr = RoundCapper
|
||||
}
|
||||
if jr == nil {
|
||||
jr = RoundJoiner
|
||||
}
|
||||
if q[0] != 0 {
|
||||
panic("freetype/raster: bad path")
|
||||
}
|
||||
i := 0
|
||||
for j := 4; j < len(q); {
|
||||
switch q[j] {
|
||||
case 0:
|
||||
stroke(p, q[i:j], width, cr, jr)
|
||||
i, j = j, j+4
|
||||
case 1:
|
||||
j += 4
|
||||
case 2:
|
||||
j += 6
|
||||
case 3:
|
||||
j += 8
|
||||
}
|
||||
}
|
||||
stroke(p, q[i:len(q)], width, cr, jr)
|
||||
}
|
||||
|
||||
// A RoundCapper adds round caps to a stroked path.
|
||||
var RoundCapper Capper = CapperFunc(func(p Adder, halfWidth Fix32, pivot, n1 Point) {
|
||||
// The cubic Bézier approximation to a circle involves the magic number
|
||||
// (√2 - 1) * 4/3, which is approximately 141/256.
|
||||
const k = 141
|
||||
e := n1.Rot90CCW()
|
||||
side := pivot.Add(e)
|
||||
start, end := pivot.Sub(n1), pivot.Add(n1)
|
||||
d, e := n1.Mul(k), e.Mul(k)
|
||||
p.Add3(start.Add(e), side.Sub(d), side)
|
||||
p.Add3(side.Add(d), end.Add(e), end)
|
||||
})
|
||||
|
||||
// A ButtCapper adds butt caps to a stroked path.
|
||||
var ButtCapper Capper = CapperFunc(func(p Adder, halfWidth Fix32, pivot, n1 Point) {
|
||||
p.Add1(pivot.Add(n1))
|
||||
})
|
||||
|
||||
// A SquareCapper adds square caps to a stroked path.
|
||||
var SquareCapper Capper = CapperFunc(func(p Adder, halfWidth Fix32, pivot, n1 Point) {
|
||||
e := n1.Rot90CCW()
|
||||
side := pivot.Add(e)
|
||||
p.Add1(side.Sub(n1))
|
||||
p.Add1(side.Add(n1))
|
||||
p.Add1(pivot.Add(n1))
|
||||
})
|
||||
|
||||
// A RoundJoiner adds round joins to a stroked path.
|
||||
var RoundJoiner Joiner = JoinerFunc(func(lhs, rhs Adder, haflWidth Fix32, pivot, n0, n1 Point) {
|
||||
dot := n0.Rot90CW().Dot(n1)
|
||||
if dot >= 0 {
|
||||
addArc(lhs, pivot, n0, n1)
|
||||
rhs.Add1(pivot.Sub(n1))
|
||||
} else {
|
||||
lhs.Add1(pivot.Add(n1))
|
||||
addArc(rhs, pivot, n0.Neg(), n1.Neg())
|
||||
}
|
||||
})
|
||||
|
||||
// A BevelJoiner adds bevel joins to a stroked path.
|
||||
var BevelJoiner Joiner = JoinerFunc(func(lhs, rhs Adder, haflWidth Fix32, pivot, n0, n1 Point) {
|
||||
lhs.Add1(pivot.Add(n1))
|
||||
rhs.Add1(pivot.Sub(n1))
|
||||
})
|
||||
|
||||
// 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 Point) {
|
||||
// r2 is the square of the length of n0.
|
||||
r2 := n0.Dot(n0)
|
||||
if r2 < 4096 {
|
||||
// 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 t = 106
|
||||
var s Point
|
||||
// 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 := n0.Rot45CW()
|
||||
m1 := n0.Rot90CW()
|
||||
m2 := m0.Rot90CW()
|
||||
if m1.Dot(n1) >= 0 {
|
||||
if n0.Dot(n1) >= 0 {
|
||||
if m2.Dot(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(t)), pivot.Add(m0))
|
||||
s = m0
|
||||
}
|
||||
} else {
|
||||
pm1, n0t := pivot.Add(m1), n0.Mul(t)
|
||||
p.Add2(pivot.Add(n0).Add(m1.Mul(t)), pivot.Add(m0))
|
||||
p.Add2(pm1.Add(n0t), pm1)
|
||||
if m0.Dot(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 n0.Dot(n1) >= 0 {
|
||||
if m0.Dot(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(t)), pivot.Sub(m2))
|
||||
s = m2.Neg()
|
||||
}
|
||||
} else {
|
||||
pm1, n0t := pivot.Sub(m1), n0.Mul(t)
|
||||
p.Add2(pivot.Add(n0).Sub(m1.Mul(t)), pivot.Sub(m2))
|
||||
p.Add2(pm1.Add(n0t), pm1)
|
||||
if m2.Dot(n1) <= 0 {
|
||||
// n1 is between 90 and 135 degrees counter-clockwise of n0.
|
||||
s = m1.Neg()
|
||||
} else {
|
||||
// n1 is between 135 and 180 degrees counter-clockwise of n0.
|
||||
p.Add2(pm1.Sub(n0t), pivot.Sub(m0))
|
||||
s = m0.Neg()
|
||||
}
|
||||
}
|
||||
}
|
||||
// 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 * s.Dot(n1) / r2
|
||||
multiple := Fix32(150 - 22*(d-181)/(256-181))
|
||||
p.Add2(pivot.Add(s.Add(n1).Mul(multiple)), pivot.Add(n1))
|
||||
}
|
||||
|
||||
// stroke adds the stroked Path q to p, where q consists of exactly one curve.
|
||||
func stroke(p Adder, q Path, width Fix32, cr Capper, jr Joiner) {
|
||||
// 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([]Fix32, 0, len(q)))
|
||||
u := width / 2
|
||||
var start, anorm Point
|
||||
a := Point{q[1], q[2]}
|
||||
i := 4
|
||||
for i < len(q) {
|
||||
switch q[i] {
|
||||
case 1:
|
||||
b := Point{q[i+1], q[i+2]}
|
||||
bnorm := b.Sub(a).Norm(u).Rot90CCW()
|
||||
if i == 4 {
|
||||
start = a.Add(bnorm)
|
||||
p.Start(start)
|
||||
r.Start(a.Sub(bnorm))
|
||||
} else {
|
||||
jr.Join(p, &r, u, a, anorm, bnorm)
|
||||
}
|
||||
p.Add1(b.Add(bnorm))
|
||||
r.Add1(b.Sub(bnorm))
|
||||
a, anorm = b, bnorm
|
||||
i += 4
|
||||
case 2:
|
||||
panic("freetype/raster: stroke unimplemented for quadratic segments")
|
||||
case 3:
|
||||
panic("freetype/raster: stroke unimplemented for cubic segments")
|
||||
default:
|
||||
panic("freetype/raster: bad path")
|
||||
}
|
||||
}
|
||||
i = len(r) - 1
|
||||
cr.Cap(p, u, Point{q[len(q)-3], q[len(q)-2]}, anorm.Neg())
|
||||
// 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:
|
||||
i := len(q) - 1
|
||||
for {
|
||||
switch r[i] {
|
||||
switch q[i] {
|
||||
case 0:
|
||||
break loop
|
||||
return
|
||||
case 1:
|
||||
i -= 4
|
||||
p.Add1(Point{r[i-2], r[i-1]})
|
||||
p.Add1(Point{q[i-2], q[i-1]})
|
||||
case 2:
|
||||
i -= 6
|
||||
p.Add2(Point{r[i+2], r[i+3]}, Point{r[i-2], r[i-1]})
|
||||
p.Add2(Point{q[i+2], q[i+3]}, Point{q[i-2], q[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]})
|
||||
p.Add3(Point{q[i+4], q[i+5]}, Point{q[i+2], q[i+3]}, Point{q[i-2], q[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.
|
||||
pivot := Point{q[1], q[2]}
|
||||
cr.Cap(p, u, pivot, start.Sub(pivot))
|
||||
}
|
||||
|
|
|
|||
466
freetype/raster/stroke.go
Normal file
466
freetype/raster/stroke.go
Normal file
|
|
@ -0,0 +1,466 @@
|
|||
// 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.
|
||||
|
||||
package raster
|
||||
|
||||
// Two points are considered practically equal if the square of the distance
|
||||
// between them is less than one quarter (i.e. 16384 / 65536 in Fix64).
|
||||
const epsilon = 16384
|
||||
|
||||
// A Capper signifies how to begin or end a stroked path.
|
||||
type Capper interface {
|
||||
// Cap adds a cap to p given a pivot point and the normal vector of a
|
||||
// terminal segment. The normal's length is half of the stroke width.
|
||||
Cap(p Adder, halfWidth Fix32, pivot, n1 Point)
|
||||
}
|
||||
|
||||
// The CapperFunc type adapts an ordinary function to be a Capper.
|
||||
type CapperFunc func(Adder, Fix32, Point, Point)
|
||||
|
||||
func (f CapperFunc) Cap(p Adder, halfWidth Fix32, pivot, n1 Point) {
|
||||
f(p, halfWidth, pivot, n1)
|
||||
}
|
||||
|
||||
// A Joiner signifies how to join interior nodes of a stroked path.
|
||||
type Joiner interface {
|
||||
// Join adds a join to the two sides of a stroked path given a pivot
|
||||
// point and the normal vectors of the trailing and leading segments.
|
||||
// Both normals have length equal to half of the stroke width.
|
||||
Join(lhs, rhs Adder, halfWidth Fix32, pivot, n0, n1 Point)
|
||||
}
|
||||
|
||||
// The JoinerFunc type adapts an ordinary function to be a Joiner.
|
||||
type JoinerFunc func(lhs, rhs Adder, halfWidth Fix32, pivot, n0, n1 Point)
|
||||
|
||||
func (f JoinerFunc) Join(lhs, rhs Adder, halfWidth Fix32, pivot, n0, n1 Point) {
|
||||
f(lhs, rhs, halfWidth, pivot, n0, n1)
|
||||
}
|
||||
|
||||
// RoundCapper adds round caps to a stroked path.
|
||||
var RoundCapper Capper = CapperFunc(roundCapper)
|
||||
|
||||
func roundCapper(p Adder, halfWidth Fix32, pivot, n1 Point) {
|
||||
// The cubic Bézier approximation to a circle involves the magic number
|
||||
// (√2 - 1) * 4/3, which is approximately 141/256.
|
||||
const k = 141
|
||||
e := n1.Rot90CCW()
|
||||
side := pivot.Add(e)
|
||||
start, end := pivot.Sub(n1), pivot.Add(n1)
|
||||
d, e := n1.Mul(k), e.Mul(k)
|
||||
p.Add3(start.Add(e), side.Sub(d), side)
|
||||
p.Add3(side.Add(d), end.Add(e), end)
|
||||
}
|
||||
|
||||
// ButtCapper adds butt caps to a stroked path.
|
||||
var ButtCapper Capper = CapperFunc(buttCapper)
|
||||
|
||||
func buttCapper(p Adder, halfWidth Fix32, pivot, n1 Point) {
|
||||
p.Add1(pivot.Add(n1))
|
||||
}
|
||||
|
||||
// SquareCapper adds square caps to a stroked path.
|
||||
var SquareCapper Capper = CapperFunc(squareCapper)
|
||||
|
||||
func squareCapper(p Adder, halfWidth Fix32, pivot, n1 Point) {
|
||||
e := n1.Rot90CCW()
|
||||
side := pivot.Add(e)
|
||||
p.Add1(side.Sub(n1))
|
||||
p.Add1(side.Add(n1))
|
||||
p.Add1(pivot.Add(n1))
|
||||
}
|
||||
|
||||
// RoundJoiner adds round joins to a stroked path.
|
||||
var RoundJoiner Joiner = JoinerFunc(roundJoiner)
|
||||
|
||||
func roundJoiner(lhs, rhs Adder, haflWidth Fix32, pivot, n0, n1 Point) {
|
||||
dot := n0.Rot90CW().Dot(n1)
|
||||
if dot >= 0 {
|
||||
addArc(lhs, pivot, n0, n1)
|
||||
rhs.Add1(pivot.Sub(n1))
|
||||
} else {
|
||||
lhs.Add1(pivot.Add(n1))
|
||||
addArc(rhs, pivot, n0.Neg(), n1.Neg())
|
||||
}
|
||||
}
|
||||
|
||||
// BevelJoiner adds bevel joins to a stroked path.
|
||||
var BevelJoiner Joiner = JoinerFunc(bevelJoiner)
|
||||
|
||||
func bevelJoiner(lhs, rhs Adder, haflWidth Fix32, pivot, n0, n1 Point) {
|
||||
lhs.Add1(pivot.Add(n1))
|
||||
rhs.Add1(pivot.Sub(n1))
|
||||
}
|
||||
|
||||
// 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 Point) {
|
||||
// r2 is the square of the length of n0.
|
||||
r2 := n0.Dot(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 Point
|
||||
// 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 := n0.Rot45CW()
|
||||
m1 := n0.Rot90CW()
|
||||
m2 := m0.Rot90CW()
|
||||
if m1.Dot(n1) >= 0 {
|
||||
if n0.Dot(n1) >= 0 {
|
||||
if m2.Dot(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 m0.Dot(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 n0.Dot(n1) >= 0 {
|
||||
if m0.Dot(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 = m2.Neg()
|
||||
}
|
||||
} 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 m2.Dot(n1) <= 0 {
|
||||
// n1 is between 90 and 135 degrees counter-clockwise of n0.
|
||||
s = m1.Neg()
|
||||
} else {
|
||||
// n1 is between 135 and 180 degrees counter-clockwise of n0.
|
||||
p.Add2(pm1.Sub(n0t), pivot.Sub(m0))
|
||||
s = m0.Neg()
|
||||
}
|
||||
}
|
||||
}
|
||||
// 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 * s.Dot(n1) / r2
|
||||
multiple := Fix32(150 - 22*(d-181)/(256-181))
|
||||
p.Add2(pivot.Add(s.Add(n1).Mul(multiple)), pivot.Add(n1))
|
||||
}
|
||||
|
||||
// midpoint returns the midpoint of two Points.
|
||||
func midpoint(a, b Point) Point {
|
||||
return Point{(a.X + b.X) / 2, (a.Y + b.Y) / 2}
|
||||
}
|
||||
|
||||
// angleGreaterThan45 returns whether the angle between two vectors is more
|
||||
// than 45 degrees.
|
||||
func angleGreaterThan45(v0, v1 Point) bool {
|
||||
v := v0.Rot45CCW()
|
||||
return v.Dot(v1) < 0 || v.Rot90CW().Dot(v1) < 0
|
||||
}
|
||||
|
||||
// interpolate returns the point (1-t)*a + t*b.
|
||||
func interpolate(a, b Point, t Fix64) Point {
|
||||
s := 65536 - t
|
||||
x := s*Fix64(a.X) + t*Fix64(b.X)
|
||||
y := s*Fix64(a.Y) + t*Fix64(b.Y)
|
||||
return Point{Fix32(x >> 16), Fix32(y >> 16)}
|
||||
}
|
||||
|
||||
// curviest2 returns the value of t for which the quadratic parametric curve
|
||||
// (1-t)²*a + 2*t*(1-t).b + t²*c has maximum curvature.
|
||||
//
|
||||
// The curvature of the parametric curve f(t) = (x(t), y(t)) is
|
||||
// |x′y″-y′x″| / (x′²+y′²)^(3/2).
|
||||
//
|
||||
// Let d = b-a and e = c-2*b+a, so that f′(t) = 2*d+2*e*t and f″(t) = 2*e.
|
||||
// The curvature's numerator is (2*dx+2*ex*t)*(2*ey)-(2*dy+2*ey*t)*(2*ex),
|
||||
// which simplifies to 4*dx*ey-4*dy*ex, which is constant with respect to t.
|
||||
//
|
||||
// Thus, curvature is extreme where the denominator is extreme, i.e. where
|
||||
// (x′²+y′²) is extreme. The first order condition is that
|
||||
// 2*x′*x″+2*y′*y″ = 0, or (dx+ex*t)*ex + (dy+ey*t)*ey = 0.
|
||||
// Solving for t gives t = -(dx*ex+dy*ey) / (ex*ex+ey*ey).
|
||||
func curviest2(a, b, c Point) Fix64 {
|
||||
dx := int64(b.X - a.X)
|
||||
dy := int64(b.Y - a.Y)
|
||||
ex := int64(c.X - 2*b.X + a.X)
|
||||
ey := int64(c.Y - 2*b.Y + a.Y)
|
||||
if ex == 0 && ey == 0 {
|
||||
return 32768
|
||||
}
|
||||
return Fix64(-65536 * (dx*ex + dy*ey) / (ex*ex + ey*ey))
|
||||
}
|
||||
|
||||
// A stroker holds state for stroking a path.
|
||||
type stroker struct {
|
||||
// p is the destination that records the stroked path.
|
||||
p Adder
|
||||
// u is the half-width of the stroke.
|
||||
u Fix32
|
||||
// cr and jr specify how to end and connect path segments.
|
||||
cr Capper
|
||||
jr Joiner
|
||||
// r is the reverse path. Stroking a path involves constructing two
|
||||
// parallel paths 2*u apart. The first path is added immediately to p,
|
||||
// the second path is accumulated in r and eventually added in reverse.
|
||||
r Path
|
||||
// a is the most recent segment point. anorm is the segment normal of
|
||||
// length u at that point.
|
||||
a, anorm Point
|
||||
}
|
||||
|
||||
// addNonCurvy2 adds a quadratic segment to the stroker, where the segment
|
||||
// defined by (k.a, b, c) achieves maximum curvature at either k.a or c.
|
||||
func (k *stroker) addNonCurvy2(b, c Point) {
|
||||
// We repeatedly divide the segment at its middle until it is straight
|
||||
// enough to approximate the stroke by just translating the control points.
|
||||
// ds and ps are stacks of depths and points. t is the top of the stack.
|
||||
const maxDepth = 5
|
||||
var (
|
||||
ds [maxDepth + 1]int
|
||||
ps [2*maxDepth + 3]Point
|
||||
t int
|
||||
)
|
||||
// Initially the ps stack has one quadratic segment of depth zero.
|
||||
ds[0] = 0
|
||||
ps[2] = k.a
|
||||
ps[1] = b
|
||||
ps[0] = c
|
||||
anorm := k.anorm
|
||||
var cnorm Point
|
||||
|
||||
for {
|
||||
depth := ds[t]
|
||||
a := ps[2*t+2]
|
||||
b := ps[2*t+1]
|
||||
c := ps[2*t+0]
|
||||
ab := b.Sub(a)
|
||||
bc := c.Sub(b)
|
||||
abIsSmall := ab.Dot(ab) < Fix64(1<<16)
|
||||
bcIsSmall := bc.Dot(bc) < Fix64(1<<16)
|
||||
if abIsSmall && bcIsSmall {
|
||||
// Approximate the segment by a circular arc.
|
||||
cnorm = bc.Norm(k.u).Rot90CCW()
|
||||
mac := midpoint(a, c)
|
||||
addArc(k.p, mac, anorm, cnorm)
|
||||
addArc(&k.r, mac, anorm.Neg(), cnorm.Neg())
|
||||
} else if depth < maxDepth && angleGreaterThan45(ab, bc) {
|
||||
// Divide the segment in two and push both halves on the stack.
|
||||
mab := midpoint(a, b)
|
||||
mbc := midpoint(b, c)
|
||||
t++
|
||||
ds[t+0] = depth + 1
|
||||
ds[t-1] = depth + 1
|
||||
ps[2*t+2] = a
|
||||
ps[2*t+1] = mab
|
||||
ps[2*t+0] = midpoint(mab, mbc)
|
||||
ps[2*t-1] = mbc
|
||||
continue
|
||||
} else {
|
||||
// Translate the control points.
|
||||
bnorm := c.Sub(a).Norm(k.u).Rot90CCW()
|
||||
cnorm = bc.Norm(k.u).Rot90CCW()
|
||||
k.p.Add2(b.Add(bnorm), c.Add(cnorm))
|
||||
k.r.Add2(b.Sub(bnorm), c.Sub(cnorm))
|
||||
}
|
||||
if t == 0 {
|
||||
k.a, k.anorm = c, cnorm
|
||||
return
|
||||
}
|
||||
t--
|
||||
anorm = cnorm
|
||||
}
|
||||
panic("unreachable")
|
||||
}
|
||||
|
||||
// Add1 adds a linear segment to the stroker.
|
||||
func (k *stroker) Add1(b Point) {
|
||||
bnorm := b.Sub(k.a).Norm(k.u).Rot90CCW()
|
||||
if len(k.r) == 0 {
|
||||
k.p.Start(k.a.Add(bnorm))
|
||||
k.r.Start(k.a.Sub(bnorm))
|
||||
} else {
|
||||
k.jr.Join(k.p, &k.r, k.u, k.a, k.anorm, bnorm)
|
||||
}
|
||||
k.p.Add1(b.Add(bnorm))
|
||||
k.r.Add1(b.Sub(bnorm))
|
||||
k.a, k.anorm = b, bnorm
|
||||
}
|
||||
|
||||
// Add2 adds a quadratic segment to the stroker.
|
||||
func (k *stroker) Add2(b, c Point) {
|
||||
ab := b.Sub(k.a)
|
||||
bc := c.Sub(b)
|
||||
abnorm := ab.Norm(k.u).Rot90CCW()
|
||||
if len(k.r) == 0 {
|
||||
k.p.Start(k.a.Add(abnorm))
|
||||
k.r.Start(k.a.Sub(abnorm))
|
||||
} else {
|
||||
k.jr.Join(k.p, &k.r, k.u, k.a, k.anorm, abnorm)
|
||||
}
|
||||
|
||||
// Approximate nearly-degenerate quadratics by linear segments.
|
||||
abIsSmall := ab.Dot(ab) < epsilon
|
||||
bcIsSmall := bc.Dot(bc) < epsilon
|
||||
if abIsSmall || bcIsSmall {
|
||||
acnorm := c.Sub(k.a).Norm(k.u).Rot90CCW()
|
||||
k.p.Add1(c.Add(acnorm))
|
||||
k.r.Add1(c.Sub(acnorm))
|
||||
k.a, k.anorm = c, acnorm
|
||||
return
|
||||
}
|
||||
|
||||
// The quadratic segment (k.a, b, c) has a point of maximum curvature.
|
||||
// If this occurs at an end point, we process the segment as a whole.
|
||||
t := curviest2(k.a, b, c)
|
||||
if t <= 0 || t >= 65536 {
|
||||
k.addNonCurvy2(b, c)
|
||||
return
|
||||
}
|
||||
|
||||
// Otherwise, we perform a de Casteljau decomposition at the point of
|
||||
// maximum curvature and process the two straighter parts.
|
||||
mab := interpolate(k.a, b, t)
|
||||
mbc := interpolate(b, c, t)
|
||||
mabc := interpolate(mab, mbc, t)
|
||||
|
||||
// If the vectors ab and bc are close to being in opposite directions,
|
||||
// then the decomposition can become unstable, so we approximate the
|
||||
// quadratic segment by two linear segments joined by an arc.
|
||||
bcnorm := bc.Norm(k.u).Rot90CCW()
|
||||
if abnorm.Dot(bcnorm) < -Fix64(k.u)*Fix64(k.u)*2047/2048 {
|
||||
pArc := abnorm.Dot(bc) < 0
|
||||
|
||||
k.p.Add1(mabc.Add(abnorm))
|
||||
if pArc {
|
||||
z := abnorm.Rot90CW()
|
||||
addArc(k.p, mabc, abnorm, z)
|
||||
addArc(k.p, mabc, z, bcnorm)
|
||||
}
|
||||
k.p.Add1(mabc.Add(bcnorm))
|
||||
k.p.Add1(c.Add(bcnorm))
|
||||
|
||||
k.r.Add1(mabc.Sub(abnorm))
|
||||
if !pArc {
|
||||
z := abnorm.Rot90CW()
|
||||
addArc(&k.r, mabc, abnorm.Neg(), z)
|
||||
addArc(&k.r, mabc, z, bcnorm.Neg())
|
||||
}
|
||||
k.r.Add1(mabc.Sub(bcnorm))
|
||||
k.r.Add1(c.Sub(bcnorm))
|
||||
|
||||
k.a, k.anorm = c, bcnorm
|
||||
return
|
||||
}
|
||||
|
||||
// Process the decomposed parts.
|
||||
k.addNonCurvy2(mab, mabc)
|
||||
k.addNonCurvy2(mbc, c)
|
||||
}
|
||||
|
||||
// Add3 adds a cubic segment to the stroker.
|
||||
func (k *stroker) Add3(b, c, d Point) {
|
||||
panic("freetype/raster: stroke unimplemented for cubic segments")
|
||||
}
|
||||
|
||||
// stroke adds the stroked Path q to p, where q consists of exactly one curve.
|
||||
func (k *stroker) stroke(q Path) {
|
||||
// Stroking is implemented by deriving two paths each k.u apart from q.
|
||||
// The left-hand-side path is added immediately to k.p; the right-hand-side
|
||||
// path is accumulated in k.r. Once we've finished adding the LHS to k.p,
|
||||
// we add the RHS in reverse order.
|
||||
k.r = Path(make([]Fix32, 0, len(q)))
|
||||
k.a = Point{q[1], q[2]}
|
||||
for i := 4; i < len(q); {
|
||||
switch q[i] {
|
||||
case 1:
|
||||
k.Add1(Point{q[i+1], q[i+2]})
|
||||
i += 4
|
||||
case 2:
|
||||
k.Add2(Point{q[i+1], q[i+2]}, Point{q[i+3], q[i+4]})
|
||||
i += 6
|
||||
case 3:
|
||||
k.Add3(Point{q[i+1], q[i+2]}, Point{q[i+3], q[i+4]}, Point{q[i+5], q[i+6]})
|
||||
i += 8
|
||||
default:
|
||||
panic("freetype/raster: bad path")
|
||||
}
|
||||
}
|
||||
if len(k.r) == 0 {
|
||||
return
|
||||
}
|
||||
// TODO(nigeltao): if q is a closed curve then we should join the first and
|
||||
// last segments instead of capping them.
|
||||
k.cr.Cap(k.p, k.u, q.lastPoint(), k.anorm.Neg())
|
||||
addPathReversed(k.p, k.r)
|
||||
pivot := q.firstPoint()
|
||||
k.cr.Cap(k.p, k.u, pivot, pivot.Sub(Point{k.r[1], k.r[2]}))
|
||||
}
|
||||
|
||||
// Stroke adds q stroked with the given width to p. The result is typically
|
||||
// self-intersecting and should be rasterized with UseNonZeroWinding.
|
||||
// cr and jr may be nil, which defaults to a RoundCapper or RoundJoiner.
|
||||
func Stroke(p Adder, q Path, width Fix32, cr Capper, jr Joiner) {
|
||||
if len(q) == 0 {
|
||||
return
|
||||
}
|
||||
if cr == nil {
|
||||
cr = RoundCapper
|
||||
}
|
||||
if jr == nil {
|
||||
jr = RoundJoiner
|
||||
}
|
||||
if q[0] != 0 {
|
||||
panic("freetype/raster: bad path")
|
||||
}
|
||||
s := stroker{p: p, u: width / 2, cr: cr, jr: jr}
|
||||
i := 0
|
||||
for j := 4; j < len(q); {
|
||||
switch q[j] {
|
||||
case 0:
|
||||
s.stroke(q[i:j])
|
||||
i, j = j, j+4
|
||||
case 1:
|
||||
j += 4
|
||||
case 2:
|
||||
j += 6
|
||||
case 3:
|
||||
j += 8
|
||||
default:
|
||||
panic("freetype/raster: bad path")
|
||||
}
|
||||
}
|
||||
s.stroke(q[i:])
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user