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