// Copyright 2016 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. //go:generate go run gen.go //go:generate asmfmt -w acc_amd64.s // asmfmt is https://github.com/klauspost/asmfmt // Package vector provides a rasterizer for 2-D vector graphics. package vector // import "golang.org/x/image/vector" // The rasterizer's design follows // https://medium.com/@raphlinus/inside-the-fastest-font-renderer-in-the-world-75ae5270c445 // // Proof of concept code is in // https://github.com/google/font-go // // See also: // http://nothings.org/gamedev/rasterize/ // http://projects.tuxee.net/cl-vectors/section-the-cl-aa-algorithm // https://people.gnome.org/~mathieu/libart/internals.html#INTERNALS-SCANLINE import ( "image" "image/color" "image/draw" "math" ) // floatingPointMathThreshold is the width or height above which the rasterizer // chooses to used floating point math instead of fixed point math. // // Both implementations of line segmentation rasterization (see raster_fixed.go // and raster_floating.go) implement the same algorithm (in ideal, infinite // precision math) but they perform differently in practice. The fixed point // math version is roughtly 1.25x faster (on GOARCH=amd64) on the benchmarks, // but at sufficiently large scales, the computations will overflow and hence // show rendering artifacts. The floating point math version has more // consistent quality over larger scales, but it is significantly slower. // // This constant determines when to use the faster implementation and when to // use the better quality implementation. // // The rationale for this particular value is that TestRasterizePolygon in // vector_test.go checks the rendering quality of polygon edges at various // angles, inscribed in a circle of diameter 512. It may be that a higher value // would still produce acceptable quality, but 512 seems to work. const floatingPointMathThreshold = 512 func lerp(t, px, py, qx, qy float32) (x, y float32) { return px + t*(qx-px), py + t*(qy-py) } func clamp(i, width int32) uint { if i < 0 { return 0 } if i < width { return uint(i) } return uint(width) } // NewRasterizer returns a new Rasterizer whose rendered mask image is bounded // by the given width and height. func NewRasterizer(w, h int) *Rasterizer { z := &Rasterizer{} z.Reset(w, h) return z } // Raster is a 2-D vector graphics rasterizer. // // The zero value is usable, in that it is a Rasterizer whose rendered mask // image has zero width and zero height. Call Reset to change its bounds. type Rasterizer struct { // bufXxx are buffers of float32 or uint32 values, holding either the // individual or cumulative area values. // // We don't actually need both values at any given time, and to conserve // memory, the integration of the individual to the cumulative could modify // the buffer in place. In other words, we could use a single buffer, say // of type []uint32, and add some math.Float32bits and math.Float32frombits // calls to satisfy the compiler's type checking. As of Go 1.7, though, // there is a performance penalty between: // bufF32[i] += x // and // bufU32[i] = math.Float32bits(x + math.Float32frombits(bufU32[i])) // // See golang.org/issue/17220 for some discussion. bufF32 []float32 bufU32 []uint32 useFloatingPointMath bool size image.Point firstX float32 firstY float32 penX float32 penY float32 // DrawOp is the operator used for the Draw method. // // The zero value is draw.Over. DrawOp draw.Op // TODO: an exported field equivalent to the mask point in the // draw.DrawMask function in the stdlib image/draw package? } // Reset resets a Rasterizer as if it was just returned by NewRasterizer. // // This includes setting z.DrawOp to draw.Over. func (z *Rasterizer) Reset(w, h int) { z.size = image.Point{w, h} z.firstX = 0 z.firstY = 0 z.penX = 0 z.penY = 0 z.DrawOp = draw.Over z.setUseFloatingPointMath(w > floatingPointMathThreshold || h > floatingPointMathThreshold) } func (z *Rasterizer) setUseFloatingPointMath(b bool) { z.useFloatingPointMath = b // Make z.bufF32 or z.bufU32 large enough to hold width * height samples. if z.useFloatingPointMath { if n := z.size.X * z.size.Y; n > cap(z.bufF32) { z.bufF32 = make([]float32, n) } else { z.bufF32 = z.bufF32[:n] for i := range z.bufF32 { z.bufF32[i] = 0 } } } else { if n := z.size.X * z.size.Y; n > cap(z.bufU32) { z.bufU32 = make([]uint32, n) } else { z.bufU32 = z.bufU32[:n] for i := range z.bufU32 { z.bufU32[i] = 0 } } } } // Size returns the width and height passed to NewRasterizer or Reset. func (z *Rasterizer) Size() image.Point { return z.size } // Bounds returns the rectangle from (0, 0) to the width and height passed to // NewRasterizer or Reset. func (z *Rasterizer) Bounds() image.Rectangle { return image.Rectangle{Max: z.size} } // Pen returns the location of the path-drawing pen: the last argument to the // most recent XxxTo call. func (z *Rasterizer) Pen() (x, y float32) { return z.penX, z.penY } // ClosePath closes the current path. func (z *Rasterizer) ClosePath() { z.LineTo(z.firstX, z.firstY) } // MoveTo starts a new path and moves the pen to (ax, ay). // // The coordinates are allowed to be out of the Rasterizer's bounds. func (z *Rasterizer) MoveTo(ax, ay float32) { z.firstX = ax z.firstY = ay z.penX = ax z.penY = ay } // LineTo adds a line segment, from the pen to (bx, by), and moves the pen to // (bx, by). // // The coordinates are allowed to be out of the Rasterizer's bounds. func (z *Rasterizer) LineTo(bx, by float32) { if z.useFloatingPointMath { z.floatingLineTo(bx, by) } else { z.fixedLineTo(bx, by) } } // QuadTo adds a quadratic Bézier segment, from the pen via (bx, by) to (cx, // cy), and moves the pen to (cx, cy). // // The coordinates are allowed to be out of the Rasterizer's bounds. func (z *Rasterizer) QuadTo(bx, by, cx, cy float32) { ax, ay := z.penX, z.penY devsq := devSquared(ax, ay, bx, by, cx, cy) if devsq >= 0.333 { const tol = 3 n := 1 + int(math.Sqrt(math.Sqrt(tol*float64(devsq)))) t, nInv := float32(0), 1/float32(n) for i := 0; i < n-1; i++ { t += nInv abx, aby := lerp(t, ax, ay, bx, by) bcx, bcy := lerp(t, bx, by, cx, cy) z.LineTo(lerp(t, abx, aby, bcx, bcy)) } } z.LineTo(cx, cy) } // CubeTo adds a cubic Bézier segment, from the pen via (bx, by) and (cx, cy) // to (dx, dy), and moves the pen to (dx, dy). // // The coordinates are allowed to be out of the Rasterizer's bounds. func (z *Rasterizer) CubeTo(bx, by, cx, cy, dx, dy float32) { ax, ay := z.penX, z.penY devsq := devSquared(ax, ay, bx, by, dx, dy) if devsqAlt := devSquared(ax, ay, cx, cy, dx, dy); devsq < devsqAlt { devsq = devsqAlt } if devsq >= 0.333 { const tol = 3 n := 1 + int(math.Sqrt(math.Sqrt(tol*float64(devsq)))) t, nInv := float32(0), 1/float32(n) for i := 0; i < n-1; i++ { t += nInv abx, aby := lerp(t, ax, ay, bx, by) bcx, bcy := lerp(t, bx, by, cx, cy) cdx, cdy := lerp(t, cx, cy, dx, dy) abcx, abcy := lerp(t, abx, aby, bcx, bcy) bcdx, bcdy := lerp(t, bcx, bcy, cdx, cdy) z.LineTo(lerp(t, abcx, abcy, bcdx, bcdy)) } } z.LineTo(dx, dy) } // devSquared returns a measure of how curvy the sequence (ax, ay) to (bx, by) // to (cx, cy) is. It determines how many line segments will approximate a // Bézier curve segment. // // http://lists.nongnu.org/archive/html/freetype-devel/2016-08/msg00080.html // gives the rationale for this evenly spaced heuristic instead of a recursive // de Casteljau approach: // // The reason for the subdivision by n is that I expect the "flatness" // computation to be semi-expensive (it's done once rather than on each // potential subdivision) and also because you'll often get fewer subdivisions. // Taking a circular arc as a simplifying assumption (ie a spherical cow), // where I get n, a recursive approach would get 2^⌈lg n⌉, which, if I haven't // made any horrible mistakes, is expected to be 33% more in the limit. func devSquared(ax, ay, bx, by, cx, cy float32) float32 { devx := ax - 2*bx + cx devy := ay - 2*by + cy return devx*devx + devy*devy } // Draw implements the Drawer interface from the standard library's image/draw // package. // // The vector paths previously added via the XxxTo calls become the mask for // drawing src onto dst. func (z *Rasterizer) Draw(dst draw.Image, r image.Rectangle, src image.Image, sp image.Point) { // TODO: adjust r and sp (and mp?) if src.Bounds() doesn't contain // r.Add(sp.Sub(r.Min)). if src, ok := src.(*image.Uniform); ok { srcR, srcG, srcB, srcA := src.RGBA() switch dst := dst.(type) { case *image.Alpha: // Fast path for glyph rendering. if srcA == 0xffff { if z.DrawOp == draw.Over { z.rasterizeDstAlphaSrcOpaqueOpOver(dst, r) } else { z.rasterizeDstAlphaSrcOpaqueOpSrc(dst, r) } return } case *image.RGBA: if z.DrawOp == draw.Over { z.rasterizeDstRGBASrcUniformOpOver(dst, r, srcR, srcG, srcB, srcA) } else { z.rasterizeDstRGBASrcUniformOpSrc(dst, r, srcR, srcG, srcB, srcA) } return } } if z.DrawOp == draw.Over { z.rasterizeOpOver(dst, r, src, sp) } else { z.rasterizeOpSrc(dst, r, src, sp) } } func (z *Rasterizer) accumulateMask() { if z.useFloatingPointMath { if n := z.size.X * z.size.Y; n > cap(z.bufU32) { z.bufU32 = make([]uint32, n) } else { z.bufU32 = z.bufU32[:n] } if haveFloatingAccumulateSIMD { floatingAccumulateMaskSIMD(z.bufU32, z.bufF32) } else { floatingAccumulateMask(z.bufU32, z.bufF32) } } else { if haveFixedAccumulateSIMD { fixedAccumulateMaskSIMD(z.bufU32) } else { fixedAccumulateMask(z.bufU32) } } } func (z *Rasterizer) rasterizeDstAlphaSrcOpaqueOpOver(dst *image.Alpha, r image.Rectangle) { // TODO: non-zero vs even-odd winding? if r == dst.Bounds() && r == z.Bounds() { // We bypass the z.accumulateMask step and convert straight from // z.bufF32 or z.bufU32 to dst.Pix. if z.useFloatingPointMath { if haveFloatingAccumulateSIMD { floatingAccumulateOpOverSIMD(dst.Pix, z.bufF32) } else { floatingAccumulateOpOver(dst.Pix, z.bufF32) } } else { if haveFixedAccumulateSIMD { fixedAccumulateOpOverSIMD(dst.Pix, z.bufU32) } else { fixedAccumulateOpOver(dst.Pix, z.bufU32) } } return } z.accumulateMask() pix := dst.Pix[dst.PixOffset(r.Min.X, r.Min.Y):] for y, y1 := 0, r.Max.Y-r.Min.Y; y < y1; y++ { for x, x1 := 0, r.Max.X-r.Min.X; x < x1; x++ { ma := z.bufU32[y*z.size.X+x] i := y*dst.Stride + x // This formula is like rasterizeOpOver's, simplified for the // concrete dst type and opaque src assumption. a := 0xffff - ma pix[i] = uint8((uint32(pix[i])*0x101*a/0xffff + ma) >> 8) } } } func (z *Rasterizer) rasterizeDstAlphaSrcOpaqueOpSrc(dst *image.Alpha, r image.Rectangle) { // TODO: non-zero vs even-odd winding? if r == dst.Bounds() && r == z.Bounds() { // We bypass the z.accumulateMask step and convert straight from // z.bufF32 or z.bufU32 to dst.Pix. if z.useFloatingPointMath { if haveFloatingAccumulateSIMD { floatingAccumulateOpSrcSIMD(dst.Pix, z.bufF32) } else { floatingAccumulateOpSrc(dst.Pix, z.bufF32) } } else { if haveFixedAccumulateSIMD { fixedAccumulateOpSrcSIMD(dst.Pix, z.bufU32) } else { fixedAccumulateOpSrc(dst.Pix, z.bufU32) } } return } z.accumulateMask() pix := dst.Pix[dst.PixOffset(r.Min.X, r.Min.Y):] for y, y1 := 0, r.Max.Y-r.Min.Y; y < y1; y++ { for x, x1 := 0, r.Max.X-r.Min.X; x < x1; x++ { ma := z.bufU32[y*z.size.X+x] // This formula is like rasterizeOpSrc's, simplified for the // concrete dst type and opaque src assumption. pix[y*dst.Stride+x] = uint8(ma >> 8) } } } func (z *Rasterizer) rasterizeDstRGBASrcUniformOpOver(dst *image.RGBA, r image.Rectangle, sr, sg, sb, sa uint32) { z.accumulateMask() pix := dst.Pix[dst.PixOffset(r.Min.X, r.Min.Y):] for y, y1 := 0, r.Max.Y-r.Min.Y; y < y1; y++ { for x, x1 := 0, r.Max.X-r.Min.X; x < x1; x++ { ma := z.bufU32[y*z.size.X+x] // This formula is like rasterizeOpOver's, simplified for the // concrete dst type and uniform src assumption. a := 0xffff - (sa * ma / 0xffff) i := y*dst.Stride + 4*x pix[i+0] = uint8(((uint32(pix[i+0])*0x101*a + sr*ma) / 0xffff) >> 8) pix[i+1] = uint8(((uint32(pix[i+1])*0x101*a + sg*ma) / 0xffff) >> 8) pix[i+2] = uint8(((uint32(pix[i+2])*0x101*a + sb*ma) / 0xffff) >> 8) pix[i+3] = uint8(((uint32(pix[i+3])*0x101*a + sa*ma) / 0xffff) >> 8) } } } func (z *Rasterizer) rasterizeDstRGBASrcUniformOpSrc(dst *image.RGBA, r image.Rectangle, sr, sg, sb, sa uint32) { z.accumulateMask() pix := dst.Pix[dst.PixOffset(r.Min.X, r.Min.Y):] for y, y1 := 0, r.Max.Y-r.Min.Y; y < y1; y++ { for x, x1 := 0, r.Max.X-r.Min.X; x < x1; x++ { ma := z.bufU32[y*z.size.X+x] // This formula is like rasterizeOpSrc's, simplified for the // concrete dst type and uniform src assumption. i := y*dst.Stride + 4*x pix[i+0] = uint8((sr * ma / 0xffff) >> 8) pix[i+1] = uint8((sg * ma / 0xffff) >> 8) pix[i+2] = uint8((sb * ma / 0xffff) >> 8) pix[i+3] = uint8((sa * ma / 0xffff) >> 8) } } } func (z *Rasterizer) rasterizeOpOver(dst draw.Image, r image.Rectangle, src image.Image, sp image.Point) { z.accumulateMask() out := color.RGBA64{} outc := color.Color(&out) for y, y1 := 0, r.Max.Y-r.Min.Y; y < y1; y++ { for x, x1 := 0, r.Max.X-r.Min.X; x < x1; x++ { sr, sg, sb, sa := src.At(sp.X+x, sp.Y+y).RGBA() ma := z.bufU32[y*z.size.X+x] // This algorithm comes from the standard library's image/draw // package. dr, dg, db, da := dst.At(r.Min.X+x, r.Min.Y+y).RGBA() a := 0xffff - (sa * ma / 0xffff) out.R = uint16((dr*a + sr*ma) / 0xffff) out.G = uint16((dg*a + sg*ma) / 0xffff) out.B = uint16((db*a + sb*ma) / 0xffff) out.A = uint16((da*a + sa*ma) / 0xffff) dst.Set(r.Min.X+x, r.Min.Y+y, outc) } } } func (z *Rasterizer) rasterizeOpSrc(dst draw.Image, r image.Rectangle, src image.Image, sp image.Point) { z.accumulateMask() out := color.RGBA64{} outc := color.Color(&out) for y, y1 := 0, r.Max.Y-r.Min.Y; y < y1; y++ { for x, x1 := 0, r.Max.X-r.Min.X; x < x1; x++ { sr, sg, sb, sa := src.At(sp.X+x, sp.Y+y).RGBA() ma := z.bufU32[y*z.size.X+x] // This algorithm comes from the standard library's image/draw // package. out.R = uint16(sr * ma / 0xffff) out.G = uint16(sg * ma / 0xffff) out.B = uint16(sb * ma / 0xffff) out.A = uint16(sa * ma / 0xffff) dst.Set(r.Min.X+x, r.Min.Y+y, outc) } } }