vector: add CubeTo.

Change-Id: Ia64b5b077172303981538de99cc14c5bcc99a3e4
Reviewed-on: https://go-review.googlesource.com/28489
Reviewed-by: David Crawshaw <crawshaw@golang.org>
This commit is contained in:
Nigel Tao 2016-09-05 19:50:44 +10:00
parent 714f2e47f7
commit bb355ba442
2 changed files with 79 additions and 30 deletions

View File

@ -134,35 +134,67 @@ func (z *Rasterizer) LineTo(b f32.Vec2) {
// //
// The coordinates are allowed to be out of the Rasterizer's bounds. // The coordinates are allowed to be out of the Rasterizer's bounds.
func (z *Rasterizer) QuadTo(b, c f32.Vec2) { func (z *Rasterizer) QuadTo(b, c f32.Vec2) {
// We make a linear approximation to the curve.
// 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.
a := z.pen a := z.pen
devx := a[0] - 2*b[0] + c[0] devsq := devSquared(a, b, c)
devy := a[1] - 2*b[1] + c[1]
devsq := devx*devx + devy*devy
if devsq >= 0.333 { if devsq >= 0.333 {
const tol = 3 const tol = 3
n := 1 + int(math.Sqrt(math.Sqrt(tol*float64(devsq)))) n := 1 + int(math.Sqrt(math.Sqrt(tol*float64(devsq))))
t, nInv := float32(0), 1/float32(n) t, nInv := float32(0), 1/float32(n)
for i := 0; i < n-1; i++ { for i := 0; i < n-1; i++ {
t += nInv t += nInv
z.LineTo(lerp(t, lerp(t, a, b), lerp(t, b, c))) ab := lerp(t, a, b)
bc := lerp(t, b, c)
z.LineTo(lerp(t, ab, bc))
} }
} }
z.LineTo(c) z.LineTo(c)
} }
// TODO: CubeTo for cubic Béziers. // CubeTo adds a cubic Bézier segment, from the pen via b and c to d, and moves
// the pen to d.
//
// The coordinates are allowed to be out of the Rasterizer's bounds.
func (z *Rasterizer) CubeTo(b, c, d f32.Vec2) {
a := z.pen
devsq := devSquared(a, b, d)
if devsqAlt := devSquared(a, c, d); 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
ab := lerp(t, a, b)
bc := lerp(t, b, c)
cd := lerp(t, c, d)
abc := lerp(t, ab, bc)
bcd := lerp(t, bc, cd)
z.LineTo(lerp(t, abc, bcd))
}
}
z.LineTo(d)
}
// devSquared returns a measure of how curvy the sequnce a to b to c 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(a, b, c f32.Vec2) float32 {
devx := a[0] - 2*b[0] + c[0]
devy := a[1] - 2*b[1] + c[1]
return devx*devx + devy*devy
}
// Draw implements the Drawer interface from the standard library's image/draw // Draw implements the Drawer interface from the standard library's image/draw
// package. // package.

View File

@ -9,35 +9,52 @@ package vector
import ( import (
"image" "image"
"image/draw" "image/draw"
"image/png"
"os"
"testing" "testing"
"golang.org/x/image/math/f32" "golang.org/x/image/math/f32"
) )
// encodePNG is useful for manually debugging the tests.
func encodePNG(dstFilename string, src image.Image) error {
f, err := os.Create(dstFilename)
if err != nil {
return err
}
encErr := png.Encode(f, src)
closeErr := f.Close()
if encErr != nil {
return encErr
}
return closeErr
}
func TestBasicPath(t *testing.T) { func TestBasicPath(t *testing.T) {
want := []byte{ want := []byte{
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0x00, 0x00, 0xd4, 0xdd, 0xc5, 0xab, 0x63, 0x12, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xe3, 0xaa, 0x3e, 0x00, 0x00, 0x00, 0x00, 0x00,
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0x00, 0x00, 0x00, 0x00, 0x9f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xc5, 0x00, 0x00, 0x00, 0x00, 0x00, 0x88, 0xfc, 0xe3, 0x43, 0x00, 0x00, 0x00, 0x00, 0x06, 0xcd, 0xdc, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x5f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xdd, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, 0x0f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x25, 0xde, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x1f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf4, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x56, 0x00, 0x00,
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} }
z := NewRasterizer(16, 16) z := NewRasterizer(16, 16)
z.MoveTo(f32.Vec2{2, 2}) z.MoveTo(f32.Vec2{2, 2})
z.LineTo(f32.Vec2{8, 2})
z.QuadTo(f32.Vec2{14, 2}, f32.Vec2{14, 14}) z.QuadTo(f32.Vec2{14, 2}, f32.Vec2{14, 14})
z.LineTo(f32.Vec2{5, 14}) z.CubeTo(f32.Vec2{8, 2}, f32.Vec2{5, 20}, f32.Vec2{2, 8})
z.ClosePath() z.ClosePath()
dst := image.NewAlpha(z.Bounds()) dst := image.NewAlpha(z.Bounds())