// 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 haveAccumulateSIMD {
floatingAccumulateMaskSIMD(z.bufU32, z.bufF32)
} else {
floatingAccumulateMask(z.bufU32, z.bufF32)
}
} else {
if haveAccumulateSIMD {
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 haveAccumulateSIMD {
floatingAccumulateOpOverSIMD(dst.Pix, z.bufF32)
} else {
floatingAccumulateOpOver(dst.Pix, z.bufF32)
}
} else {
if haveAccumulateSIMD {
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 haveAccumulateSIMD {
floatingAccumulateOpSrcSIMD(dst.Pix, z.bufF32)
} else {
floatingAccumulateOpSrc(dst.Pix, z.bufF32)
}
} else {
if haveAccumulateSIMD {
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)
}
}
}
