gio/gpu/gpu.go

// SPDX-License-Identifier: Unlicense OR MIT

/*
Package gpu implements the rendering of Gio drawing operations. It
is used by package app and package app/headless and is otherwise not
useful except for integrating with external window implementations.
*/
package gpu

import (
	"encoding/binary"
	"errors"
	"fmt"
	"image"
	"image/color"
	"math"
	"os"
	"reflect"
	"time"
	"unsafe"

	"gioui.org/f32"
	"gioui.org/gpu/internal/driver"
	"gioui.org/internal/byteslice"
	"gioui.org/internal/f32color"
	"gioui.org/internal/opconst"
	"gioui.org/internal/ops"
	"gioui.org/internal/scene"
	"gioui.org/internal/stroke"
	"gioui.org/layout"
	"gioui.org/op"
	"gioui.org/op/clip"

	// Register backends.
	_ "gioui.org/gpu/internal/d3d11"
	_ "gioui.org/gpu/internal/opengl"
)

type GPU interface {
	// Release non-Go resources. The GPU is no longer valid after Release.
	Release()
	// Clear sets the clear color for the next Frame.
	Clear(color color.NRGBA)
	// Collect the graphics operations from frame, given the viewport.
	Collect(viewport image.Point, frame *op.Ops)
	// Frame clears the color buffer and draws the collected operations.
	Frame() error
	// Profile returns the last available profiling information. Profiling
	// information is requested when Collect sees a ProfileOp, and the result
	// is available through Profile at some later time.
	Profile() string
}

type gpu struct {
	cache *resourceCache

	profile                                           string
	timers                                            *timers
	frameStart                                        time.Time
	zopsTimer, stencilTimer, coverTimer, cleanupTimer *timer
	drawOps                                           drawOps
	ctx                                               driver.Device
	renderer                                          *renderer
}

type renderer struct {
	ctx           driver.Device
	blitter       *blitter
	pather        *pather
	packer        packer
	intersections packer
}

type drawOps struct {
	profile    bool
	reader     ops.Reader
	states     []drawState
	cache      *resourceCache
	vertCache  []byte
	viewport   image.Point
	clear      bool
	clearColor f32color.RGBA
	// allImageOps is the combined list of imageOps and
	// zimageOps, in drawing order.
	allImageOps []imageOp
	imageOps    []imageOp
	// zimageOps are the rectangle clipped opaque images
	// that can use fast front-to-back rendering with z-test
	// and no blending.
	zimageOps   []imageOp
	pathOps     []*pathOp
	pathOpCache []pathOp
	qs          quadSplitter
	pathCache   *opCache
	// hack for the compute renderer to access
	// converted path data.
	compute bool
}

type drawState struct {
	clip  f32.Rectangle
	t     f32.Affine2D
	cpath *pathOp
	rect  bool

	matType materialType
	// Current paint.ImageOp
	image imageOpData
	// Current paint.ColorOp, if any.
	color color.NRGBA

	// Current paint.LinearGradientOp.
	stop1  f32.Point
	stop2  f32.Point
	color1 color.NRGBA
	color2 color.NRGBA
}

type pathOp struct {
	off f32.Point
	// clip is the union of all
	// later clip rectangles.
	clip      image.Rectangle
	bounds    f32.Rectangle
	pathKey   ops.Key
	path      bool
	pathVerts []byte
	parent    *pathOp
	place     placement

	// For compute
	trans  f32.Affine2D
	stroke clip.StrokeStyle
	dashes stroke.DashOp
}

type imageOp struct {
	z        float32
	path     *pathOp
	clip     image.Rectangle
	material material
	clipType clipType
	place    placement
}

func decodeDashOp(data []byte) stroke.DashOp {
	_ = data[5]
	if opconst.OpType(data[0]) != opconst.TypeDash {
		panic("invalid op")
	}
	bo := binary.LittleEndian
	return stroke.DashOp{
		Phase:  math.Float32frombits(bo.Uint32(data[1:])),
		Dashes: make([]float32, data[5]),
	}
}

func decodeStrokeOp(data []byte) clip.StrokeStyle {
	_ = data[10]
	if opconst.OpType(data[0]) != opconst.TypeStroke {
		panic("invalid op")
	}
	bo := binary.LittleEndian
	return clip.StrokeStyle{
		Width: math.Float32frombits(bo.Uint32(data[1:])),
		Miter: math.Float32frombits(bo.Uint32(data[5:])),
		Cap:   clip.StrokeCap(data[9]),
		Join:  clip.StrokeJoin(data[10]),
	}
}

type quadsOp struct {
	key ops.Key
	aux []byte
}

type material struct {
	material materialType
	opaque   bool
	// For materialTypeColor.
	color f32color.RGBA
	// For materialTypeLinearGradient.
	color1 f32color.RGBA
	color2 f32color.RGBA
	// For materialTypeTexture.
	data    imageOpData
	uvTrans f32.Affine2D

	// For the compute backend.
	trans f32.Affine2D
}

// clipOp is the shadow of clip.Op.
type clipOp struct {
	// TODO: Use image.Rectangle?
	bounds  f32.Rectangle
	outline bool
}

// imageOpData is the shadow of paint.ImageOp.
type imageOpData struct {
	src    *image.RGBA
	handle interface{}
}

type linearGradientOpData struct {
	stop1  f32.Point
	color1 color.NRGBA
	stop2  f32.Point
	color2 color.NRGBA
}

func (op *clipOp) decode(data []byte) {
	if opconst.OpType(data[0]) != opconst.TypeClip {
		panic("invalid op")
	}
	bo := binary.LittleEndian
	r := image.Rectangle{
		Min: image.Point{
			X: int(int32(bo.Uint32(data[1:]))),
			Y: int(int32(bo.Uint32(data[5:]))),
		},
		Max: image.Point{
			X: int(int32(bo.Uint32(data[9:]))),
			Y: int(int32(bo.Uint32(data[13:]))),
		},
	}
	*op = clipOp{
		bounds:  layout.FRect(r),
		outline: data[17] == 1,
	}
}

func decodeImageOp(data []byte, refs []interface{}) imageOpData {
	if opconst.OpType(data[0]) != opconst.TypeImage {
		panic("invalid op")
	}
	handle := refs[1]
	if handle == nil {
		return imageOpData{}
	}
	return imageOpData{
		src:    refs[0].(*image.RGBA),
		handle: handle,
	}
}

func decodeColorOp(data []byte) color.NRGBA {
	if opconst.OpType(data[0]) != opconst.TypeColor {
		panic("invalid op")
	}
	return color.NRGBA{
		R: data[1],
		G: data[2],
		B: data[3],
		A: data[4],
	}
}

func decodeLinearGradientOp(data []byte) linearGradientOpData {
	if opconst.OpType(data[0]) != opconst.TypeLinearGradient {
		panic("invalid op")
	}
	bo := binary.LittleEndian
	return linearGradientOpData{
		stop1: f32.Point{
			X: math.Float32frombits(bo.Uint32(data[1:])),
			Y: math.Float32frombits(bo.Uint32(data[5:])),
		},
		stop2: f32.Point{
			X: math.Float32frombits(bo.Uint32(data[9:])),
			Y: math.Float32frombits(bo.Uint32(data[13:])),
		},
		color1: color.NRGBA{
			R: data[17+0],
			G: data[17+1],
			B: data[17+2],
			A: data[17+3],
		},
		color2: color.NRGBA{
			R: data[21+0],
			G: data[21+1],
			B: data[21+2],
			A: data[21+3],
		},
	}
}

type clipType uint8

type resource interface {
	release()
}

type texture struct {
	src *image.RGBA
	tex driver.Texture
}

type blitter struct {
	ctx                    driver.Device
	viewport               image.Point
	prog                   [3]*program
	layout                 driver.InputLayout
	colUniforms            *blitColUniforms
	texUniforms            *blitTexUniforms
	linearGradientUniforms *blitLinearGradientUniforms
	quadVerts              driver.Buffer
}

type blitColUniforms struct {
	vert struct {
		blitUniforms
		_ [12]byte // Padding to a multiple of 16.
	}
	frag struct {
		colorUniforms
	}
}

type blitTexUniforms struct {
	vert struct {
		blitUniforms
		_ [12]byte // Padding to a multiple of 16.
	}
}

type blitLinearGradientUniforms struct {
	vert struct {
		blitUniforms
		_ [12]byte // Padding to a multiple of 16.
	}
	frag struct {
		gradientUniforms
	}
}

type uniformBuffer struct {
	buf driver.Buffer
	ptr []byte
}

type program struct {
	prog         driver.Program
	vertUniforms *uniformBuffer
	fragUniforms *uniformBuffer
}

type blitUniforms struct {
	transform     [4]float32
	uvTransformR1 [4]float32
	uvTransformR2 [4]float32
	z             float32
}

type colorUniforms struct {
	color f32color.RGBA
}

type gradientUniforms struct {
	color1 f32color.RGBA
	color2 f32color.RGBA
}

type materialType uint8

const (
	clipTypeNone clipType = iota
	clipTypePath
	clipTypeIntersection
)

const (
	materialColor materialType = iota
	materialLinearGradient
	materialTexture
)

func New(api API) (GPU, error) {
	d, err := driver.NewDevice(api)
	if err != nil {
		return nil, err
	}
	forceCompute := os.Getenv("GIORENDERER") == "forcecompute"
	feats := d.Caps().Features
	switch {
	case !forceCompute && feats.Has(driver.FeatureFloatRenderTargets):
		return newGPU(d)
	case feats.Has(driver.FeatureCompute):
		return newCompute(d)
	default:
		return nil, errors.New("gpu: no support for float render targets nor compute")
	}
}

func newGPU(ctx driver.Device) (*gpu, error) {
	g := &gpu{
		cache: newResourceCache(),
	}
	g.drawOps.pathCache = newOpCache()
	if err := g.init(ctx); err != nil {
		return nil, err
	}
	return g, nil
}

func (g *gpu) init(ctx driver.Device) error {
	g.ctx = ctx
	g.renderer = newRenderer(ctx)
	return nil
}

func (g *gpu) Clear(col color.NRGBA) {
	g.drawOps.clear = true
	g.drawOps.clearColor = f32color.LinearFromSRGB(col)
}

func (g *gpu) Release() {
	g.renderer.release()
	g.drawOps.pathCache.release()
	g.cache.release()
	if g.timers != nil {
		g.timers.release()
	}
	g.ctx.Release()
}

func (g *gpu) Collect(viewport image.Point, frameOps *op.Ops) {
	g.renderer.blitter.viewport = viewport
	g.renderer.pather.viewport = viewport
	g.drawOps.reset(g.cache, viewport)
	g.drawOps.collect(g.ctx, g.cache, frameOps, viewport)
	g.frameStart = time.Now()
	if g.drawOps.profile && g.timers == nil && g.ctx.Caps().Features.Has(driver.FeatureTimers) {
		g.timers = newTimers(g.ctx)
		g.zopsTimer = g.timers.newTimer()
		g.stencilTimer = g.timers.newTimer()
		g.coverTimer = g.timers.newTimer()
		g.cleanupTimer = g.timers.newTimer()
	}
}

func (g *gpu) Frame() error {
	defFBO := g.ctx.BeginFrame()
	defer g.ctx.EndFrame()
	viewport := g.renderer.blitter.viewport
	for _, img := range g.drawOps.imageOps {
		expandPathOp(img.path, img.clip)
	}
	if g.drawOps.profile {
		g.zopsTimer.begin()
	}
	g.ctx.BindFramebuffer(defFBO)
	g.ctx.DepthFunc(driver.DepthFuncGreater)
	// Note that Clear must be before ClearDepth if nothing else is rendered
	// (len(zimageOps) == 0). If not, the Fairphone 2 will corrupt the depth buffer.
	if g.drawOps.clear {
		g.drawOps.clear = false
		g.ctx.Clear(g.drawOps.clearColor.Float32())
	}
	g.ctx.ClearDepth(0.0)
	g.ctx.Viewport(0, 0, viewport.X, viewport.Y)
	g.renderer.drawZOps(g.cache, g.drawOps.zimageOps)
	g.zopsTimer.end()
	g.stencilTimer.begin()
	g.ctx.SetBlend(true)
	g.renderer.packStencils(&g.drawOps.pathOps)
	g.renderer.stencilClips(g.drawOps.pathCache, g.drawOps.pathOps)
	g.renderer.packIntersections(g.drawOps.imageOps)
	g.renderer.intersect(g.drawOps.imageOps)
	g.stencilTimer.end()
	g.coverTimer.begin()
	g.ctx.BindFramebuffer(defFBO)
	g.ctx.Viewport(0, 0, viewport.X, viewport.Y)
	g.renderer.drawOps(g.cache, g.drawOps.imageOps)
	g.ctx.SetBlend(false)
	g.renderer.pather.stenciler.invalidateFBO()
	g.coverTimer.end()
	g.ctx.BindFramebuffer(defFBO)
	g.cleanupTimer.begin()
	g.cache.frame()
	g.drawOps.pathCache.frame()
	g.cleanupTimer.end()
	if g.drawOps.profile && g.timers.ready() {
		zt, st, covt, cleant := g.zopsTimer.Elapsed, g.stencilTimer.Elapsed, g.coverTimer.Elapsed, g.cleanupTimer.Elapsed
		ft := zt + st + covt + cleant
		q := 100 * time.Microsecond
		zt, st, covt = zt.Round(q), st.Round(q), covt.Round(q)
		frameDur := time.Since(g.frameStart).Round(q)
		ft = ft.Round(q)
		g.profile = fmt.Sprintf("draw:%7s gpu:%7s zt:%7s st:%7s cov:%7s", frameDur, ft, zt, st, covt)
	}
	return nil
}

func (g *gpu) Profile() string {
	return g.profile
}

func (r *renderer) texHandle(cache *resourceCache, data imageOpData) driver.Texture {
	var tex *texture
	t, exists := cache.get(data.handle)
	if !exists {
		t = &texture{
			src: data.src,
		}
		cache.put(data.handle, t)
	}
	tex = t.(*texture)
	if tex.tex != nil {
		return tex.tex
	}
	handle, err := r.ctx.NewTexture(driver.TextureFormatSRGB, data.src.Bounds().Dx(), data.src.Bounds().Dy(), driver.FilterLinear, driver.FilterLinear, driver.BufferBindingTexture)
	if err != nil {
		panic(err)
	}
	driver.UploadImage(handle, image.Pt(0, 0), data.src)
	tex.tex = handle
	return tex.tex
}

func (t *texture) release() {
	if t.tex != nil {
		t.tex.Release()
	}
}

func newRenderer(ctx driver.Device) *renderer {
	r := &renderer{
		ctx:     ctx,
		blitter: newBlitter(ctx),
		pather:  newPather(ctx),
	}

	maxDim := ctx.Caps().MaxTextureSize
	// Large atlas textures cause artifacts due to precision loss in
	// shaders.
	if cap := 8192; maxDim > cap {
		maxDim = cap
	}

	r.packer.maxDim = maxDim
	r.intersections.maxDim = maxDim
	return r
}

func (r *renderer) release() {
	r.pather.release()
	r.blitter.release()
}

func newBlitter(ctx driver.Device) *blitter {
	quadVerts, err := ctx.NewImmutableBuffer(driver.BufferBindingVertices,
		byteslice.Slice([]float32{
			-1, +1, 0, 0,
			+1, +1, 1, 0,
			-1, -1, 0, 1,
			+1, -1, 1, 1,
		}),
	)
	if err != nil {
		panic(err)
	}
	b := &blitter{
		ctx:       ctx,
		quadVerts: quadVerts,
	}
	b.colUniforms = new(blitColUniforms)
	b.texUniforms = new(blitTexUniforms)
	b.linearGradientUniforms = new(blitLinearGradientUniforms)
	prog, layout, err := createColorPrograms(ctx, shader_blit_vert, shader_blit_frag,
		[3]interface{}{&b.colUniforms.vert, &b.linearGradientUniforms.vert, &b.texUniforms.vert},
		[3]interface{}{&b.colUniforms.frag, &b.linearGradientUniforms.frag, nil},
	)
	if err != nil {
		panic(err)
	}
	b.prog = prog
	b.layout = layout
	return b
}

func (b *blitter) release() {
	b.quadVerts.Release()
	for _, p := range b.prog {
		p.Release()
	}
	b.layout.Release()
}

func createColorPrograms(b driver.Device, vsSrc driver.ShaderSources, fsSrc [3]driver.ShaderSources, vertUniforms, fragUniforms [3]interface{}) ([3]*program, driver.InputLayout, error) {
	var progs [3]*program
	{
		prog, err := b.NewProgram(vsSrc, fsSrc[materialTexture])
		if err != nil {
			return progs, nil, err
		}
		var vertBuffer, fragBuffer *uniformBuffer
		if u := vertUniforms[materialTexture]; u != nil {
			vertBuffer = newUniformBuffer(b, u)
			prog.SetVertexUniforms(vertBuffer.buf)
		}
		if u := fragUniforms[materialTexture]; u != nil {
			fragBuffer = newUniformBuffer(b, u)
			prog.SetFragmentUniforms(fragBuffer.buf)
		}
		progs[materialTexture] = newProgram(prog, vertBuffer, fragBuffer)
	}
	{
		var vertBuffer, fragBuffer *uniformBuffer
		prog, err := b.NewProgram(vsSrc, fsSrc[materialColor])
		if err != nil {
			progs[materialTexture].Release()
			return progs, nil, err
		}
		if u := vertUniforms[materialColor]; u != nil {
			vertBuffer = newUniformBuffer(b, u)
			prog.SetVertexUniforms(vertBuffer.buf)
		}
		if u := fragUniforms[materialColor]; u != nil {
			fragBuffer = newUniformBuffer(b, u)
			prog.SetFragmentUniforms(fragBuffer.buf)
		}
		progs[materialColor] = newProgram(prog, vertBuffer, fragBuffer)
	}
	{
		var vertBuffer, fragBuffer *uniformBuffer
		prog, err := b.NewProgram(vsSrc, fsSrc[materialLinearGradient])
		if err != nil {
			progs[materialTexture].Release()
			progs[materialColor].Release()
			return progs, nil, err
		}
		if u := vertUniforms[materialLinearGradient]; u != nil {
			vertBuffer = newUniformBuffer(b, u)
			prog.SetVertexUniforms(vertBuffer.buf)
		}
		if u := fragUniforms[materialLinearGradient]; u != nil {
			fragBuffer = newUniformBuffer(b, u)
			prog.SetFragmentUniforms(fragBuffer.buf)
		}
		progs[materialLinearGradient] = newProgram(prog, vertBuffer, fragBuffer)
	}
	layout, err := b.NewInputLayout(vsSrc, []driver.InputDesc{
		{Type: driver.DataTypeFloat, Size: 2, Offset: 0},
		{Type: driver.DataTypeFloat, Size: 2, Offset: 4 * 2},
	})
	if err != nil {
		progs[materialTexture].Release()
		progs[materialColor].Release()
		progs[materialLinearGradient].Release()
		return progs, nil, err
	}
	return progs, layout, nil
}

func (r *renderer) stencilClips(pathCache *opCache, ops []*pathOp) {
	if len(r.packer.sizes) == 0 {
		return
	}
	fbo := -1
	r.pather.begin(r.packer.sizes)
	for _, p := range ops {
		if fbo != p.place.Idx {
			fbo = p.place.Idx
			f := r.pather.stenciler.cover(fbo)
			r.ctx.BindFramebuffer(f.fbo)
			r.ctx.Clear(0.0, 0.0, 0.0, 0.0)
		}
		v, _ := pathCache.get(p.pathKey)
		r.pather.stencilPath(p.clip, p.off, p.place.Pos, v.data)
	}
}

func (r *renderer) intersect(ops []imageOp) {
	if len(r.intersections.sizes) == 0 {
		return
	}
	fbo := -1
	r.pather.stenciler.beginIntersect(r.intersections.sizes)
	r.ctx.BindVertexBuffer(r.blitter.quadVerts, 4*4, 0)
	r.ctx.BindInputLayout(r.pather.stenciler.iprog.layout)
	for _, img := range ops {
		if img.clipType != clipTypeIntersection {
			continue
		}
		if fbo != img.place.Idx {
			fbo = img.place.Idx
			f := r.pather.stenciler.intersections.fbos[fbo]
			r.ctx.BindFramebuffer(f.fbo)
			r.ctx.Clear(1.0, 0.0, 0.0, 0.0)
		}
		r.ctx.Viewport(img.place.Pos.X, img.place.Pos.Y, img.clip.Dx(), img.clip.Dy())
		r.intersectPath(img.path, img.clip)
	}
}

func (r *renderer) intersectPath(p *pathOp, clip image.Rectangle) {
	if p.parent != nil {
		r.intersectPath(p.parent, clip)
	}
	if !p.path {
		return
	}
	uv := image.Rectangle{
		Min: p.place.Pos,
		Max: p.place.Pos.Add(p.clip.Size()),
	}
	o := clip.Min.Sub(p.clip.Min)
	sub := image.Rectangle{
		Min: o,
		Max: o.Add(clip.Size()),
	}
	fbo := r.pather.stenciler.cover(p.place.Idx)
	r.ctx.BindTexture(0, fbo.tex)
	coverScale, coverOff := texSpaceTransform(layout.FRect(uv), fbo.size)
	subScale, subOff := texSpaceTransform(layout.FRect(sub), p.clip.Size())
	r.pather.stenciler.iprog.uniforms.vert.uvTransform = [4]float32{coverScale.X, coverScale.Y, coverOff.X, coverOff.Y}
	r.pather.stenciler.iprog.uniforms.vert.subUVTransform = [4]float32{subScale.X, subScale.Y, subOff.X, subOff.Y}
	r.pather.stenciler.iprog.prog.UploadUniforms()
	r.ctx.DrawArrays(driver.DrawModeTriangleStrip, 0, 4)
}

func (r *renderer) packIntersections(ops []imageOp) {
	r.intersections.clear()
	for i, img := range ops {
		var npaths int
		var onePath *pathOp
		for p := img.path; p != nil; p = p.parent {
			if p.path {
				onePath = p
				npaths++
			}
		}
		switch npaths {
		case 0:
		case 1:
			place := onePath.place
			place.Pos = place.Pos.Sub(onePath.clip.Min).Add(img.clip.Min)
			ops[i].place = place
			ops[i].clipType = clipTypePath
		default:
			sz := image.Point{X: img.clip.Dx(), Y: img.clip.Dy()}
			place, ok := r.intersections.add(sz)
			if !ok {
				panic("internal error: if the intersection fit, the intersection should fit as well")
			}
			ops[i].clipType = clipTypeIntersection
			ops[i].place = place
		}
	}
}

func (r *renderer) packStencils(pops *[]*pathOp) {
	r.packer.clear()
	ops := *pops
	// Allocate atlas space for cover textures.
	var i int
	for i < len(ops) {
		p := ops[i]
		if p.clip.Empty() {
			ops[i] = ops[len(ops)-1]
			ops = ops[:len(ops)-1]
			continue
		}
		sz := image.Point{X: p.clip.Dx(), Y: p.clip.Dy()}
		place, ok := r.packer.add(sz)
		if !ok {
			// The clip area is at most the entire screen. Hopefully no
			// screen is larger than GL_MAX_TEXTURE_SIZE.
			panic(fmt.Errorf("clip area %v is larger than maximum texture size %dx%d", p.clip, r.packer.maxDim, r.packer.maxDim))
		}
		p.place = place
		i++
	}
	*pops = ops
}

// intersects intersects clip and b where b is offset by off.
// ceilRect returns a bounding image.Rectangle for a f32.Rectangle.
func boundRectF(r f32.Rectangle) image.Rectangle {
	return image.Rectangle{
		Min: image.Point{
			X: int(floor(r.Min.X)),
			Y: int(floor(r.Min.Y)),
		},
		Max: image.Point{
			X: int(ceil(r.Max.X)),
			Y: int(ceil(r.Max.Y)),
		},
	}
}

func ceil(v float32) int {
	return int(math.Ceil(float64(v)))
}

func floor(v float32) int {
	return int(math.Floor(float64(v)))
}

func (d *drawOps) reset(cache *resourceCache, viewport image.Point) {
	d.profile = false
	d.cache = cache
	d.viewport = viewport
	d.imageOps = d.imageOps[:0]
	d.allImageOps = d.allImageOps[:0]
	d.zimageOps = d.zimageOps[:0]
	d.pathOps = d.pathOps[:0]
	d.pathOpCache = d.pathOpCache[:0]
	d.vertCache = d.vertCache[:0]
}

func (d *drawOps) collect(ctx driver.Device, cache *resourceCache, root *op.Ops, viewport image.Point) {
	clip := f32.Rectangle{
		Max: f32.Point{X: float32(viewport.X), Y: float32(viewport.Y)},
	}
	d.reader.Reset(root)
	state := drawState{
		clip:  clip,
		rect:  true,
		color: color.NRGBA{A: 0xff},
	}
	d.collectOps(&d.reader, state)
	for _, p := range d.pathOps {
		if v, exists := d.pathCache.get(p.pathKey); !exists || v.data.data == nil {
			data := buildPath(ctx, p.pathVerts)
			var computePath encoder
			if d.compute {
				computePath = encodePath(p)
			}
			d.pathCache.put(p.pathKey, opCacheValue{
				data:        data,
				bounds:      p.bounds,
				computePath: computePath,
			})
		}
		p.pathVerts = nil
	}
}

func (d *drawOps) newPathOp() *pathOp {
	d.pathOpCache = append(d.pathOpCache, pathOp{})
	return &d.pathOpCache[len(d.pathOpCache)-1]
}

func (d *drawOps) addClipPath(state *drawState, aux []byte, auxKey ops.Key, bounds f32.Rectangle, off f32.Point, tr f32.Affine2D, stroke clip.StrokeStyle, dashes stroke.DashOp) {
	npath := d.newPathOp()
	*npath = pathOp{
		parent: state.cpath,
		bounds: bounds,
		off:    off,
		trans:  tr,
		stroke: stroke,
		dashes: dashes,
	}
	state.cpath = npath
	if len(aux) > 0 {
		state.rect = false
		state.cpath.pathKey = auxKey
		state.cpath.path = true
		state.cpath.pathVerts = aux
		d.pathOps = append(d.pathOps, state.cpath)
	}
}

// split a transform into two parts, one which is pur offset and the
// other representing the scaling, shearing and rotation part
func splitTransform(t f32.Affine2D) (srs f32.Affine2D, offset f32.Point) {
	sx, hx, ox, hy, sy, oy := t.Elems()
	offset = f32.Point{X: ox, Y: oy}
	srs = f32.NewAffine2D(sx, hx, 0, hy, sy, 0)
	return
}

func (d *drawOps) save(id int, state drawState) {
	if extra := id - len(d.states) + 1; extra > 0 {
		d.states = append(d.states, make([]drawState, extra)...)
	}
	d.states[id] = state
}

func (d *drawOps) collectOps(r *ops.Reader, state drawState) {
	var (
		quads  quadsOp
		str    clip.StrokeStyle
		dashes stroke.DashOp
		z      int
	)
	d.save(opconst.InitialStateID, state)
loop:
	for encOp, ok := r.Decode(); ok; encOp, ok = r.Decode() {
		switch opconst.OpType(encOp.Data[0]) {
		case opconst.TypeProfile:
			d.profile = true
		case opconst.TypeTransform:
			dop := ops.DecodeTransform(encOp.Data)
			state.t = state.t.Mul(dop)

		case opconst.TypeDash:
			dashes = decodeDashOp(encOp.Data)
			if len(dashes.Dashes) > 0 {
				encOp, ok = r.Decode()
				if !ok {
					panic("gpu: could not decode dashes pattern")
				}
				data := encOp.Data[1:]
				bo := binary.LittleEndian
				for i := range dashes.Dashes {
					dashes.Dashes[i] = math.Float32frombits(bo.Uint32(
						data[i*4:],
					))
				}
			}

		case opconst.TypeStroke:
			str = decodeStrokeOp(encOp.Data)

		case opconst.TypePath:
			encOp, ok = r.Decode()
			if !ok {
				break loop
			}
			quads.aux = encOp.Data[opconst.TypeAuxLen:]
			quads.key = encOp.Key

		case opconst.TypeClip:
			var op clipOp
			op.decode(encOp.Data)
			bounds := op.bounds
			trans, off := splitTransform(state.t)
			if len(quads.aux) > 0 {
				// There is a clipping path, build the gpu data and update the
				// cache key such that it will be equal only if the transform is the
				// same also. Use cached data if we have it.
				quads.key = quads.key.SetTransform(trans)
				if v, ok := d.pathCache.get(quads.key); ok {
					// Since the GPU data exists in the cache aux will not be used.
					// Why is this not used for the offset shapes?
					op.bounds = v.bounds
				} else {
					pathData, bounds := d.buildVerts(
						quads.aux, trans, op.outline, str, dashes,
					)
					op.bounds = bounds
					if !d.compute {
						quads.aux = pathData
					}
					// add it to the cache, without GPU data, so the transform can be
					// reused.
					d.pathCache.put(quads.key, opCacheValue{bounds: op.bounds})
				}
			} else {
				quads.aux, op.bounds, _ = d.boundsForTransformedRect(bounds, trans)
				quads.key = encOp.Key
				quads.key.SetTransform(trans)
			}
			state.clip = state.clip.Intersect(op.bounds.Add(off))
			d.addClipPath(&state, quads.aux, quads.key, op.bounds, off, state.t, str, dashes)
			quads = quadsOp{}
			str = clip.StrokeStyle{}
			dashes = stroke.DashOp{}

		case opconst.TypeColor:
			state.matType = materialColor
			state.color = decodeColorOp(encOp.Data)
		case opconst.TypeLinearGradient:
			state.matType = materialLinearGradient
			op := decodeLinearGradientOp(encOp.Data)
			state.stop1 = op.stop1
			state.stop2 = op.stop2
			state.color1 = op.color1
			state.color2 = op.color2
		case opconst.TypeImage:
			state.matType = materialTexture
			state.image = decodeImageOp(encOp.Data, encOp.Refs)
		case opconst.TypePaint:
			// Transform (if needed) the painting rectangle and if so generate a clip path,
			// for those cases also compute a partialTrans that maps texture coordinates between
			// the new bounding rectangle and the transformed original paint rectangle.
			trans, off := splitTransform(state.t)
			// Fill the clip area, unless the material is a (bounded) image.
			// TODO: Find a tighter bound.
			inf := float32(1e6)
			dst := f32.Rect(-inf, -inf, inf, inf)
			if state.matType == materialTexture {
				dst = layout.FRect(state.image.src.Rect)
			}
			clipData, bnd, partialTrans := d.boundsForTransformedRect(dst, trans)
			cl := state.clip.Intersect(bnd.Add(off))
			if cl.Empty() {
				continue
			}

			wasrect := state.rect
			if clipData != nil {
				// The paint operation is sheared or rotated, add a clip path representing
				// this transformed rectangle.
				encOp.Key.SetTransform(trans)
				d.addClipPath(&state, clipData, encOp.Key, bnd, off, state.t, clip.StrokeStyle{}, stroke.DashOp{})
			}

			bounds := boundRectF(cl)
			mat := state.materialFor(bnd, off, partialTrans, bounds, state.t)

			if bounds.Min == (image.Point{}) && bounds.Max == d.viewport && state.rect && mat.opaque && (mat.material == materialColor) {
				// The image is a uniform opaque color and takes up the whole screen.
				// Scrap images up to and including this image and set clear color.
				d.allImageOps = d.allImageOps[:0]
				d.zimageOps = d.zimageOps[:0]
				d.imageOps = d.imageOps[:0]
				z = 0
				d.clearColor = mat.color.Opaque()
				d.clear = true
				continue
			}
			z++
			if z != int(uint16(z)) {
				// TODO(eliasnaur) gioui.org/issue/127.
				panic("more than 65k paint objects not supported")
			}
			// Assume 16-bit depth buffer.
			const zdepth = 1 << 16
			// Convert z to window-space, assuming depth range [0;1].
			zf := float32(z)*2/zdepth - 1.0
			img := imageOp{
				z:        zf,
				path:     state.cpath,
				clip:     bounds,
				material: mat,
			}

			d.allImageOps = append(d.allImageOps, img)
			if state.rect && img.material.opaque {
				d.zimageOps = append(d.zimageOps, img)
			} else {
				d.imageOps = append(d.imageOps, img)
			}
			if clipData != nil {
				// we added a clip path that should not remain
				state.cpath = state.cpath.parent
				state.rect = wasrect
			}
		case opconst.TypeSave:
			id := ops.DecodeSave(encOp.Data)
			d.save(id, state)
		case opconst.TypeLoad:
			id, mask := ops.DecodeLoad(encOp.Data)
			s := d.states[id]
			if mask&opconst.TransformState != 0 {
				state.t = s.t
			}
			if mask&^opconst.TransformState != 0 {
				state = s
			}
		}
	}
}

func expandPathOp(p *pathOp, clip image.Rectangle) {
	for p != nil {
		pclip := p.clip
		if !pclip.Empty() {
			clip = clip.Union(pclip)
		}
		p.clip = clip
		p = p.parent
	}
}

func (d *drawState) materialFor(rect f32.Rectangle, off f32.Point, partTrans f32.Affine2D, clip image.Rectangle, trans f32.Affine2D) material {
	var m material
	switch d.matType {
	case materialColor:
		m.material = materialColor
		m.color = f32color.LinearFromSRGB(d.color)
		m.opaque = m.color.A == 1.0
	case materialLinearGradient:
		m.material = materialLinearGradient

		m.color1 = f32color.LinearFromSRGB(d.color1)
		m.color2 = f32color.LinearFromSRGB(d.color2)
		m.opaque = m.color1.A == 1.0 && m.color2.A == 1.0

		m.uvTrans = partTrans.Mul(gradientSpaceTransform(clip, off, d.stop1, d.stop2))
	case materialTexture:
		m.material = materialTexture
		dr := boundRectF(rect.Add(off))
		sz := d.image.src.Bounds().Size()
		sr := f32.Rectangle{
			Max: f32.Point{
				X: float32(sz.X),
				Y: float32(sz.Y),
			},
		}
		dx := float32(dr.Dx())
		sdx := sr.Dx()
		sr.Min.X += float32(clip.Min.X-dr.Min.X) * sdx / dx
		sr.Max.X -= float32(dr.Max.X-clip.Max.X) * sdx / dx
		dy := float32(dr.Dy())
		sdy := sr.Dy()
		sr.Min.Y += float32(clip.Min.Y-dr.Min.Y) * sdy / dy
		sr.Max.Y -= float32(dr.Max.Y-clip.Max.Y) * sdy / dy
		uvScale, uvOffset := texSpaceTransform(sr, sz)
		m.uvTrans = partTrans.Mul(f32.Affine2D{}.Scale(f32.Point{}, uvScale).Offset(uvOffset))
		m.trans = trans
		m.data = d.image
	}
	return m
}

func (r *renderer) drawZOps(cache *resourceCache, ops []imageOp) {
	r.ctx.SetDepthTest(true)
	r.ctx.BindVertexBuffer(r.blitter.quadVerts, 4*4, 0)
	r.ctx.BindInputLayout(r.blitter.layout)
	// Render front to back.
	for i := len(ops) - 1; i >= 0; i-- {
		img := ops[i]
		m := img.material
		switch m.material {
		case materialTexture:
			r.ctx.BindTexture(0, r.texHandle(cache, m.data))
		}
		drc := img.clip
		scale, off := clipSpaceTransform(drc, r.blitter.viewport)
		r.blitter.blit(img.z, m.material, m.color, m.color1, m.color2, scale, off, m.uvTrans)
	}
	r.ctx.SetDepthTest(false)
}

func (r *renderer) drawOps(cache *resourceCache, ops []imageOp) {
	r.ctx.SetDepthTest(true)
	r.ctx.DepthMask(false)
	r.ctx.BlendFunc(driver.BlendFactorOne, driver.BlendFactorOneMinusSrcAlpha)
	r.ctx.BindVertexBuffer(r.blitter.quadVerts, 4*4, 0)
	r.ctx.BindInputLayout(r.pather.coverer.layout)
	var coverTex driver.Texture
	for _, img := range ops {
		m := img.material
		switch m.material {
		case materialTexture:
			r.ctx.BindTexture(0, r.texHandle(cache, m.data))
		}
		drc := img.clip

		scale, off := clipSpaceTransform(drc, r.blitter.viewport)
		var fbo stencilFBO
		switch img.clipType {
		case clipTypeNone:
			r.blitter.blit(img.z, m.material, m.color, m.color1, m.color2, scale, off, m.uvTrans)
			continue
		case clipTypePath:
			fbo = r.pather.stenciler.cover(img.place.Idx)
		case clipTypeIntersection:
			fbo = r.pather.stenciler.intersections.fbos[img.place.Idx]
		}
		if coverTex != fbo.tex {
			coverTex = fbo.tex
			r.ctx.BindTexture(1, coverTex)
		}
		uv := image.Rectangle{
			Min: img.place.Pos,
			Max: img.place.Pos.Add(drc.Size()),
		}
		coverScale, coverOff := texSpaceTransform(layout.FRect(uv), fbo.size)
		r.pather.cover(img.z, m.material, m.color, m.color1, m.color2, scale, off, m.uvTrans, coverScale, coverOff)
	}
	r.ctx.DepthMask(true)
	r.ctx.SetDepthTest(false)
}

func (b *blitter) blit(z float32, mat materialType, col f32color.RGBA, col1, col2 f32color.RGBA, scale, off f32.Point, uvTrans f32.Affine2D) {
	p := b.prog[mat]
	b.ctx.BindProgram(p.prog)
	var uniforms *blitUniforms
	switch mat {
	case materialColor:
		b.colUniforms.frag.color = col
		uniforms = &b.colUniforms.vert.blitUniforms
	case materialTexture:
		t1, t2, t3, t4, t5, t6 := uvTrans.Elems()
		b.texUniforms.vert.blitUniforms.uvTransformR1 = [4]float32{t1, t2, t3, 0}
		b.texUniforms.vert.blitUniforms.uvTransformR2 = [4]float32{t4, t5, t6, 0}
		uniforms = &b.texUniforms.vert.blitUniforms
	case materialLinearGradient:
		b.linearGradientUniforms.frag.color1 = col1
		b.linearGradientUniforms.frag.color2 = col2

		t1, t2, t3, t4, t5, t6 := uvTrans.Elems()
		b.linearGradientUniforms.vert.blitUniforms.uvTransformR1 = [4]float32{t1, t2, t3, 0}
		b.linearGradientUniforms.vert.blitUniforms.uvTransformR2 = [4]float32{t4, t5, t6, 0}
		uniforms = &b.linearGradientUniforms.vert.blitUniforms
	}
	uniforms.z = z
	uniforms.transform = [4]float32{scale.X, scale.Y, off.X, off.Y}
	p.UploadUniforms()
	b.ctx.DrawArrays(driver.DrawModeTriangleStrip, 0, 4)
}

// newUniformBuffer creates a new GPU uniform buffer backed by the
// structure uniformBlock points to.
func newUniformBuffer(b driver.Device, uniformBlock interface{}) *uniformBuffer {
	ref := reflect.ValueOf(uniformBlock)
	// Determine the size of the uniforms structure, *uniforms.
	size := ref.Elem().Type().Size()
	// Map the uniforms structure as a byte slice.
	ptr := (*[1 << 30]byte)(unsafe.Pointer(ref.Pointer()))[:size:size]
	ubuf, err := b.NewBuffer(driver.BufferBindingUniforms, len(ptr))
	if err != nil {
		panic(err)
	}
	return &uniformBuffer{buf: ubuf, ptr: ptr}
}

func (u *uniformBuffer) Upload() {
	u.buf.Upload(u.ptr)
}

func (u *uniformBuffer) Release() {
	u.buf.Release()
	u.buf = nil
}

func newProgram(prog driver.Program, vertUniforms, fragUniforms *uniformBuffer) *program {
	if vertUniforms != nil {
		prog.SetVertexUniforms(vertUniforms.buf)
	}
	if fragUniforms != nil {
		prog.SetFragmentUniforms(fragUniforms.buf)
	}
	return &program{prog: prog, vertUniforms: vertUniforms, fragUniforms: fragUniforms}
}

func (p *program) UploadUniforms() {
	if p.vertUniforms != nil {
		p.vertUniforms.Upload()
	}
	if p.fragUniforms != nil {
		p.fragUniforms.Upload()
	}
}

func (p *program) Release() {
	p.prog.Release()
	p.prog = nil
	if p.vertUniforms != nil {
		p.vertUniforms.Release()
		p.vertUniforms = nil
	}
	if p.fragUniforms != nil {
		p.fragUniforms.Release()
		p.fragUniforms = nil
	}
}

// texSpaceTransform return the scale and offset that transforms the given subimage
// into quad texture coordinates.
func texSpaceTransform(r f32.Rectangle, bounds image.Point) (f32.Point, f32.Point) {
	size := f32.Point{X: float32(bounds.X), Y: float32(bounds.Y)}
	scale := f32.Point{X: r.Dx() / size.X, Y: r.Dy() / size.Y}
	offset := f32.Point{X: r.Min.X / size.X, Y: r.Min.Y / size.Y}
	return scale, offset
}

// gradientSpaceTransform transforms stop1 and stop2 to [(0,0), (1,1)].
func gradientSpaceTransform(clip image.Rectangle, off f32.Point, stop1, stop2 f32.Point) f32.Affine2D {
	d := stop2.Sub(stop1)
	l := float32(math.Sqrt(float64(d.X*d.X + d.Y*d.Y)))
	a := float32(math.Atan2(float64(-d.Y), float64(d.X)))

	// TODO: optimize
	zp := f32.Point{}
	return f32.Affine2D{}.
		Scale(zp, layout.FPt(clip.Size())).            // scale to pixel space
		Offset(zp.Sub(off).Add(layout.FPt(clip.Min))). // offset to clip space
		Offset(zp.Sub(stop1)).                         // offset to first stop point
		Rotate(zp, a).                                 // rotate to align gradient
		Scale(zp, f32.Pt(1/l, 1/l))                    // scale gradient to right size
}

// clipSpaceTransform returns the scale and offset that transforms the given
// rectangle from a viewport into OpenGL clip space.
func clipSpaceTransform(r image.Rectangle, viewport image.Point) (f32.Point, f32.Point) {
	// First, transform UI coordinates to OpenGL coordinates:
	//
	//	[(-1, +1) (+1, +1)]
	//	[(-1, -1) (+1, -1)]
	//
	x, y := float32(r.Min.X), float32(r.Min.Y)
	w, h := float32(r.Dx()), float32(r.Dy())
	vx, vy := 2/float32(viewport.X), 2/float32(viewport.Y)
	x = x*vx - 1
	y = 1 - y*vy
	w *= vx
	h *= vy

	// Then, compute the transformation from the fullscreen quad to
	// the rectangle at (x, y) and dimensions (w, h).
	scale := f32.Point{X: w * .5, Y: h * .5}
	offset := f32.Point{X: x + w*.5, Y: y - h*.5}

	return scale, offset
}

// Fill in maximal Y coordinates of the NW and NE corners.
func fillMaxY(verts []byte) {
	contour := 0
	bo := binary.LittleEndian
	for len(verts) > 0 {
		maxy := float32(math.Inf(-1))
		i := 0
		for ; i+vertStride*4 <= len(verts); i += vertStride * 4 {
			vert := verts[i : i+vertStride]
			// MaxY contains the integer contour index.
			pathContour := int(bo.Uint32(vert[int(unsafe.Offsetof(((*vertex)(nil)).MaxY)):]))
			if contour != pathContour {
				contour = pathContour
				break
			}
			fromy := math.Float32frombits(bo.Uint32(vert[int(unsafe.Offsetof(((*vertex)(nil)).FromY)):]))
			ctrly := math.Float32frombits(bo.Uint32(vert[int(unsafe.Offsetof(((*vertex)(nil)).CtrlY)):]))
			toy := math.Float32frombits(bo.Uint32(vert[int(unsafe.Offsetof(((*vertex)(nil)).ToY)):]))
			if fromy > maxy {
				maxy = fromy
			}
			if ctrly > maxy {
				maxy = ctrly
			}
			if toy > maxy {
				maxy = toy
			}
		}
		fillContourMaxY(maxy, verts[:i])
		verts = verts[i:]
	}
}

func fillContourMaxY(maxy float32, verts []byte) {
	bo := binary.LittleEndian
	for i := 0; i < len(verts); i += vertStride {
		off := int(unsafe.Offsetof(((*vertex)(nil)).MaxY))
		bo.PutUint32(verts[i+off:], math.Float32bits(maxy))
	}
}

func (d *drawOps) writeVertCache(n int) []byte {
	d.vertCache = append(d.vertCache, make([]byte, n)...)
	return d.vertCache[len(d.vertCache)-n:]
}

// transform, split paths as needed, calculate maxY, bounds and create GPU vertices.
func (d *drawOps) buildVerts(pathData []byte, tr f32.Affine2D, outline bool, str clip.StrokeStyle, dashes stroke.DashOp) (verts []byte, bounds f32.Rectangle) {
	inf := float32(math.Inf(+1))
	d.qs.bounds = f32.Rectangle{
		Min: f32.Point{X: inf, Y: inf},
		Max: f32.Point{X: -inf, Y: -inf},
	}
	d.qs.d = d
	startLength := len(d.vertCache)

	switch {
	case str.Width > 0:
		// Stroke path.
		quads := decodeToStrokeQuads(pathData)
		ss := stroke.StrokeStyle{
			Width: str.Width,
			Miter: str.Miter,
			Cap:   stroke.StrokeCap(str.Cap),
			Join:  stroke.StrokeJoin(str.Join),
		}
		quads = quads.Stroke(ss, dashes)
		for _, quad := range quads {
			d.qs.contour = quad.Contour
			quad.Quad = quad.Quad.Transform(tr)

			d.qs.splitAndEncode(quad.Quad)
		}

	case outline:
		decodeToOutlineQuads(&d.qs, tr, pathData)
	}

	fillMaxY(d.vertCache[startLength:])
	return d.vertCache[startLength:], d.qs.bounds
}

// decodeOutlineQuads decodes scene commands, splits them into quadratic béziers
// as needed and feeds them to the supplied splitter.
func decodeToOutlineQuads(qs *quadSplitter, tr f32.Affine2D, pathData []byte) {
	for len(pathData) >= scene.CommandSize+4 {
		qs.contour = bo.Uint32(pathData)
		cmd := ops.DecodeCommand(pathData[4:])
		switch cmd.Op() {
		case scene.OpLine:
			var q stroke.QuadSegment
			q.From, q.To = scene.DecodeLine(cmd)
			q.Ctrl = q.From.Add(q.To).Mul(.5)
			q = q.Transform(tr)
			qs.splitAndEncode(q)
		case scene.OpQuad:
			var q stroke.QuadSegment
			q.From, q.Ctrl, q.To = scene.DecodeQuad(cmd)
			q = q.Transform(tr)
			qs.splitAndEncode(q)
		case scene.OpCubic:
			for _, q := range splitCubic(scene.DecodeCubic(cmd)) {
				q = q.Transform(tr)
				qs.splitAndEncode(q)
			}
		default:
			panic("unsupported scene command")
		}
		pathData = pathData[scene.CommandSize+4:]
	}
}

// decodeToStrokeQuads is like decodeOutlineQuads, except it returns a list of stroke
// quads ready to stroke.
func decodeToStrokeQuads(pathData []byte) stroke.StrokeQuads {
	quads := make(stroke.StrokeQuads, 0, 2*len(pathData)/(scene.CommandSize+4))
	for len(pathData) >= scene.CommandSize+4 {
		contour := bo.Uint32(pathData)
		cmd := ops.DecodeCommand(pathData[4:])
		switch cmd.Op() {
		case scene.OpLine:
			var q stroke.QuadSegment
			q.From, q.To = scene.DecodeLine(cmd)
			q.Ctrl = q.From.Add(q.To).Mul(.5)
			quad := stroke.StrokeQuad{
				Contour: contour,
				Quad:    q,
			}
			quads = append(quads, quad)
		case scene.OpQuad:
			var q stroke.QuadSegment
			q.From, q.Ctrl, q.To = scene.DecodeQuad(cmd)
			quad := stroke.StrokeQuad{
				Contour: contour,
				Quad:    q,
			}
			quads = append(quads, quad)
		case scene.OpCubic:
			for _, q := range splitCubic(scene.DecodeCubic(cmd)) {
				quad := stroke.StrokeQuad{
					Contour: contour,
					Quad:    q,
				}
				quads = append(quads, quad)
			}
		default:
			panic("unsupported scene command")
		}
		pathData = pathData[scene.CommandSize+4:]
	}
	return quads
}

// create GPU vertices for transformed r, find the bounds and establish texture transform.
func (d *drawOps) boundsForTransformedRect(r f32.Rectangle, tr f32.Affine2D) (aux []byte, bnd f32.Rectangle, ptr f32.Affine2D) {
	if isPureOffset(tr) {
		// fast-path to allow blitting of pure rectangles
		_, _, ox, _, _, oy := tr.Elems()
		off := f32.Pt(ox, oy)
		bnd.Min = r.Min.Add(off)
		bnd.Max = r.Max.Add(off)
		return
	}

	// transform all corners, find new bounds
	corners := [4]f32.Point{
		tr.Transform(r.Min), tr.Transform(f32.Pt(r.Max.X, r.Min.Y)),
		tr.Transform(r.Max), tr.Transform(f32.Pt(r.Min.X, r.Max.Y)),
	}
	bnd.Min = f32.Pt(math.MaxFloat32, math.MaxFloat32)
	bnd.Max = f32.Pt(-math.MaxFloat32, -math.MaxFloat32)
	for _, c := range corners {
		if c.X < bnd.Min.X {
			bnd.Min.X = c.X
		}
		if c.Y < bnd.Min.Y {
			bnd.Min.Y = c.Y
		}
		if c.X > bnd.Max.X {
			bnd.Max.X = c.X
		}
		if c.Y > bnd.Max.Y {
			bnd.Max.Y = c.Y
		}
	}

	// build the GPU vertices
	l := len(d.vertCache)
	if !d.compute {
		d.vertCache = append(d.vertCache, make([]byte, vertStride*4*4)...)
		aux = d.vertCache[l:]
		encodeQuadTo(aux, 0, corners[0], corners[0].Add(corners[1]).Mul(0.5), corners[1])
		encodeQuadTo(aux[vertStride*4:], 0, corners[1], corners[1].Add(corners[2]).Mul(0.5), corners[2])
		encodeQuadTo(aux[vertStride*4*2:], 0, corners[2], corners[2].Add(corners[3]).Mul(0.5), corners[3])
		encodeQuadTo(aux[vertStride*4*3:], 0, corners[3], corners[3].Add(corners[0]).Mul(0.5), corners[0])
		fillMaxY(aux)
	} else {
		d.vertCache = append(d.vertCache, make([]byte, (scene.CommandSize+4)*4)...)
		aux = d.vertCache[l:]
		buf := aux
		bo := binary.LittleEndian
		bo.PutUint32(buf, 0) // Contour
		ops.EncodeCommand(buf[4:], scene.Line(r.Min, f32.Pt(r.Max.X, r.Min.Y)))
		buf = buf[4+scene.CommandSize:]
		bo.PutUint32(buf, 0)
		ops.EncodeCommand(buf[4:], scene.Line(f32.Pt(r.Max.X, r.Min.Y), r.Max))
		buf = buf[4+scene.CommandSize:]
		bo.PutUint32(buf, 0)
		ops.EncodeCommand(buf[4:], scene.Line(r.Max, f32.Pt(r.Min.X, r.Max.Y)))
		buf = buf[4+scene.CommandSize:]
		bo.PutUint32(buf, 0)
		ops.EncodeCommand(buf[4:], scene.Line(f32.Pt(r.Min.X, r.Max.Y), r.Min))
	}

	// establish the transform mapping from bounds rectangle to transformed corners
	var P1, P2, P3 f32.Point
	P1.X = (corners[1].X - bnd.Min.X) / (bnd.Max.X - bnd.Min.X)
	P1.Y = (corners[1].Y - bnd.Min.Y) / (bnd.Max.Y - bnd.Min.Y)
	P2.X = (corners[2].X - bnd.Min.X) / (bnd.Max.X - bnd.Min.X)
	P2.Y = (corners[2].Y - bnd.Min.Y) / (bnd.Max.Y - bnd.Min.Y)
	P3.X = (corners[3].X - bnd.Min.X) / (bnd.Max.X - bnd.Min.X)
	P3.Y = (corners[3].Y - bnd.Min.Y) / (bnd.Max.Y - bnd.Min.Y)
	sx, sy := P2.X-P3.X, P2.Y-P3.Y
	ptr = f32.NewAffine2D(sx, P2.X-P1.X, P1.X-sx, sy, P2.Y-P1.Y, P1.Y-sy).Invert()

	return
}

func isPureOffset(t f32.Affine2D) bool {
	a, b, _, d, e, _ := t.Elems()
	return a == 1 && b == 0 && d == 0 && e == 1
}

func splitCubic(from, ctrl0, ctrl1, to f32.Point) []stroke.QuadSegment {
	quads := make([]stroke.QuadSegment, 0, 10)
	// Set the maximum distance proportionally to the longest side
	// of the bounding rectangle.
	hull := f32.Rectangle{
		Min: from,
		Max: ctrl0,
	}.Canon().Add(ctrl1).Add(to)
	l := hull.Dx()
	if h := hull.Dy(); h > l {
		l = h
	}
	approxCubeTo(&quads, 0, l*0.001, from, ctrl0, ctrl1, to)
	return quads
}

// approxCube approximates a cubic Bézier by a series of quadratic
// curves.
func approxCubeTo(quads *[]stroke.QuadSegment, splits int, maxDist float32, from, ctrl0, ctrl1, to f32.Point) int {
	// The idea is from
	// https://caffeineowl.com/graphics/2d/vectorial/cubic2quad01.html
	// where a quadratic approximates a cubic by eliminating its t³ term
	// from its polynomial expression anchored at the starting point:
	//
	// P(t) = pen + 3t(ctrl0 - pen) + 3t²(ctrl1 - 2ctrl0 + pen) + t³(to - 3ctrl1 + 3ctrl0 - pen)
	//
	// The control point for the new quadratic Q1 that shares starting point, pen, with P is
	//
	// C1 = (3ctrl0 - pen)/2
	//
	// The reverse cubic anchored at the end point has the polynomial
	//
	// P'(t) = to + 3t(ctrl1 - to) + 3t²(ctrl0 - 2ctrl1 + to) + t³(pen - 3ctrl0 + 3ctrl1 - to)
	//
	// The corresponding quadratic Q2 that shares the end point, to, with P has control
	// point
	//
	// C2 = (3ctrl1 - to)/2
	//
	// The combined quadratic Bézier, Q, shares both start and end points with its cubic
	// and use the midpoint between the two curves Q1 and Q2 as control point:
	//
	// C = (3ctrl0 - pen + 3ctrl1 - to)/4
	c := ctrl0.Mul(3).Sub(from).Add(ctrl1.Mul(3)).Sub(to).Mul(1.0 / 4.0)
	const maxSplits = 32
	if splits >= maxSplits {
		*quads = append(*quads, stroke.QuadSegment{From: from, Ctrl: c, To: to})
		return splits
	}
	// The maximum distance between the cubic P and its approximation Q given t
	// can be shown to be
	//
	// d = sqrt(3)/36*|to - 3ctrl1 + 3ctrl0 - pen|
	//
	// To save a square root, compare d² with the squared tolerance.
	v := to.Sub(ctrl1.Mul(3)).Add(ctrl0.Mul(3)).Sub(from)
	d2 := (v.X*v.X + v.Y*v.Y) * 3 / (36 * 36)
	if d2 <= maxDist*maxDist {
		*quads = append(*quads, stroke.QuadSegment{From: from, Ctrl: c, To: to})
		return splits
	}
	// De Casteljau split the curve and approximate the halves.
	t := float32(0.5)
	c0 := from.Add(ctrl0.Sub(from).Mul(t))
	c1 := ctrl0.Add(ctrl1.Sub(ctrl0).Mul(t))
	c2 := ctrl1.Add(to.Sub(ctrl1).Mul(t))
	c01 := c0.Add(c1.Sub(c0).Mul(t))
	c12 := c1.Add(c2.Sub(c1).Mul(t))
	c0112 := c01.Add(c12.Sub(c01).Mul(t))
	splits++
	splits = approxCubeTo(quads, splits, maxDist, from, c0, c01, c0112)
	splits = approxCubeTo(quads, splits, maxDist, c0112, c12, c2, to)
	return splits
}