From 84d2482ddbff9564c9ad75b2d30af66e3ddfd44d Mon Sep 17 00:00:00 2001 From: Christopher Speller Date: Thu, 12 May 2016 15:08:58 -0400 Subject: Updating go depencancies. Switching to go1.6 vendoring (#2949) --- vendor/github.com/golang/freetype/raster/stroke.go | 483 +++++++++++++++++++++ 1 file changed, 483 insertions(+) create mode 100644 vendor/github.com/golang/freetype/raster/stroke.go (limited to 'vendor/github.com/golang/freetype/raster/stroke.go') diff --git a/vendor/github.com/golang/freetype/raster/stroke.go b/vendor/github.com/golang/freetype/raster/stroke.go new file mode 100644 index 000000000..bcc66b268 --- /dev/null +++ b/vendor/github.com/golang/freetype/raster/stroke.go @@ -0,0 +1,483 @@ +// 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 + +import ( + "golang.org/x/image/math/fixed" +) + +// Two points are considered practically equal if the square of the distance +// between them is less than one quarter (i.e. 1024 / 4096). +const epsilon = fixed.Int52_12(1024) + +// 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 fixed.Int26_6, pivot, n1 fixed.Point26_6) +} + +// The CapperFunc type adapts an ordinary function to be a Capper. +type CapperFunc func(Adder, fixed.Int26_6, fixed.Point26_6, fixed.Point26_6) + +func (f CapperFunc) Cap(p Adder, halfWidth fixed.Int26_6, pivot, n1 fixed.Point26_6) { + 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 fixed.Int26_6, pivot, n0, n1 fixed.Point26_6) +} + +// The JoinerFunc type adapts an ordinary function to be a Joiner. +type JoinerFunc func(lhs, rhs Adder, halfWidth fixed.Int26_6, pivot, n0, n1 fixed.Point26_6) + +func (f JoinerFunc) Join(lhs, rhs Adder, halfWidth fixed.Int26_6, pivot, n0, n1 fixed.Point26_6) { + 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 fixed.Int26_6, pivot, n1 fixed.Point26_6) { + // The cubic Bézier approximation to a circle involves the magic number + // (√2 - 1) * 4/3, which is approximately 35/64. + const k = 35 + e := pRot90CCW(n1) + 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 fixed.Int26_6, pivot, n1 fixed.Point26_6) { + p.Add1(pivot.Add(n1)) +} + +// SquareCapper adds square caps to a stroked path. +var SquareCapper Capper = CapperFunc(squareCapper) + +func squareCapper(p Adder, halfWidth fixed.Int26_6, pivot, n1 fixed.Point26_6) { + e := pRot90CCW(n1) + 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 fixed.Int26_6, pivot, n0, n1 fixed.Point26_6) { + dot := pDot(pRot90CW(n0), n1) + if dot >= 0 { + addArc(lhs, pivot, n0, n1) + rhs.Add1(pivot.Sub(n1)) + } else { + lhs.Add1(pivot.Add(n1)) + addArc(rhs, pivot, pNeg(n0), pNeg(n1)) + } +} + +// BevelJoiner adds bevel joins to a stroked path. +var BevelJoiner Joiner = JoinerFunc(bevelJoiner) + +func bevelJoiner(lhs, rhs Adder, haflWidth fixed.Int26_6, pivot, n0, n1 fixed.Point26_6) { + 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 fixed.Point26_6) { + // r2 is the square of the length of n0. + r2 := pDot(n0, 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 27/64. + const tpo8 = 27 + var s fixed.Point26_6 + // 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 := pRot45CW(n0) + m1 := pRot90CW(n0) + m2 := pRot90CW(m0) + if pDot(m1, n1) >= 0 { + if pDot(n0, n1) >= 0 { + if pDot(m2, 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 pDot(m0, 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 pDot(n0, n1) >= 0 { + if pDot(m0, 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 = pNeg(m2) + } + } 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 pDot(m2, n1) <= 0 { + // n1 is between 90 and 135 degrees counter-clockwise of n0. + s = pNeg(m1) + } else { + // n1 is between 135 and 180 degrees counter-clockwise of n0. + p.Add2(pm1.Sub(n0t), pivot.Sub(m0)) + s = pNeg(m0) + } + } + } + // 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 * pDot(s, n1) / r2 + multiple := fixed.Int26_6(150-(150-128)*(d-181)/(256-181)) >> 2 + p.Add2(pivot.Add(s.Add(n1).Mul(multiple)), pivot.Add(n1)) +} + +// midpoint returns the midpoint of two Points. +func midpoint(a, b fixed.Point26_6) fixed.Point26_6 { + return fixed.Point26_6{(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 fixed.Point26_6) bool { + v := pRot45CCW(v0) + return pDot(v, v1) < 0 || pDot(pRot90CW(v), v1) < 0 +} + +// interpolate returns the point (1-t)*a + t*b. +func interpolate(a, b fixed.Point26_6, t fixed.Int52_12) fixed.Point26_6 { + s := 1<<12 - t + x := s*fixed.Int52_12(a.X) + t*fixed.Int52_12(b.X) + y := s*fixed.Int52_12(a.Y) + t*fixed.Int52_12(b.Y) + return fixed.Point26_6{fixed.Int26_6(x >> 12), fixed.Int26_6(y >> 12)} +} + +// 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 fixed.Point26_6) fixed.Int52_12 { + 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 2048 + } + return fixed.Int52_12(-4096 * (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 fixed.Int26_6 + // 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 fixed.Point26_6 +} + +// 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 fixed.Point26_6) { + // 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]fixed.Point26_6 + 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 fixed.Point26_6 + + 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 := pDot(ab, ab) < fixed.Int52_12(1<<12) + bcIsSmall := pDot(bc, bc) < fixed.Int52_12(1<<12) + if abIsSmall && bcIsSmall { + // Approximate the segment by a circular arc. + cnorm = pRot90CCW(pNorm(bc, k.u)) + mac := midpoint(a, c) + addArc(k.p, mac, anorm, cnorm) + addArc(&k.r, mac, pNeg(anorm), pNeg(cnorm)) + } 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 := pRot90CCW(pNorm(c.Sub(a), k.u)) + cnorm = pRot90CCW(pNorm(bc, k.u)) + 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 fixed.Point26_6) { + bnorm := pRot90CCW(pNorm(b.Sub(k.a), k.u)) + 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 fixed.Point26_6) { + ab := b.Sub(k.a) + bc := c.Sub(b) + abnorm := pRot90CCW(pNorm(ab, k.u)) + 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 := pDot(ab, ab) < epsilon + bcIsSmall := pDot(bc, bc) < epsilon + if abIsSmall || bcIsSmall { + acnorm := pRot90CCW(pNorm(c.Sub(k.a), k.u)) + 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 || 4096 <= t { + 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 := pRot90CCW(pNorm(bc, k.u)) + if pDot(abnorm, bcnorm) < -fixed.Int52_12(k.u)*fixed.Int52_12(k.u)*2047/2048 { + pArc := pDot(abnorm, bc) < 0 + + k.p.Add1(mabc.Add(abnorm)) + if pArc { + z := pRot90CW(abnorm) + 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 := pRot90CW(abnorm) + addArc(&k.r, mabc, pNeg(abnorm), z) + addArc(&k.r, mabc, z, pNeg(bcnorm)) + } + 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 fixed.Point26_6) { + 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 = fixed.Point26_6{q[1], q[2]} + for i := 4; i < len(q); { + switch q[i] { + case 1: + k.Add1( + fixed.Point26_6{q[i+1], q[i+2]}, + ) + i += 4 + case 2: + k.Add2( + fixed.Point26_6{q[i+1], q[i+2]}, + fixed.Point26_6{q[i+3], q[i+4]}, + ) + i += 6 + case 3: + k.Add3( + fixed.Point26_6{q[i+1], q[i+2]}, + fixed.Point26_6{q[i+3], q[i+4]}, + fixed.Point26_6{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(), pNeg(k.anorm)) + addPathReversed(k.p, k.r) + pivot := q.firstPoint() + k.cr.Cap(k.p, k.u, pivot, pivot.Sub(fixed.Point26_6{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 fixed.Int26_6, 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:]) +} -- cgit v1.2.3-1-g7c22