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-rw-r--r--Godeps/_workspace/src/code.google.com/p/freetype-go/freetype/raster/stroke.go466
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diff --git a/Godeps/_workspace/src/code.google.com/p/freetype-go/freetype/raster/stroke.go b/Godeps/_workspace/src/code.google.com/p/freetype-go/freetype/raster/stroke.go
deleted file mode 100644
index d49b1cee9..000000000
--- a/Godeps/_workspace/src/code.google.com/p/freetype-go/freetype/raster/stroke.go
+++ /dev/null
@@ -1,466 +0,0 @@
-// 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 = make(Path, 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:])
-}
generated by cgit v1.2.3-1-g7c22 (git 2.25.1) at 2024-07-05 08:07:52 +0000